Datasets:
pkuAI4M
/
lean_github

Dataset card Data Studio Files
xet
Community
1
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stringclasses
147 values
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2.09M
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.IF.equivalent
[100, 1]
[149, 10]
simp[TopM.mapDenoteRegion]
r₁ rβ‚‚ : Region scf b : Bool ⊒ run (OpM.toTopM (TopM.mapDenoteRegion scf [r₁, rβ‚‚]) (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] (OpM.denoteRegions [r₁, rβ‚‚] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else rβ‚‚) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
r₁ rβ‚‚ : Region scf b : Bool ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] (OpM.denoteRegions [r₁, rβ‚‚] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else rβ‚‚) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
Please generate a tactic in lean4 to solve the state. STATE: r₁ rβ‚‚ : Region scf b : Bool ⊒ run (OpM.toTopM (TopM.mapDenoteRegion scf [r₁, rβ‚‚]) (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] (OpM.denoteRegions [r₁, rβ‚‚] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else rβ‚‚) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.IF.equivalent
[100, 1]
[149, 10]
simp[OpM.denoteRegions]
r₁ rβ‚‚ : Region scf b : Bool ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] (OpM.denoteRegions [r₁, rβ‚‚] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else rβ‚‚) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
r₁ rβ‚‚ : Region scf b : Bool ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] [OpM.denoteRegion r₁ 0, OpM.denoteRegion rβ‚‚ 1] (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else rβ‚‚) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
Please generate a tactic in lean4 to solve the state. STATE: r₁ rβ‚‚ : Region scf b : Bool ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] (OpM.denoteRegions [r₁, rβ‚‚] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else rβ‚‚) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.IF.equivalent
[100, 1]
[149, 10]
simp[Semantics.semantics_op]
r₁ rβ‚‚ : Region scf b : Bool ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] [OpM.denoteRegion r₁ 0, OpM.denoteRegion rβ‚‚ 1] (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else rβ‚‚) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
r₁ rβ‚‚ : Region scf b : Bool ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (scf_semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] [OpM.denoteRegion r₁ 0, OpM.denoteRegion rβ‚‚ 1] (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else rβ‚‚) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
Please generate a tactic in lean4 to solve the state. STATE: r₁ rβ‚‚ : Region scf b : Bool ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (Semantics.semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] [OpM.denoteRegion r₁ 0, OpM.denoteRegion rβ‚‚ 1] (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else rβ‚‚) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.IF.equivalent
[100, 1]
[149, 10]
simp[scf_semantics_op]
r₁ rβ‚‚ : Region scf b : Bool ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (scf_semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] [OpM.denoteRegion r₁ 0, OpM.denoteRegion rβ‚‚ 1] (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else rβ‚‚) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
r₁ rβ‚‚ : Region scf b : Bool ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (ite (b = false β†’ False) (OpM.denoteRegion r₁ 0) (OpM.denoteRegion rβ‚‚ 1) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else rβ‚‚) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
Please generate a tactic in lean4 to solve the state. STATE: r₁ rβ‚‚ : Region scf b : Bool ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (scf_semantics_op (IOp.mk "scf.if" [] [{ fst := MLIRType.int Signedness.Signless 1, snd := if b = true then 1 else 0 }] [OpM.denoteRegion r₁ 0, OpM.denoteRegion rβ‚‚ 1] (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else rβ‚‚) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.IF.equivalent
[100, 1]
[149, 10]
cases b <;> simp
r₁ rβ‚‚ : Region scf b : Bool ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (ite (b = false β†’ False) (OpM.denoteRegion r₁ 0) (OpM.denoteRegion rβ‚‚ 1) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else rβ‚‚) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty)
case false r₁ rβ‚‚ : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (OpM.denoteRegion rβ‚‚ 1 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf rβ‚‚ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) case true r₁ rβ‚‚ : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (OpM.denoteRegion r₁ 0 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₁ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty)
Please generate a tactic in lean4 to solve the state. STATE: r₁ rβ‚‚ : Region scf b : Bool ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (ite (b = false β†’ False) (OpM.denoteRegion r₁ 0) (OpM.denoteRegion rβ‚‚ 1) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) = run (TopM.scoped (denoteRegion scf (if b = true then r₁ else rβ‚‚) [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 (if b = true then 1 else 0) SSAEnv.empty) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.IF.equivalent
[100, 1]
[149, 10]
case false => { rw[OpM_toTopM_denoteRegion]; simp[TopM.denoteRegionsByIx]; }
r₁ rβ‚‚ : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (OpM.denoteRegion rβ‚‚ 1 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf rβ‚‚ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty)
no goals
Please generate a tactic in lean4 to solve the state. STATE: r₁ rβ‚‚ : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (OpM.denoteRegion rβ‚‚ 1 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf rβ‚‚ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.IF.equivalent
[100, 1]
[149, 10]
case true => { sorry }
r₁ rβ‚‚ : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (OpM.denoteRegion r₁ 0 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₁ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty)
no goals
