url stringclasses 147 values | commit stringclasses 147 values | file_path stringlengths 7 101 | full_name stringlengths 1 94 | start stringlengths 6 10 | end stringlengths 6 11 | tactic stringlengths 1 11.2k | state_before stringlengths 3 2.09M | state_after stringlengths 6 2.09M | input stringlengths 73 2.09M |
|---|---|---|---|---|---|---|---|---|---|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_denoteOps_singleton | [1318, 1] | [1322, 2] | simp[denoteOps] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
op : Op Δ
⊢ run (denoteOps Δ [op]) env = run (denoteOp Δ op) env | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
op : Op Δ
⊢ run (denoteOps Δ [op]) env = run (denoteOp Δ op) env
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_denoteOp | [1324, 1] | [1350, 2] | simp [denoteOp] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
name : String
res args : List (TypedSSAVal Δ)
regions : List (Region Δ)
attrs : AttrDict Δ
⊢ run (denoteOp Δ (Op.mk name res args regions attrs)) env =
run
(do
let args ← denoteOpArgs Δ args
let ret ←
OpM.toTopM (TopM.mapDenoteRegion Δ regions)
(Semantics.semantics_op (IOp.mk name (List.map Prod.snd res) args (OpM.denoteRegions regions 0) attrs))
match res with
| [] => pure ret
| [res] =>
match ret with
| [{ fst := τ, snd := v }] => do
TopM.set τ res.fst v
pure ret
| x => do
TopM.raiseUB (toString "denoteOp: expected 1 return value, got '" ++ toString ret ++ toString "'")
pure ret
| x => do
TopM.raiseUB (toString "denoteOp: expected 0 or 1 results, got '" ++ toString res ++ toString "'")
pure ret)
env | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
name : String
res args : List (TypedSSAVal Δ)
regions : List (Region Δ)
attrs : AttrDict Δ
⊢ run (denoteOp Δ (Op.mk name res args regions attrs)) env =
run
(do
let args ← denoteOpArgs Δ args
let ret ←
OpM.toTopM (TopM.mapDenoteRegion Δ regions)
(Semantics.semantics_op (IOp.mk name (List.map Prod.snd res) args (OpM.denoteRegions regions 0) attrs))
match res with
| [] => pure ret
| [res] =>
match ret with
| [{ fst := τ, snd := v }] => do
TopM.set τ res.fst v
pure ret
| x => do
TopM.raiseUB (toString "denoteOp: expected 1 return value, got '" ++ toString ret ++ toString "'")
pure ret
| x => do
TopM.raiseUB (toString "denoteOp: expected 0 or 1 results, got '" ++ toString res ++ toString "'")
pure ret)
env
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_denoteOpArgs_cons_ | [1356, 1] | [1364, 2] | simp[denoteOpArgs] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
name : SSAVal
ty : MLIRType Δ
args : List (TypedSSAVal Δ)
⊢ run (denoteOpArgs Δ ((name, ty) :: args)) env =
run
(do
let x ← TopM.get ty name
let xs ← denoteOpArgs Δ args
pure ({ fst := ty, snd := x } :: xs))
env | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
name : SSAVal
ty : MLIRType Δ
args : List (TypedSSAVal Δ)
⊢ run (denoteOpArgs Δ ((name, ty) :: args)) env =
run
(do
let x ← TopM.get ty name
let xs ← denoteOpArgs Δ args
pure ({ fst := ty, snd := x } :: xs))
env
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_TopM_get_ | [1370, 1] | [1382, 2] | simp[TopM.get, run, StateT.run, StateT.get, bind, StateT.bind, Except.bind, pure,
Except.pure, StateT.pure] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
env : SSAEnv Δ
ty : MLIRType Δ
name : SSAVal
⊢ run (TopM.get ty name) env =
Except.ok
(match SSAEnv.get name ty env with
| some v => v
| none => default,
env) | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
env : SSAEnv Δ
ty : MLIRType Δ
name : SSAVal
⊢ (match SSAEnv.get name ty env with
| some v => fun s => Except.ok (v, s)
| none => fun s => Except.ok (default, s))
env =
Except.ok
(match SSAEnv.get name ty env with
| some v => v
| none => default,
env) | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
env : SSAEnv Δ
ty : MLIRType Δ
name : SSAVal
⊢ run (TopM.get ty name) env =
Except.ok
(match SSAEnv.get name ty env with
| some v => v
| none => default,
env)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_TopM_get_ | [1370, 1] | [1382, 2] | cases H:SSAEnv.get name ty env <;> simp | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
env : SSAEnv Δ
ty : MLIRType Δ
name : SSAVal
⊢ (match SSAEnv.get name ty env with
| some v => fun s => Except.ok (v, s)
| none => fun s => Except.ok (default, s))
env =
Except.ok