Please generate a tactic in lean4 to solve the state. STATE: r₁ rβ‚‚ : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (OpM.denoteRegion r₁ 0 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₁ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.IF.equivalent
[100, 1]
[149, 10]
rw[OpM_toTopM_denoteRegion]
r₁ rβ‚‚ : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (OpM.denoteRegion rβ‚‚ 1 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf rβ‚‚ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty)
r₁ rβ‚‚ : Region scf ⊒ run (TopM.denoteRegionsByIx [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] 1 []) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf rβ‚‚ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty)
Please generate a tactic in lean4 to solve the state. STATE: r₁ rβ‚‚ : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (OpM.denoteRegion rβ‚‚ 1 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf rβ‚‚ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.IF.equivalent
[100, 1]
[149, 10]
simp[TopM.denoteRegionsByIx]
r₁ rβ‚‚ : Region scf ⊒ run (TopM.denoteRegionsByIx [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] 1 []) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf rβ‚‚ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty)
no goals
Please generate a tactic in lean4 to solve the state. STATE: r₁ rβ‚‚ : Region scf ⊒ run (TopM.denoteRegionsByIx [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] 1 []) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf rβ‚‚ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 0 SSAEnv.empty) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.IF.equivalent
[100, 1]
[149, 10]
sorry
r₁ rβ‚‚ : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (OpM.denoteRegion r₁ 0 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₁ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty)
no goals
Please generate a tactic in lean4 to solve the state. STATE: r₁ rβ‚‚ : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r₁, TopM.scoped ∘ denoteRegion scf rβ‚‚] (OpM.denoteRegion r₁ 0 [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty) = run (TopM.scoped (denoteRegion scf r₁ [])) (SSAEnv.set (SSAVal.SSAVal "b") MLIRType.i1 1 SSAEnv.empty) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.CORRECT_r
[184, 1]
[186, 9]
sorry
n : β„• r : Region scf args : TypedArgs scf ⊒ run (denoteRegion scf r args) (INPUT n) = Except.ok ([], INPUT n)
no goals
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf args : TypedArgs scf ⊒ run (denoteRegion scf r args) (INPUT n) = Except.ok ([], INPUT n) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.identity₁
[206, 9]
[208, 8]
sorry
n : β„• ⊒ Int.toNat (Int.ofNat n + 1 - 0) = n + 1
no goals
Please generate a tactic in lean4 to solve the state. STATE: n : β„• ⊒ Int.toNat (Int.ofNat n + 1 - 0) = n + 1 TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[LHS, RHS]
n : β„• r : Region scf ⊒ run ⟦ LHS r ⟧ (INPUT n) = run ⟦ RHS r ⟧ (INPUT n)
n : β„• r : Region scf ⊒ run (denoteRegion scf (Region.mk "entry" [] [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) []) (INPUT n) = run (denoteRegion scf (Region.mk "entry" [] [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) []) (INPUT n)
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ run ⟦ LHS r ⟧ (INPUT n) = run ⟦ RHS r ⟧ (INPUT n) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_denoteRegion]
n : β„• r : Region scf ⊒ run (denoteRegion scf (Region.mk "entry" [] [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) []) (INPUT n) = run (denoteRegion scf (Region.mk "entry" [] [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) []) (INPUT n)
n : β„• r : Region scf ⊒ run (do denoteTypedArgs [] [] denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) = run (do denoteTypedArgs [] [] denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ run (denoteRegion scf (Region.mk "entry" [] [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) []) (INPUT n) = run (denoteRegion scf (Region.mk "entry" [] [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) []) (INPUT n) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_bind]
n : β„• r : Region scf ⊒ run (do denoteTypedArgs [] [] denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) = run (do denoteTypedArgs [] [] denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)
n : β„• r : Region scf ⊒ (match run (denoteTypedArgs [] []) (INPUT n) with | Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' | Except.error e => Except.error e) = match run (denoteTypedArgs [] []) (INPUT n) with | Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' | Except.error e => Except.error e
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ run (do denoteTypedArgs [] [] denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) = run (do denoteTypedArgs [] [] denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_denoteTypedArgs_nil]
n : β„• r : Region scf ⊒ (match run (denoteTypedArgs [] []) (INPUT n) with | Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' | Except.error e => Except.error e) = match run (denoteTypedArgs [] []) (INPUT n) with | Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' | Except.error e => Except.error e
n : β„• r : Region scf ⊒ run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ (match run (denoteTypedArgs [] []) (INPUT n) with | Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' | Except.error e => Except.error e) = match run (denoteTypedArgs [] []) (INPUT n) with | Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' | Except.error e => Except.error e TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_denoteOps_singleton]
n : β„• r : Region scf ⊒ run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)
n : β„• r : Region scf ⊒ run (denoteOp scf (Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk []))) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_denoteOp]
n : β„• r : Region scf ⊒ run (denoteOp scf (Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk []))) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)
n : β„• r : Region scf ⊒ run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ run (denoteOp scf (Op.mk "scf.for'" [] [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk []))) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_bind]