(match SSAEnv.get name ty env with
| some v => v
| none => default,
env) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
env : SSAEnv Δ
ty : MLIRType Δ
name : SSAVal
⊢ (match SSAEnv.get name ty env with
| some v => fun s => Except.ok (v, s)
| none => fun s => Except.ok (default, s))
env =
Except.ok
(match SSAEnv.get name ty env with
| some v => v
| none => default,
env)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_TopM_get_success | [1384, 1] | [1394, 2] | simp[run_TopM_get_, ENV] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
⊢ run (TopM.get ty name) env = Except.ok (v, env) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
⊢ run (TopM.get ty name) env = Except.ok (v, env)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_denoteOpArgs_cons_success | [1400, 1] | [1417, 2] | simp[run_denoteOpArgs_cons_] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ run (denoteOpArgs Δ ((name, ty) :: args)) env =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ run
(do
let x ← TopM.get ty name
let xs ← denoteOpArgs Δ args
pure ({ fst := ty, snd := x } :: xs))
env =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ run (denoteOpArgs Δ ((name, ty) :: args)) env =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_denoteOpArgs_cons_success | [1400, 1] | [1417, 2] | simp [run_bind] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ run
(do
let x ← TopM.get ty name
let xs ← denoteOpArgs Δ args
pure ({ fst := ty, snd := x } :: xs))
env =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ (match run (TopM.get ty name) env with
| Except.ok (a, env') =>
match run (denoteOpArgs Δ args) env' with
| Except.ok (a_1, env') => run (pure ({ fst := ty, snd := a } :: a_1)) env'
| Except.error e => Except.error e
| Except.error e => Except.error e) =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ run
(do
let x ← TopM.get ty name
let xs ← denoteOpArgs Δ args
pure ({ fst := ty, snd := x } :: xs))
env =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_denoteOpArgs_cons_success | [1400, 1] | [1417, 2] | simp[run_TopM_get_success (ENV := ENV)] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ (match run (TopM.get ty name) env with
| Except.ok (a, env') =>
match run (denoteOpArgs Δ args) env' with
| Except.ok (a_1, env') => run (pure ({ fst := ty, snd := a } :: a_1)) env'
| Except.error e => Except.error e
| Except.error e => Except.error e) =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ (match run (denoteOpArgs Δ args) env with
| Except.ok (a, env') => run (pure ({ fst := ty, snd := v } :: a)) env'
| Except.error e => Except.error e) =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ (match run (TopM.get ty name) env with
| Except.ok (a, env') =>
match run (denoteOpArgs Δ args) env' with
| Except.ok (a_1, env') => run (pure ({ fst := ty, snd := a } :: a_1)) env'
| Except.error e => Except.error e
| Except.error e => Except.error e) =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_denoteOpArgs_cons_success | [1400, 1] | [1417, 2] | simp[pure, StateT.pure, run, StateT.run, Except.pure] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ (match run (denoteOpArgs Δ args) env with
| Except.ok (a, env') => run (pure ({ fst := ty, snd := v } :: a)) env'
| Except.error e => Except.error e) =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ (match denoteOpArgs Δ args env with
| Except.ok (a, env') => Except.ok ({ fst := ty, snd := v } :: a, env')
| Except.error e => Except.error e) =
match denoteOpArgs Δ args env with
| Except.ok (a, env') => Except.ok ({ fst := ty, snd := v } :: a, env')
| Except.error e => Except.error e | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ (match run (denoteOpArgs Δ args) env with
| Except.ok (a, env') => run (pure ({ fst := ty, snd := v } :: a)) env'
| Except.error e => Except.error e) =
match run (denoteOpArgs Δ args) env with
| Except.ok (xs, env') => Except.ok ({ fst := ty, snd := v } :: xs, env')
| Except.error e => Except.error e
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_denoteOpArgs_cons_success | [1400, 1] | [1417, 2] | cases denoteOpArgs Δ args env <;> simp | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ (match denoteOpArgs Δ args env with
| Except.ok (a, env') => Except.ok ({ fst := ty, snd := v } :: a, env')
| Except.error e => Except.error e) =