n : β„• r : Region scf ⊒ run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)
n : β„• r : Region scf ⊒ (match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (INPUT n) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (INPUT n) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[INPUT]
n : β„• r : Region scf ⊒ (match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (INPUT n) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n)
n : β„• r : Region scf ⊒ (match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ (match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (INPUT n) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (INPUT n) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_denoteOpArgs_cons_]
n : β„• r : Region scf ⊒ (match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))
n : β„• r : Region scf ⊒ (match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c0") let xs ← denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ (match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_bind]
n : β„• r : Region scf ⊒ (match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c0") let xs ← denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))
n : β„• r : Region scf ⊒ (match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c0")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ (match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c0") let xs ← denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
rw[run_TopM_get_]
n : β„• r : Region scf ⊒ (match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c0")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))
n : β„• r : Region scf ⊒ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ (match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c0")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
rw[SSAEnv.get_set_ne_val]
n : β„• r : Region scf ⊒ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))))
n : β„• r : Region scf ⊒ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
rw[SSAEnv.get_set_ne_val]
n : β„• r : Region scf ⊒ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
n : β„• r : Region scf ⊒ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
rw[SSAEnv.get_set_eq_val] <;> simp
n : β„• r : Region scf ⊒ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
n : β„• r : Region scf ⊒ (match match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ (match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_denoteOpArgs_cons_]
n : β„• r : Region scf ⊒ (match match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
n : β„• r : Region scf ⊒ (match match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "cn_plus_1") let xs ← denoteOpArgs scf [] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ (match match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_bind]
n : β„• r : Region scf ⊒ (match match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "cn_plus_1") let xs ← denoteOpArgs scf [] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
n : β„• r : Region scf ⊒ (match match match run (TopM.get MLIRType.index (SSAVal.SSAVal "cn_plus_1")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ (match match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "cn_plus_1") let xs ← denoteOpArgs scf [] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
rw[run_TopM_get_]
n : β„• r : Region scf ⊒ (match match match run (TopM.get MLIRType.index (SSAVal.SSAVal "cn_plus_1")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
n : β„• r : Region scf ⊒ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "cn_plus_1") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ (match match match run (TopM.get MLIRType.index (SSAVal.SSAVal "cn_plus_1")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
rw[SSAEnv.get_set_ne_val]
n : β„• r : Region scf ⊒ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "cn_plus_1") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
n : β„• r : Region scf ⊒ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "cn_plus_1") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "cn_plus_1") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
rw[SSAEnv.get_set_eq_val] <;> simp
n : β„• r : Region scf ⊒ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "cn_plus_1") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
n : β„• r : Region scf ⊒ (match match match run (denoteOpArgs scf []) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := ↑n + 1 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "cn_plus_1") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_denoteOpArgs_nil]
n : β„• r : Region scf ⊒ (match match match run (denoteOpArgs scf []) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := ↑n + 1 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
n : β„• r : Region scf ⊒ (match match run (pure [{ fst := MLIRType.index, snd := ↑n + 1 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ (match match match run (denoteOpArgs scf []) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := ↑n + 1 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_pure]
n : β„• r : Region scf ⊒ (match match run (pure [{ fst := MLIRType.index, snd := ↑n + 1 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
n : β„• r : Region scf ⊒ run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ (match match run (pure [{ fst := MLIRType.index, snd := ↑n + 1 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[TopM.mapDenoteRegion]
n : β„• r : Region scf ⊒ run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
n : β„• r : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[Semantics.semantics_op, scf_semantics_op]
n : β„• r : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
n : β„• r : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[OpM.denoteRegions]
n : β„• r : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
n : β„• r : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] [{ fst := MLIRType.index, snd := 0 }, { fst := MLIRType.index, snd := ↑n + 1 }] (OpM.denoteRegions [r] 0) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
apply Eq.symm