match denoteOpArgs Δ args env with
| Except.ok (a, env') => Except.ok ({ fst := ty, snd := v } :: a, env')
| Except.error e => Except.error e | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
ty : MLIRType Δ
v : MLIRType.eval ty
name : SSAVal
ENV : SSAEnv.get name ty env = some v
args : List (TypedSSAVal Δ)
⊢ (match denoteOpArgs Δ args env with
| Except.ok (a, env') => Except.ok ({ fst := ty, snd := v } :: a, env')
| Except.error e => Except.error e) =
match denoteOpArgs Δ args env with
| Except.ok (a, env') => Except.ok ({ fst := ty, snd := v } :: a, env')
| Except.error e => Except.error e
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_denoteOpArgs_nil | [1421, 1] | [1426, 2] | simp[denoteOpArgs] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
⊢ run (denoteOpArgs Δ []) env = Except.ok ([], env) | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
⊢ run (pure []) env = Except.ok ([], env) | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
⊢ run (denoteOpArgs Δ []) env = Except.ok ([], env)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_denoteOpArgs_nil | [1421, 1] | [1426, 2] | simp[run, pure, StateT.run, StateT.pure, Except.pure] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
⊢ run (pure []) env = Except.ok ([], env) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
env : SSAEnv Δ
⊢ run (pure []) env = Except.ok ([], env)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_pure | [1428, 1] | [1433, 2] | simp[run, pure, StateT.run, StateT.pure, Except.pure] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
a : Type
Δ : Dialect α σ ε
env : SSAEnv Δ
v : a
⊢ run (pure v) env = Except.ok (v, env) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
a : Type
Δ : Dialect α σ ε
env : SSAEnv Δ
v : a
⊢ run (pure v) env = Except.ok (v, env)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | OpM_toTopM_denoteRegion | [1435, 1] | [1444, 2] | simp[OpM.denoteRegion] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
ix : ℕ
Δ : Dialect α σ ε
args : TypedArgs Δ
r : Region Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ OpM.toTopM rs (OpM.denoteRegion r ix args) = TopM.denoteRegionsByIx rs ix args | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
ix : ℕ
Δ : Dialect α σ ε
args : TypedArgs Δ
r : Region Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ OpM.toTopM rs (OpM.RunRegion ix args fun retvals => OpM.Ret retvals) = TopM.denoteRegionsByIx rs ix args | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
ix : ℕ
Δ : Dialect α σ ε
args : TypedArgs Δ
r : Region Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ OpM.toTopM rs (OpM.denoteRegion r ix args) = TopM.denoteRegionsByIx rs ix args
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | OpM_toTopM_denoteRegion | [1435, 1] | [1444, 2] | simp[OpM.toTopM] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
ix : ℕ
Δ : Dialect α σ ε
args : TypedArgs Δ
r : Region Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ OpM.toTopM rs (OpM.RunRegion ix args fun retvals => OpM.Ret retvals) = TopM.denoteRegionsByIx rs ix args | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
ix : ℕ
Δ : Dialect α σ ε
args : TypedArgs Δ
r : Region Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ OpM.toTopM rs (OpM.RunRegion ix args fun retvals => OpM.Ret retvals) = TopM.denoteRegionsByIx rs ix args
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_OpM_toTopM_denoteRegion | [1446, 1] | [1456, 2] | simp[OpM.denoteRegion] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
ix : ℕ
Δ : Dialect α σ ε
args : TypedArgs Δ
r : Region Δ
env : SSAEnv Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ run (OpM.toTopM rs (OpM.denoteRegion r ix args)) env = run (TopM.denoteRegionsByIx rs ix args) env | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
ix : ℕ
Δ : Dialect α σ ε
args : TypedArgs Δ
r : Region Δ
env : SSAEnv Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ run (OpM.toTopM rs (OpM.RunRegion ix args fun retvals => OpM.Ret retvals)) env =
run (TopM.denoteRegionsByIx rs ix args) env | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
ix : ℕ
Δ : Dialect α σ ε
args : TypedArgs Δ
r : Region Δ
env : SSAEnv Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ run (OpM.toTopM rs (OpM.denoteRegion r ix args)) env = run (TopM.denoteRegionsByIx rs ix args) env
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_OpM_toTopM_denoteRegion | [1446, 1] | [1456, 2] | simp[OpM.toTopM] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
ix : ℕ
Δ : Dialect α σ ε
args : TypedArgs Δ
r : Region Δ
env : SSAEnv Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ run (OpM.toTopM rs (OpM.RunRegion ix args fun retvals => OpM.Ret retvals)) env =
run (TopM.denoteRegionsByIx rs ix args) env | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
ix : ℕ
Δ : Dialect α σ ε
args : TypedArgs Δ
r : Region Δ
env : SSAEnv Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ run (OpM.toTopM rs (OpM.RunRegion ix args fun retvals => OpM.Ret retvals)) env =
run (TopM.denoteRegionsByIx rs ix args) env
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_OpM_toTopM_Ret | [1458, 1] | [1467, 3] | simp[OpM.toTopM] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
env : SSAEnv Δ
v : TypedArgs Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ run (OpM.toTopM rs (OpM.Ret v)) env = Except.ok (v, env) | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
env : SSAEnv Δ
v : TypedArgs Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ run (pure v) env = Except.ok (v, env) | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
env : SSAEnv Δ
v : TypedArgs Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ run (OpM.toTopM rs (OpM.Ret v)) env = Except.ok (v, env)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_OpM_toTopM_Ret | [1458, 1] | [1467, 3] | simp[run_pure] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
env : SSAEnv Δ
v : TypedArgs Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ run (pure v) env = Except.ok (v, env) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
env : SSAEnv Δ
v : TypedArgs Δ
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
⊢ run (pure v) env = Except.ok (v, env)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | TopM_mapDenoteRegion_cons | [1469, 1] | [1476, 2] | simp[TopM.mapDenoteRegion] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
r : Region Δ
rs : List (Region Δ)
⊢ TopM.mapDenoteRegion Δ (r :: rs) = TopM.scoped ∘ denoteRegion Δ r :: TopM.mapDenoteRegion Δ rs | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
r : Region Δ
rs : List (Region Δ)
⊢ TopM.mapDenoteRegion Δ (r :: rs) = TopM.scoped ∘ denoteRegion Δ r :: TopM.mapDenoteRegion Δ rs
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | TopM_mapDenoteRegion_nil | [1477, 1] | [1481, 2] | simp[TopM.mapDenoteRegion] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
⊢ TopM.mapDenoteRegion Δ [] = [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
S : Semantics Δ
⊢ TopM.mapDenoteRegion Δ [] = []
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | OpM_denoteRegions_cons | [1483, 1] | [1492, 2] | simp[OpM.denoteRegions] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
r : Region Δ
rs : List (Region Δ)
ix : ℕ
⊢ OpM.denoteRegions (r :: rs) ix = OpM.denoteRegion r ix :: OpM.denoteRegions rs (ix + 1) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
r : Region Δ
rs : List (Region Δ)
ix : ℕ
⊢ OpM.denoteRegions (r :: rs) ix = OpM.denoteRegion r ix :: OpM.denoteRegions rs (ix + 1)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | OpM_denoteRegions_nil | [1493, 1] | [1497, 2] | simp[OpM.denoteRegions] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
ix : ℕ
⊢ OpM.denoteRegions [] ix = [] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
ix : ℕ
⊢ OpM.denoteRegions [] ix = []
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Semantics.lean | run_TopM_denoteRegionsByIx_cons | [1499, 1] | [1511, 2] | simp[TopM.denoteRegionsByIx] | α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
ix : ℕ
r : TypedArgs Δ → TopM Δ (TypedArgs Δ)
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
args : TypedArgs Δ
env : SSAEnv Δ
⊢ run (TopM.denoteRegionsByIx (r :: rs) ix args) env =
run
(match ix with
| 0 => r args
| Nat.succ ix' => TopM.denoteRegionsByIx rs ix' args)
env | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
α₁ σ₁ : Type
ε₁ : σ₁ → Type
δ₁ : Dialect α₁ σ₁ ε₁
α₂ σ₂ : Type
ε₂ : σ₂ → Type
δ₂ : Dialect α₂ σ₂ ε₂
α σ : Type
ε : σ → Type
Δ : Dialect α σ ε
ix : ℕ
r : TypedArgs Δ → TopM Δ (TypedArgs Δ)
rs : List (TypedArgs Δ → TopM Δ (TypedArgs Δ))