n : β„• r : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: n : β„• r : Region scf ⊒ run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_denoteOps_cons]
case h n : β„• r : Region scf ⊒ run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ run (do let _ ← denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk [])) denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ run (denoteOps scf [Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []), Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_bind]
case h n : β„• r : Region scf ⊒ run (do let _ ← denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk [])) denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match run (denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ run (do let _ ← denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk [])) denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_denoteOps_singleton]
case h n : β„• r : Region scf ⊒ (match run (denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match run (denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (denoteOp scf (Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk []))) env' | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match run (denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (denoteOps scf [Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk [])]) env' | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_denoteOp]
case h n : β„• r : Region scf ⊒ (match run (denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (denoteOp scf (Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk []))) env' | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match run (denoteOp scf (Op.mk "scf.execute_region" [] [(SSAVal.SSAVal "c0", MLIRType.index)] [r] (AttrDict.mk []))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (denoteOp scf (Op.mk "scf.for'" [] [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] [r] (AttrDict.mk []))) env' | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_bind]
case h n : β„• r : Region scf ⊒ (match run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (do let args ← denoteOpArgs scf [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)] OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] args (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_denoteOpArgs_cons_]
case h n : β„• r : Region scf ⊒ (match match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c0") let xs ← denoteOpArgs scf [] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c1") let xs ← denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)] pure ({ fst := MLIRType.index, snd := x } :: xs)) env' with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match match run (denoteOpArgs scf [(SSAVal.SSAVal "c0", MLIRType.index)]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "c1", MLIRType.index), (SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_bind]
case h n : β„• r : Region scf ⊒ (match match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c0") let xs ← denoteOpArgs scf [] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c1") let xs ← denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)] pure ({ fst := MLIRType.index, snd := x } :: xs)) env' with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c0")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c0") let xs ← denoteOpArgs scf [] pure ({ fst := MLIRType.index, snd := x } :: xs)) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match run (do let x ← TopM.get MLIRType.index (SSAVal.SSAVal "c1") let xs ← denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)] pure ({ fst := MLIRType.index, snd := x } :: xs)) env' with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
rw[run_TopM_get_]
case h n : β„• r : Region scf ⊒ (match match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c0")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c0")) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
rw[SSAEnv.get_set_ne_val]
case h n : β„• r : Region scf ⊒ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
rw[SSAEnv.get_set_ne_val]
case h n : β„• r : Region scf ⊒ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty))) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
rw[SSAEnv.get_set_eq_val]
case h n : β„• r : Region scf ⊒ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match match match Except.ok (match if H' : MLIRType.index = MLIRType.index then some (cast (_ : (match MLIRType.index with | MLIRType.float a => Float | MLIRType.int signedness sz => FinInt sz | MLIRType.tensor1d => Tensor1D | MLIRType.tensor2d => Tensor2D | MLIRType.tensor4d => Tensor4D | MLIRType.index => β„€ | MLIRType.undefined a => Unit | MLIRType.extended Οƒ => Unit | MLIRType.erased => Unit) = match MLIRType.index with | MLIRType.float a => Float | MLIRType.int signedness sz => FinInt sz | MLIRType.tensor1d => Tensor1D | MLIRType.tensor2d => Tensor2D | MLIRType.tensor4d => Tensor4D | MLIRType.index => β„€ | MLIRType.undefined a => Unit | MLIRType.extended Οƒ => Unit | MLIRType.erased => Unit) 0) else none with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match match match Except.ok (match SSAEnv.get (SSAVal.SSAVal "c0") MLIRType.index (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)) with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp
case h n : β„• r : Region scf ⊒ (match match match Except.ok (match if H' : MLIRType.index = MLIRType.index then some (cast (_ : (match MLIRType.index with | MLIRType.float a => Float | MLIRType.int signedness sz => FinInt sz | MLIRType.tensor1d => Tensor1D | MLIRType.tensor2d => Tensor2D | MLIRType.tensor4d => Tensor4D | MLIRType.index => β„€ | MLIRType.undefined a => Unit | MLIRType.extended Οƒ => Unit | MLIRType.erased => Unit) = match MLIRType.index with | MLIRType.float a => Float | MLIRType.int signedness sz => FinInt sz | MLIRType.tensor1d => Tensor1D | MLIRType.tensor2d => Tensor2D | MLIRType.tensor4d => Tensor4D | MLIRType.index => β„€ | MLIRType.undefined a => Unit | MLIRType.extended Οƒ => Unit | MLIRType.erased => Unit) 0) else none with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match match match run (denoteOpArgs scf []) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match match match Except.ok (match if H' : MLIRType.index = MLIRType.index then some (cast (_ : (match MLIRType.index with | MLIRType.float a => Float | MLIRType.int signedness sz => FinInt sz | MLIRType.tensor1d => Tensor1D | MLIRType.tensor2d => Tensor2D | MLIRType.tensor4d => Tensor4D | MLIRType.index => β„€ | MLIRType.undefined a => Unit | MLIRType.extended Οƒ => Unit | MLIRType.erased => Unit) = match MLIRType.index with | MLIRType.float a => Float | MLIRType.int signedness sz => FinInt sz | MLIRType.tensor1d => Tensor1D | MLIRType.tensor2d => Tensor2D | MLIRType.tensor4d => Tensor4D | MLIRType.index => β„€ | MLIRType.undefined a => Unit | MLIRType.extended Οƒ => Unit | MLIRType.erased => Unit) 0) else none with | some v => v | none => default, SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match run (denoteOpArgs scf []) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_denoteOpArgs_nil]
case h n : β„• r : Region scf ⊒ (match match match run (denoteOpArgs scf []) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match match run (pure [{ fst := MLIRType.index, snd := 0 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match match match run (denoteOpArgs scf []) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (pure ({ fst := MLIRType.index, snd := 0 } :: a)) env' | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_pure]
case h n : β„• r : Region scf ⊒ (match match run (pure [{ fst := MLIRType.index, snd := 0 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match match run (pure [{ fst := MLIRType.index, snd := 0 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => run (pure ({ fst := MLIRType.index, snd := a } :: a_1)) env' | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[TopM_mapDenoteRegion_cons]
case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM (TopM.scoped ∘ denoteRegion scf r :: TopM.mapDenoteRegion scf []) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.scoped ∘ denoteRegion scf r :: TopM.mapDenoteRegion scf []) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.mapDenoteRegion scf [r]) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[TopM_mapDenoteRegion_nil]
case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM (TopM.scoped ∘ denoteRegion scf r :: TopM.mapDenoteRegion scf []) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.scoped ∘ denoteRegion scf r :: TopM.mapDenoteRegion scf []) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM (TopM.scoped ∘ denoteRegion scf r :: TopM.mapDenoteRegion scf []) (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM (TopM.scoped ∘ denoteRegion scf r :: TopM.mapDenoteRegion scf []) (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[Semantics.semantics_op, scf_semantics_op]
case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (Semantics.semantics_op (IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk [])))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[OpM_denoteRegions_cons]
case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegion r 0 :: OpM.denoteRegions [] 1) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a (OpM.denoteRegion r 0 :: OpM.denoteRegions [] 1) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegions [r] 0) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a (OpM.denoteRegions [r] 0) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[OpM_denoteRegions_nil]
case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegion r 0 :: OpM.denoteRegions [] 1) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a (OpM.denoteRegion r 0 :: OpM.denoteRegions [] 1) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (OpM.denoteRegion r 0 [{ fst := MLIRType.index, snd := 0 }])) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.execute_region" [] [{ fst := MLIRType.index, snd := 0 }] (OpM.denoteRegion r 0 :: OpM.denoteRegions [] 1) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a (OpM.denoteRegion r 0 :: OpM.denoteRegions [] 1) (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_OpM_toTopM_denoteRegion]
case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (OpM.denoteRegion r 0 [{ fst := MLIRType.index, snd := 0 }])) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match run (TopM.denoteRegionsByIx [TopM.scoped ∘ denoteRegion scf r] 0 [{ fst := MLIRType.index, snd := 0 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (OpM.denoteRegion r 0 [{ fst := MLIRType.index, snd := 0 }])) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp[run_TopM_denoteRegionsByIx_cons]
case h n : β„• r : Region scf ⊒ (match run (TopM.denoteRegionsByIx [TopM.scoped ∘ denoteRegion scf r] 0 [{ fst := MLIRType.index, snd := 0 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h n : β„• r : Region scf ⊒ (match run (TopM.scoped (denoteRegion scf r [{ fst := MLIRType.index, snd := 0 }])) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match run (TopM.denoteRegionsByIx [TopM.scoped ∘ denoteRegion scf r] 0 [{ fst := MLIRType.index, snd := 0 }]) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
sorry
case h n : β„• r : Region scf ⊒ (match run (TopM.scoped (denoteRegion scf r [{ fst := MLIRType.index, snd := 0 }])) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h n : β„• r : Region scf ⊒ (match run (TopM.scoped (denoteRegion scf r [{ fst := MLIRType.index, snd := 0 }])) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) with | Except.ok (a, env') => match match run (TopM.get MLIRType.index (SSAVal.SSAVal "c1")) env' with | Except.ok (a, env') => match run (denoteOpArgs scf [(SSAVal.SSAVal "cn_plus_1", MLIRType.index)]) env' with | Except.ok (a_1, env') => Except.ok ({ fst := MLIRType.index, snd := a } :: a_1, env') | Except.error e => Except.error e | Except.error e => Except.error e with | Except.ok (a, env') => run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (match IOp.mk "scf.for'" [] a [OpM.denoteRegion r 0] (AttrDict.mk []) with | IOp.mk "scf.if" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := b }] [rthen, relse] attrs => ite (b = 1) rthen relse [] | IOp.mk "scf.for" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }, { fst := MLIRType.index, snd := step }] [body] attrs => do let _ ← run_loop_bounded_stepped (Int.toNat ((hi - lo) / step)) lo step default fun i x => body [{ fst := MLIRType.index, snd := i }] pure [] | IOp.mk "scf.for'" resTy [{ fst := MLIRType.index, snd := lo }, { fst := MLIRType.index, snd := hi }] [body] attrs => run_loop_bounded (Int.toNat (hi - lo)) lo [] body | IOp.mk "scf.yield" resTy vs [] attrs => pure vs | IOp.mk "scf.assert" resTy [{ fst := MLIRType.int Signedness.Signless 1, snd := arg }] [] attrs => if arg = 0 then OpM.Error (toString "" ++ toString (match AttrDict.find attrs "msg" with | some (AttrValue.str str) => str | x => "") ++ toString ": " ++ toString arg ++ toString " <assert failed>") else pure [] | IOp.mk "scf.execute_region" resTy args [rgn] attrs => rgn args | IOp.mk name resTy args regions attrs => OpM.Unhandled ("scf unhandled: " ++ name))) env' | Except.error e => Except.error e | Except.error e => Except.error e) = run (OpM.toTopM [TopM.scoped ∘ denoteRegion scf r] (run_loop_bounded (Int.toNat (↑n + 1)) 0 [] (OpM.denoteRegion r 0))) (SSAEnv.set (SSAVal.SSAVal "cn") MLIRType.index (↑n) (SSAEnv.set (SSAVal.SSAVal "cn_plus_1") MLIRType.index (↑n + 1) (SSAEnv.set (SSAVal.SSAVal "c0") MLIRType.index 0 (SSAEnv.set (SSAVal.SSAVal "c1") MLIRType.index 1 SSAEnv.empty)))) case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
sorry
case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp
case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case h.a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp
case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "cn_plus_1" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp
case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
Please generate a tactic in lean4 to solve the state. STATE: case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn_plus_1" β‰  SSAVal.SSAVal "c0" case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Dialects/ScfSemantics.lean
SCF.FOR_PEELING.equivalent
[214, 1]
[270, 2]
simp
case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0"
no goals
Please generate a tactic in lean4 to solve the state. STATE: case a n : β„• r : Region scf ⊒ SSAVal.SSAVal "cn" β‰  SSAVal.SSAVal "c0" TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.all_one
[10, 1]
[12, 20]
simp [all, foldr]
Ξ± : Type u_1 P : Ξ± β†’ Bool a : Ξ± ⊒ all [a] P = true ↔ P a = true
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type u_1 P : Ξ± β†’ Bool a : Ξ± ⊒ all [a] P = true ↔ P a = true TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.ne_mem_cons
[20, 1]
[25, 28]
intros Hne
Ξ± : Type u_1 x a : Ξ± as : List Ξ± ⊒ Β¬x ∈ a :: as β†’ x β‰  a ∧ Β¬x ∈ as
Ξ± : Type u_1 x a : Ξ± as : List Ξ± Hne : Β¬x ∈ a :: as ⊒ x β‰  a ∧ Β¬x ∈ as
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type u_1 x a : Ξ± as : List Ξ± ⊒ Β¬x ∈ a :: as β†’ x β‰  a ∧ Β¬x ∈ as TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.ne_mem_cons
[20, 1]
[25, 28]
apply And.intro <;> intros _ <;> apply Hne
Ξ± : Type u_1 x a : Ξ± as : List Ξ± Hne : Β¬x ∈ a :: as ⊒ x β‰  a ∧ Β¬x ∈ as
case left α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x = a ⊒ x ∈ a :: as case right α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x ∈ as ⊒ x ∈ a :: as
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type u_1 x a : Ξ± as : List Ξ± Hne : Β¬x ∈ a :: as ⊒ x β‰  a ∧ Β¬x ∈ as TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.ne_mem_cons
[20, 1]
[25, 28]
. subst x; constructor
case left α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x = a ⊒ x ∈ a :: as case right α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x ∈ as ⊒ x ∈ a :: as
case right α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x ∈ as ⊒ x ∈ a :: as
Please generate a tactic in lean4 to solve the state. STATE: case left α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x = a ⊒ x ∈ a :: as case right α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x ∈ as ⊒ x ∈ a :: as TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.ne_mem_cons
[20, 1]
[25, 28]
. constructor; assumption
case right α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x ∈ as ⊒ x ∈ a :: as
no goals
Please generate a tactic in lean4 to solve the state. STATE: case right α : Type u_1 x a : α as : List α Hne : ¬x ∈ a :: as a✝ : x ∈ as ⊒ x ∈ a :: as TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.List.getF_implies_mem
[100, 1]
[120, 2]
intros Ξ± xs
⊒ βˆ€ {Ξ± : Type} (xs : List Ξ±) (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs
Ξ± : Type xs : List Ξ± ⊒ βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs
Please generate a tactic in lean4 to solve the state. STATE: ⊒ βˆ€ {Ξ± : Type} (xs : List Ξ±) (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.List.getF_implies_mem
[100, 1]
[120, 2]
induction xs
Ξ± : Type xs : List Ξ± ⊒ βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs
case nil Ξ± : Type ⊒ βˆ€ (i : β„•) (INBOUND : i < length []), Mem (getF [] i INBOUND) [] case cons Ξ± : Type head✝ : Ξ± tail✝ : List Ξ± tail_ih✝ : βˆ€ (i : β„•) (INBOUND : i < length tail✝), Mem (getF tail✝ i INBOUND) tail✝ ⊒ βˆ€ (i : β„•) (INBOUND : i < length (head✝ :: tail✝)), Mem (getF (head✝ :: tail✝) i INBOUND) (head✝ :: tail✝)
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type xs : List Ξ± ⊒ βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.List.getF_implies_mem
[100, 1]
[120, 2]
case nil => { intros i INBOUND; simp at INBOUND; }
Ξ± : Type ⊒ βˆ€ (i : β„•) (INBOUND : i < length []), Mem (getF [] i INBOUND) []
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type ⊒ βˆ€ (i : β„•) (INBOUND : i < length []), Mem (getF [] i INBOUND) [] TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.List.getF_implies_mem
[100, 1]
[120, 2]
case cons x' xs IH => { intros i INBOUND; cases i; case zero => { simp [List.getF]; constructor; } case succ i' => { simp [List.getF]; constructor; apply IH; } }
Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs ⊒ βˆ€ (i : β„•) (INBOUND : i < length (x' :: xs)), Mem (getF (x' :: xs) i INBOUND) (x' :: xs)
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs ⊒ βˆ€ (i : β„•) (INBOUND : i < length (x' :: xs)), Mem (getF (x' :: xs) i INBOUND) (x' :: xs) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.List.getF_implies_mem
[100, 1]
[120, 2]
intros i INBOUND