args : TypedArgs Δ
env : SSAEnv Δ
⊢ run (TopM.denoteRegionsByIx (r :: rs) ix args) env =
run
(match ix with
| 0 => r args
| Nat.succ ix' => TopM.denoteRegionsByIx rs ix' args)
env
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.bind_ret' | [200, 9] | [204, 34] | induction t with
| Ret _ => rfl
| Vis _ _ ih => simp [bind, ih] | E✝ : Type → Type
R✝ : Type
t : Fitree E✝ R✝
⊢ (bind t fun r => ret r) = t | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E✝ : Type → Type
R✝ : Type
t : Fitree E✝ R✝
⊢ (bind t fun r => ret r) = t
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.bind_ret' | [200, 9] | [204, 34] | rfl | case Ret
E✝ : Type → Type
R✝ : Type
r✝ : R✝
⊢ (bind (Ret r✝) fun r => ret r) = Ret r✝ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Ret
E✝ : Type → Type
R✝ : Type
r✝ : R✝
⊢ (bind (Ret r✝) fun r => ret r) = Ret r✝
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.bind_ret' | [200, 9] | [204, 34] | simp [bind, ih] | case Vis
E✝ : Type → Type
R✝ T✝ : Type
e✝ : E✝ T✝
k✝ : T✝ → Fitree E✝ R✝
ih : ∀ (a : T✝), (bind (k✝ a) fun r => ret r) = k✝ a
⊢ (bind (Vis e✝ k✝) fun r => ret r) = Vis e✝ k✝ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E✝ : Type → Type
R✝ T✝ : Type
e✝ : E✝ T✝
k✝ : T✝ → Fitree E✝ R✝
ih : ∀ (a : T✝), (bind (k✝ a) fun r => ret r) = k✝ a
⊢ (bind (Vis e✝ k✝) fun r => ret r) = Vis e✝ k✝
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.bind_Ret' | [206, 9] | [210, 34] | induction t with
| Ret _ => rfl
| Vis _ _ ih => simp [bind, ih] | E✝ : Type → Type
R✝ : Type
t : Fitree E✝ R✝
⊢ (bind t fun r => Ret r) = t | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E✝ : Type → Type
R✝ : Type
t : Fitree E✝ R✝
⊢ (bind t fun r => Ret r) = t
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.bind_Ret' | [206, 9] | [210, 34] | rfl | case Ret
E✝ : Type → Type
R✝ : Type
r✝ : R✝
⊢ (bind (Ret r✝) fun r => Ret r) = Ret r✝ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Ret
E✝ : Type → Type
R✝ : Type
r✝ : R✝
⊢ (bind (Ret r✝) fun r => Ret r) = Ret r✝
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.bind_Ret' | [206, 9] | [210, 34] | simp [bind, ih] | case Vis
E✝ : Type → Type
R✝ T✝ : Type
e✝ : E✝ T✝
k✝ : T✝ → Fitree E✝ R✝
ih : ∀ (a : T✝), (bind (k✝ a) fun r => Ret r) = k✝ a
⊢ (bind (Vis e✝ k✝) fun r => Ret r) = Vis e✝ k✝ | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E✝ : Type → Type
R✝ T✝ : Type
e✝ : E✝ T✝
k✝ : T✝ → Fitree E✝ R✝
ih : ∀ (a : T✝), (bind (k✝ a) fun r => Ret r) = k✝ a
⊢ (bind (Vis e✝ k✝) fun r => Ret r) = Vis e✝ k✝
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.bind_bind | [212, 9] | [217, 34] | induction t with
| Ret _ => rfl
| Vis _ _ ih => simp [bind, ih] | E✝ : Type → Type
R✝² : Type
t : Fitree E✝ R✝²
R✝¹ : Type
k : R✝² → Fitree E✝ R✝¹
R✝ : Type
k' : R✝¹ → Fitree E✝ R✝
⊢ bind (bind t k) k' = bind t fun x => bind (k x) k' | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E✝ : Type → Type
R✝² : Type
t : Fitree E✝ R✝²
R✝¹ : Type
k : R✝² → Fitree E✝ R✝¹
R✝ : Type
k' : R✝¹ → Fitree E✝ R✝
⊢ bind (bind t k) k' = bind t fun x => bind (k x) k'
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.bind_bind | [212, 9] | [217, 34] | rfl | case Ret
E✝ : Type → Type
R✝² R✝¹ : Type
k : R✝² → Fitree E✝ R✝¹
R✝ : Type
k' : R✝¹ → Fitree E✝ R✝
r✝ : R✝²
⊢ bind (bind (Ret r✝) k) k' = bind (Ret r✝) fun x => bind (k x) k' | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Ret
E✝ : Type → Type
R✝² R✝¹ : Type
k : R✝² → Fitree E✝ R✝¹
R✝ : Type
k' : R✝¹ → Fitree E✝ R✝
r✝ : R✝²
⊢ bind (bind (Ret r✝) k) k' = bind (Ret r✝) fun x => bind (k x) k'
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.bind_bind | [212, 9] | [217, 34] | simp [bind, ih] | case Vis
E✝ : Type → Type
R✝² R✝¹ : Type
k : R✝² → Fitree E✝ R✝¹
R✝ : Type
k' : R✝¹ → Fitree E✝ R✝
T✝ : Type
e✝ : E✝ T✝
k✝ : T✝ → Fitree E✝ R✝²
ih : ∀ (a : T✝), bind (bind (k✝ a) k) k' = bind (k✝ a) fun x => bind (k x) k'
⊢ bind (bind (Vis e✝ k✝) k) k' = bind (Vis e✝ k✝) fun x => bind (k x) k' | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E✝ : Type → Type
R✝² R✝¹ : Type
k : R✝² → Fitree E✝ R✝¹
R✝ : Type
k' : R✝¹ → Fitree E✝ R✝
T✝ : Type
e✝ : E✝ T✝
k✝ : T✝ → Fitree E✝ R✝²
ih : ∀ (a : T✝), bind (bind (k✝ a) k) k' = bind (k✝ a) fun x => bind (k x) k'
⊢ bind (bind (Vis e✝ k✝) k) k' = bind (Vis e✝ k✝) fun x => bind (k x) k'
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interp_bind | [353, 1] | [358, 34] | induction t with
| Ret _ => rfl
| Vis _ _ ih => simp [bind, ih] | E✝¹ E✝ : Type → Type
h : E✝¹ ~> Fitree E✝
R✝¹ : Type
t : Fitree E✝¹ R✝¹
R✝ : Type
k : R✝¹ → Fitree E✝¹ R✝
⊢ interp h (bind t k) = bind (interp h t) fun x => interp h (k x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E✝¹ E✝ : Type → Type
h : E✝¹ ~> Fitree E✝
R✝¹ : Type
t : Fitree E✝¹ R✝¹
R✝ : Type
k : R✝¹ → Fitree E✝¹ R✝
⊢ interp h (bind t k) = bind (interp h t) fun x => interp h (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interp_bind | [353, 1] | [358, 34] | rfl | case Ret
E✝¹ E✝ : Type → Type
h : E✝¹ ~> Fitree E✝
R✝¹ R✝ : Type
k : R✝¹ → Fitree E✝¹ R✝
r✝ : R✝¹
⊢ interp h (bind (Ret r✝) k) = bind (interp h (Ret r✝)) fun x => interp h (k x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Ret
E✝¹ E✝ : Type → Type
h : E✝¹ ~> Fitree E✝
R✝¹ R✝ : Type
k : R✝¹ → Fitree E✝¹ R✝
r✝ : R✝¹
⊢ interp h (bind (Ret r✝) k) = bind (interp h (Ret r✝)) fun x => interp h (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interp_bind | [353, 1] | [358, 34] | simp [bind, ih] | case Vis
E✝¹ E✝ : Type → Type
h : E✝¹ ~> Fitree E✝
R✝¹ R✝ : Type
k : R✝¹ → Fitree E✝¹ R✝
T✝ : Type
e✝ : E✝¹ T✝
k✝ : T✝ → Fitree E✝¹ R✝¹
ih : ∀ (a : T✝), interp h (bind (k✝ a) k) = bind (interp h (k✝ a)) fun x => interp h (k x)
⊢ interp h (bind (Vis e✝ k✝) k) = bind (interp h (Vis e✝ k✝)) fun x => interp h (k x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E✝¹ E✝ : Type → Type
h : E✝¹ ~> Fitree E✝
R✝¹ R✝ : Type
k : R✝¹ → Fitree E✝¹ R✝
T✝ : Type
e✝ : E✝¹ T✝
k✝ : T✝ → Fitree E✝¹ R✝¹
ih : ∀ (a : T✝), interp h (bind (k✝ a) k) = bind (interp h (k✝ a)) fun x => interp h (k x)
⊢ interp h (bind (Vis e✝ k✝) k) = bind (interp h (Vis e✝ k✝)) fun x => interp h (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interp'_bind | [360, 1] | [363, 30] | simp [interp', interp_bind] | E✝ : Type → Type
h : E✝ ~> Fitree Void1
F✝ : Type → Type
R✝¹ : Type
t : Fitree (E✝ +' F✝) R✝¹
R✝ : Type
k : R✝¹ → Fitree (E✝ +' F✝) R✝
⊢ interp' h (bind t k) = bind (interp' h t) fun x => interp' h (k x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E✝ : Type → Type
h : E✝ ~> Fitree Void1
F✝ : Type → Type
R✝¹ : Type
t : Fitree (E✝ +' F✝) R✝¹
R✝ : Type
k : R✝¹ → Fitree (E✝ +' F✝) R✝
⊢ interp' h (bind t k) = bind (interp' h t) fun x => interp' h (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpState_bind | [368, 1] | [378, 14] | revert s | E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
s : S
h : E ~> StateT S (Fitree F)
t : Fitree E R
⊢ interpState h (bind t k) s =
bind (interpState h t s) fun x =>
match x with
| (x, s') => interpState h (k x) s' | E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
t : Fitree E R
⊢ ∀ {s : S},
interpState h (bind t k) s =
bind (interpState h t s) fun x =>
match x with
| (x, s') => interpState h (k x) s' | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
s : S
h : E ~> StateT S (Fitree F)
t : Fitree E R
⊢ interpState h (bind t k) s =
bind (interpState h t s) fun x =>
match x with
| (x, s') => interpState h (k x) s'
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpState_bind | [368, 1] | [378, 14] | induction t with
| Ret _ => intros s; rfl
| Vis _ _ ih =>
simp [interpState] at *
simp [interp, Bind.bind, StateT.bind]
simp [ih] | E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
t : Fitree E R
⊢ ∀ {s : S},
interpState h (bind t k) s =
bind (interpState h t s) fun x =>
match x with
| (x, s') => interpState h (k x) s' | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
t : Fitree E R
⊢ ∀ {s : S},
interpState h (bind t k) s =
bind (interpState h t s) fun x =>
match x with
| (x, s') => interpState h (k x) s'
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpState_bind | [368, 1] | [378, 14] | intros s | case Ret
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
r✝ : R
⊢ ∀ {s : S},
interpState h (bind (Ret r✝) k) s =
bind (interpState h (Ret r✝) s) fun x =>
match x with
| (x, s') => interpState h (k x) s' | case Ret
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
r✝ : R
s : S
⊢ interpState h (bind (Ret r✝) k) s =
bind (interpState h (Ret r✝) s) fun x =>
match x with
| (x, s') => interpState h (k x) s' | Please generate a tactic in lean4 to solve the state.