Ξ± : Type ⊒ βˆ€ (i : β„•) (INBOUND : i < length []), Mem (getF [] i INBOUND) []
Ξ± : Type i : β„• INBOUND : i < length [] ⊒ Mem (getF [] i INBOUND) []
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type ⊒ βˆ€ (i : β„•) (INBOUND : i < length []), Mem (getF [] i INBOUND) [] TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.List.getF_implies_mem
[100, 1]
[120, 2]
simp at INBOUND
Ξ± : Type i : β„• INBOUND : i < length [] ⊒ Mem (getF [] i INBOUND) []
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type i : β„• INBOUND : i < length [] ⊒ Mem (getF [] i INBOUND) [] TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.List.getF_implies_mem
[100, 1]
[120, 2]
intros i INBOUND
Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs ⊒ βˆ€ (i : β„•) (INBOUND : i < length (x' :: xs)), Mem (getF (x' :: xs) i INBOUND) (x' :: xs)
Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i : β„• INBOUND : i < length (x' :: xs) ⊒ Mem (getF (x' :: xs) i INBOUND) (x' :: xs)
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs ⊒ βˆ€ (i : β„•) (INBOUND : i < length (x' :: xs)), Mem (getF (x' :: xs) i INBOUND) (x' :: xs) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.List.getF_implies_mem
[100, 1]
[120, 2]
cases i
Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i : β„• INBOUND : i < length (x' :: xs) ⊒ Mem (getF (x' :: xs) i INBOUND) (x' :: xs)
case zero Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊒ Mem (getF (x' :: xs) Nat.zero INBOUND) (x' :: xs) case succ Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs n✝ : β„• INBOUND : Nat.succ n✝ < length (x' :: xs) ⊒ Mem (getF (x' :: xs) (Nat.succ n✝) INBOUND) (x' :: xs)
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i : β„• INBOUND : i < length (x' :: xs) ⊒ Mem (getF (x' :: xs) i INBOUND) (x' :: xs) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.List.getF_implies_mem
[100, 1]
[120, 2]
case zero => { simp [List.getF]; constructor; }
Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊒ Mem (getF (x' :: xs) Nat.zero INBOUND) (x' :: xs)
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊒ Mem (getF (x' :: xs) Nat.zero INBOUND) (x' :: xs) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.List.getF_implies_mem
[100, 1]
[120, 2]
case succ i' => { simp [List.getF]; constructor; apply IH; }
Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : β„• INBOUND : Nat.succ i' < length (x' :: xs) ⊒ Mem (getF (x' :: xs) (Nat.succ i') INBOUND) (x' :: xs)
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : β„• INBOUND : Nat.succ i' < length (x' :: xs) ⊒ Mem (getF (x' :: xs) (Nat.succ i') INBOUND) (x' :: xs) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.List.getF_implies_mem
[100, 1]
[120, 2]
simp [List.getF]
Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊒ Mem (getF (x' :: xs) Nat.zero INBOUND) (x' :: xs)
Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊒ Mem x' (x' :: xs)
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊒ Mem (getF (x' :: xs) Nat.zero INBOUND) (x' :: xs) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.List.getF_implies_mem
[100, 1]
[120, 2]
constructor
Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊒ Mem x' (x' :: xs)
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs INBOUND : Nat.zero < length (x' :: xs) ⊒ Mem x' (x' :: xs) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.List.getF_implies_mem
[100, 1]
[120, 2]
simp [List.getF]
Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : β„• INBOUND : Nat.succ i' < length (x' :: xs) ⊒ Mem (getF (x' :: xs) (Nat.succ i') INBOUND) (x' :: xs)
Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : β„• INBOUND : Nat.succ i' < length (x' :: xs) ⊒ Mem (getF xs i' (_ : i' < length xs)) (x' :: xs)
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : β„• INBOUND : Nat.succ i' < length (x' :: xs) ⊒ Mem (getF (x' :: xs) (Nat.succ i') INBOUND) (x' :: xs) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.List.getF_implies_mem
[100, 1]
[120, 2]
constructor
Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : β„• INBOUND : Nat.succ i' < length (x' :: xs) ⊒ Mem (getF xs i' (_ : i' < length xs)) (x' :: xs)
case a Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : β„• INBOUND : Nat.succ i' < length (x' :: xs) ⊒ Mem (getF xs i' (_ : i' < length xs)) xs
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : β„• INBOUND : Nat.succ i' < length (x' :: xs) ⊒ Mem (getF xs i' (_ : i' < length xs)) (x' :: xs) TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.List.getF_implies_mem
[100, 1]
[120, 2]
apply IH
case a Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : β„• INBOUND : Nat.succ i' < length (x' :: xs) ⊒ Mem (getF xs i' (_ : i' < length xs)) xs
no goals
Please generate a tactic in lean4 to solve the state. STATE: case a Ξ± : Type x' : Ξ± xs : List Ξ± IH : βˆ€ (i : β„•) (INBOUND : i < length xs), Mem (getF xs i INBOUND) xs i' : β„• INBOUND : Nat.succ i' < length (x' :: xs) ⊒ Mem (getF xs i' (_ : i' < length xs)) xs TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.length_uniform
[132, 1]
[133, 45]
induction n <;> simp [uniform]
Ξ± : Type u_1 v : Ξ± n : β„• ⊒ length (uniform v n) = n
case succ Ξ± : Type u_1 v : Ξ± n✝ : β„• n_ih✝ : length (uniform v n✝) = n✝ ⊒ length (uniform v n✝) = n✝
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type u_1 v : Ξ± n : β„• ⊒ length (uniform v n) = n TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.length_uniform
[132, 1]
[133, 45]
assumption
case succ Ξ± : Type u_1 v : Ξ± n✝ : β„• n_ih✝ : length (uniform v n✝) = n✝ ⊒ length (uniform v n✝) = n✝
no goals
Please generate a tactic in lean4 to solve the state. STATE: case succ Ξ± : Type u_1 v : Ξ± n✝ : β„• n_ih✝ : length (uniform v n✝) = n✝ ⊒ length (uniform v n✝) = n✝ TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.length_rangeF
[144, 1]
[148, 35]
induction n with | zero => simp | succ m ih => simp [rangeF, ih]
n : β„• ⊒ length (rangeF n) = n
no goals
Please generate a tactic in lean4 to solve the state. STATE: n : β„• ⊒ length (rangeF n) = n TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.length_rangeF
[144, 1]
[148, 35]
simp
case zero ⊒ length (rangeF Nat.zero) = Nat.zero
no goals