STATE:
case Ret
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
r✝ : R
⊢ ∀ {s : S},
interpState h (bind (Ret r✝) k) s =
bind (interpState h (Ret r✝) s) fun x =>
match x with
| (x, s') => interpState h (k x) s'
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpState_bind | [368, 1] | [378, 14] | rfl | case Ret
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
r✝ : R
s : S
⊢ interpState h (bind (Ret r✝) k) s =
bind (interpState h (Ret r✝) s) fun x =>
match x with
| (x, s') => interpState h (k x) s' | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Ret
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
r✝ : R
s : S
⊢ interpState h (bind (Ret r✝) k) s =
bind (interpState h (Ret r✝) s) fun x =>
match x with
| (x, s') => interpState h (k x) s'
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpState_bind | [368, 1] | [378, 14] | simp [interpState] at * | case Vis
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E R
ih :
∀ (a : T✝) {s : S},
interpState h (bind (k✝ a) k) s =
bind (interpState h (k✝ a) s) fun x =>
match x with
| (x, s') => interpState h (k x) s'
⊢ ∀ {s : S},
interpState h (bind (Vis e✝ k✝) k) s =
bind (interpState h (Vis e✝ k✝) s) fun x =>
match x with
| (x, s') => interpState h (k x) s' | case Vis
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E R
ih : ∀ (a : T✝) {s : S}, interp h (bind (k✝ a) k) s = bind (interp h (k✝ a) s) fun x => interp h (k x.fst) x.snd
⊢ ∀ {s : S}, interp h (bind (Vis e✝ k✝) k) s = bind (interp h (Vis e✝ k✝) s) fun x => interp h (k x.fst) x.snd | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E R
ih :
∀ (a : T✝) {s : S},
interpState h (bind (k✝ a) k) s =
bind (interpState h (k✝ a) s) fun x =>
match x with
| (x, s') => interpState h (k x) s'
⊢ ∀ {s : S},
interpState h (bind (Vis e✝ k✝) k) s =
bind (interpState h (Vis e✝ k✝) s) fun x =>
match x with
| (x, s') => interpState h (k x) s'
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpState_bind | [368, 1] | [378, 14] | simp [interp, Bind.bind, StateT.bind] | case Vis
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E R
ih : ∀ (a : T✝) {s : S}, interp h (bind (k✝ a) k) s = bind (interp h (k✝ a) s) fun x => interp h (k x.fst) x.snd
⊢ ∀ {s : S}, interp h (bind (Vis e✝ k✝) k) s = bind (interp h (Vis e✝ k✝) s) fun x => interp h (k x.fst) x.snd | case Vis
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E R
ih : ∀ (a : T✝) {s : S}, interp h (bind (k✝ a) k) s = bind (interp h (k✝ a) s) fun x => interp h (k x.fst) x.snd
⊢ ∀ {s : S},
(bind (h T✝ e✝ s) fun __discr => interp h (bind (k✝ __discr.fst) k) __discr.snd) =
bind (h T✝ e✝ s) fun x => bind (interp h (k✝ x.fst) x.snd) fun x => interp h (k x.fst) x.snd | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E R
ih : ∀ (a : T✝) {s : S}, interp h (bind (k✝ a) k) s = bind (interp h (k✝ a) s) fun x => interp h (k x.fst) x.snd
⊢ ∀ {s : S}, interp h (bind (Vis e✝ k✝) k) s = bind (interp h (Vis e✝ k✝) s) fun x => interp h (k x.fst) x.snd
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpState_bind | [368, 1] | [378, 14] | simp [ih] | case Vis
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E R
ih : ∀ (a : T✝) {s : S}, interp h (bind (k✝ a) k) s = bind (interp h (k✝ a) s) fun x => interp h (k x.fst) x.snd
⊢ ∀ {s : S},
(bind (h T✝ e✝ s) fun __discr => interp h (bind (k✝ __discr.fst) k) __discr.snd) =
bind (h T✝ e✝ s) fun x => bind (interp h (k✝ x.fst) x.snd) fun x => interp h (k x.fst) x.snd | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E : Type → Type
S : Type
F : Type → Type
R R✝ : Type
k : R → Fitree E R✝
h : E ~> StateT S (Fitree F)
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E R
ih : ∀ (a : T✝) {s : S}, interp h (bind (k✝ a) k) s = bind (interp h (k✝ a) s) fun x => interp h (k x.fst) x.snd
⊢ ∀ {s : S},
(bind (h T✝ e✝ s) fun __discr => interp h (bind (k✝ __discr.fst) k) __discr.snd) =
bind (h T✝ e✝ s) fun x => bind (interp h (k✝ x.fst) x.snd) fun x => interp h (k x.fst) x.snd
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpWriter_bind | [383, 1] | [404, 19] | induction t with
| Ret _ =>
simp [bind, interpWriter]
have h₁: forall x, "" ++ x = x := by
simp [HAppend.hAppend, Append.append, String.append]
simp [List.nil_append]
simp [h₁]
have h₂: forall (α β: Type) (x: α × β), (x.fst, x.snd) = x := by simp
simp [h₂]
| Vis _ _ ih =>
simp [interpWriter] at *
simp [interp, Bind.bind, WriterT.bindCont, WriterT.mk]
have h: forall (x y z: String), x ++ (y ++ z) = x ++ y ++ z := by
simp [HAppend.hAppend, Append.append, String.append]
simp [List.append_assoc]
simp [ih, h] | E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
t : Fitree E T
k : T → Fitree E R
⊢ interpWriter h (bind t k) =
bind (interpWriter h t) fun x =>
match x with
| (x, s₁) =>
bind (interpWriter h (k x)) fun x =>
match x with
| (y, s₂) => ret (y, s₁ ++ s₂) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
t : Fitree E T
k : T → Fitree E R
⊢ interpWriter h (bind t k) =
bind (interpWriter h t) fun x =>
match x with
| (x, s₁) =>
bind (interpWriter h (k x)) fun x =>
match x with
| (y, s₂) => ret (y, s₁ ++ s₂)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpWriter_bind | [383, 1] | [404, 19] | simp [bind, interpWriter] | case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ interpWriter h (bind (Ret r✝) k) =
bind (interpWriter h (Ret r✝)) fun x =>
match x with
| (x, s₁) =>
bind (interpWriter h (k x)) fun x =>
match x with
| (y, s₂) => ret (y, s₁ ++ s₂) | case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, "" ++ x.snd) | Please generate a tactic in lean4 to solve the state.
STATE:
case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ interpWriter h (bind (Ret r✝) k) =
bind (interpWriter h (Ret r✝)) fun x =>
match x with
| (x, s₁) =>
bind (interpWriter h (k x)) fun x =>
match x with
| (y, s₂) => ret (y, s₁ ++ s₂)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpWriter_bind | [383, 1] | [404, 19] | have h₁: forall x, "" ++ x = x := by
simp [HAppend.hAppend, Append.append, String.append]
simp [List.nil_append] | case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, "" ++ x.snd) | case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, "" ++ x.snd) | Please generate a tactic in lean4 to solve the state.
STATE:
case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, "" ++ x.snd)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpWriter_bind | [383, 1] | [404, 19] | simp [h₁] | case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, "" ++ x.snd) | case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, x.snd) | Please generate a tactic in lean4 to solve the state.
STATE:
case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, "" ++ x.snd)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpWriter_bind | [383, 1] | [404, 19] | have h₂: forall (α β: Type) (x: α × β), (x.fst, x.snd) = x := by simp | case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, x.snd) | case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
h₂ : ∀ (α β : Type) (x : α × β), (x.fst, x.snd) = x
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, x.snd) | Please generate a tactic in lean4 to solve the state.
STATE:
case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, x.snd)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpWriter_bind | [383, 1] | [404, 19] | simp [h₂] | case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
h₂ : ∀ (α β : Type) (x : α × β), (x.fst, x.snd) = x
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, x.snd) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Ret
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
h₂ : ∀ (α β : Type) (x : α × β), (x.fst, x.snd) = x
⊢ interp h (k r✝) = bind (interp h (k r✝)) fun x => ret (x.fst, x.snd)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpWriter_bind | [383, 1] | [404, 19] | simp [HAppend.hAppend, Append.append, String.append] | E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ ∀ (x : String), "" ++ x = x | E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ ∀ (x : String), { data := [] ++ x.data } = x | Please generate a tactic in lean4 to solve the state.
STATE:
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ ∀ (x : String), "" ++ x = x
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpWriter_bind | [383, 1] | [404, 19] | simp [List.nil_append] | E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ ∀ (x : String), { data := [] ++ x.data } = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ ∀ (x : String), { data := [] ++ x.data } = x
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpWriter_bind | [383, 1] | [404, 19] | simp | E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
⊢ ∀ (α β : Type) (x : α × β), (x.fst, x.snd) = x | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
r✝ : T
h₁ : ∀ (x : String), "" ++ x = x
⊢ ∀ (α β : Type) (x : α × β), (x.fst, x.snd) = x
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpWriter_bind | [383, 1] | [404, 19] | simp [interpWriter] at * | case Vis
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interpWriter h (bind (k✝ a) k) =
bind (interpWriter h (k✝ a)) fun x =>
match x with
| (x, s₁) =>
bind (interpWriter h (k x)) fun x =>
match x with
| (y, s₂) => ret (y, s₁ ++ s₂)
⊢ interpWriter h (bind (Vis e✝ k✝) k) =
bind (interpWriter h (Vis e✝ k✝)) fun x =>
match x with
| (x, s₁) =>
bind (interpWriter h (k x)) fun x =>
match x with
| (y, s₂) => ret (y, s₁ ++ s₂) | case Vis
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ interp h (bind (Vis e✝ k✝) k) =
bind (interp h (Vis e✝ k✝)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interpWriter h (bind (k✝ a) k) =
bind (interpWriter h (k✝ a)) fun x =>
match x with
| (x, s₁) =>
bind (interpWriter h (k x)) fun x =>
match x with
| (y, s₂) => ret (y, s₁ ++ s₂)
⊢ interpWriter h (bind (Vis e✝ k✝