Please generate a tactic in lean4 to solve the state. STATE: case zero ⊒ length (rangeF Nat.zero) = Nat.zero TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.length_rangeF
[144, 1]
[148, 35]
simp [rangeF, ih]
case succ m : β„• ih : length (rangeF m) = m ⊒ length (rangeF (Nat.succ m)) = Nat.succ m
no goals
Please generate a tactic in lean4 to solve the state. STATE: case succ m : β„• ih : length (rangeF m) = m ⊒ length (rangeF (Nat.succ m)) = Nat.succ m TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.getF_rangeF
[151, 1]
[161, 42]
simp at h
n i : β„• h : i < length (rangeF n) ⊒ i < n
n i : β„• h : i < n ⊒ i < n
Please generate a tactic in lean4 to solve the state. STATE: n i : β„• h : i < length (rangeF n) ⊒ i < n TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.getF_rangeF
[151, 1]
[161, 42]
apply h
n i : β„• h : i < n ⊒ i < n
no goals
Please generate a tactic in lean4 to solve the state. STATE: n i : β„• h : i < n ⊒ i < n TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.getF_rangeF
[151, 1]
[161, 42]
induction n with | zero => intro i h; simp; | succ m ih => intro i exact match i with | 0 => by simp [getF] | j+1 => by simp [rangeF, getF, ih]
n : β„• ⊒ βˆ€ (i : β„•) (h : i < length (rangeF n)), getF (rangeF n) i h = { val := i, isLt := (_ : i < n) }
no goals
Please generate a tactic in lean4 to solve the state. STATE: n : β„• ⊒ βˆ€ (i : β„•) (h : i < length (rangeF n)), getF (rangeF n) i h = { val := i, isLt := (_ : i < n) } TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.getF_rangeF
[151, 1]
[161, 42]
intro i h
case zero ⊒ βˆ€ (i : β„•) (h : i < length (rangeF Nat.zero)), getF (rangeF Nat.zero) i h = { val := i, isLt := (_ : i < Nat.zero) }
case zero i : β„• h : i < length (rangeF Nat.zero) ⊒ getF (rangeF Nat.zero) i h = { val := i, isLt := (_ : i < Nat.zero) }
Please generate a tactic in lean4 to solve the state. STATE: case zero ⊒ βˆ€ (i : β„•) (h : i < length (rangeF Nat.zero)), getF (rangeF Nat.zero) i h = { val := i, isLt := (_ : i < Nat.zero) } TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.getF_rangeF
[151, 1]
[161, 42]
simp
case zero i : β„• h : i < length (rangeF Nat.zero) ⊒ getF (rangeF Nat.zero) i h = { val := i, isLt := (_ : i < Nat.zero) }
no goals
Please generate a tactic in lean4 to solve the state. STATE: case zero i : β„• h : i < length (rangeF Nat.zero) ⊒ getF (rangeF Nat.zero) i h = { val := i, isLt := (_ : i < Nat.zero) } TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.getF_rangeF
[151, 1]
[161, 42]
intro i
case succ m : β„• ih : βˆ€ (i : β„•) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } ⊒ βˆ€ (i : β„•) (h : i < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) i h = { val := i, isLt := (_ : i < Nat.succ m) }
case succ m : β„• ih : βˆ€ (i : β„•) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } i : β„• ⊒ βˆ€ (h : i < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) i h = { val := i, isLt := (_ : i < Nat.succ m) }
Please generate a tactic in lean4 to solve the state. STATE: case succ m : β„• ih : βˆ€ (i : β„•) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } ⊒ βˆ€ (i : β„•) (h : i < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) i h = { val := i, isLt := (_ : i < Nat.succ m) } TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.getF_rangeF
[151, 1]
[161, 42]
exact match i with | 0 => by simp [getF] | j+1 => by simp [rangeF, getF, ih]
case succ m : β„• ih : βˆ€ (i : β„•) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } i : β„• ⊒ βˆ€ (h : i < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) i h = { val := i, isLt := (_ : i < Nat.succ m) }
no goals
Please generate a tactic in lean4 to solve the state. STATE: case succ m : β„• ih : βˆ€ (i : β„•) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } i : β„• ⊒ βˆ€ (h : i < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) i h = { val := i, isLt := (_ : i < Nat.succ m) } TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.getF_rangeF
[151, 1]
[161, 42]
simp [getF]
m : β„• ih : βˆ€ (i : β„•) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } i : β„• ⊒ βˆ€ (h : 0 < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) 0 h = { val := 0, isLt := (_ : 0 < Nat.succ m) }
no goals
Please generate a tactic in lean4 to solve the state. STATE: m : β„• ih : βˆ€ (i : β„•) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } i : β„• ⊒ βˆ€ (h : 0 < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) 0 h = { val := 0, isLt := (_ : 0 < Nat.succ m) } TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.getF_rangeF
[151, 1]
[161, 42]
simp [rangeF, getF, ih]
m : β„• ih : βˆ€ (i : β„•) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } i j : β„• ⊒ βˆ€ (h : j + 1 < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) (j + 1) h = { val := j + 1, isLt := (_ : j + 1 < Nat.succ m) }
no goals
Please generate a tactic in lean4 to solve the state. STATE: m : β„• ih : βˆ€ (i : β„•) (h : i < length (rangeF m)), getF (rangeF m) i h = { val := i, isLt := (_ : i < m) } i j : β„• ⊒ βˆ€ (h : j + 1 < length (rangeF (Nat.succ m))), getF (rangeF (Nat.succ m)) (j + 1) h = { val := j + 1, isLt := (_ : j + 1 < Nat.succ m) } TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.length_remap
[169, 1]
[171, 15]
simp [remap]
Ξ± : Type u_1 l : List Ξ± f : β„• β†’ β„• h : βˆ€ (n : β„•), n < length l β†’ f n < length l ⊒ length (remap l f h) = length l
no goals
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type u_1 l : List Ξ± f : β„• β†’ β„• h : βˆ€ (n : β„•), n < length l β†’ f n < length l ⊒ length (remap l f h) = length l TACTIC:
https://github.com/opencompl/lean-mlir.git
e43d21592801e5e40477b14b7a554e356060c40c
MLIR/Util/List.lean
List.getF_remap
[174, 1]
[177, 15]
apply h_f
Ξ± : Type ?u.30674 l : List Ξ± f : β„• β†’ β„• h_f : βˆ€ (n : β„•), n < length l β†’ f n < length l n : β„• h_n : n < length (remap l f h_f) ⊒ f n < length l
case a Ξ± : Type ?u.30674 l : List Ξ± f : β„• β†’ β„• h_f : βˆ€ (n : β„•), n < length l β†’ f n < length l n : β„• h_n : n < length (remap l f h_f) ⊒ n < length l
Please generate a tactic in lean4 to solve the state. STATE: Ξ± : Type ?u.30674 l : List Ξ± f : β„• β†’ β„• h_f : βˆ€ (n : β„•), n < length l β†’ f n < length l n : β„• h_n : n < length (remap l f h_f) ⊒ f n < length l TACTIC: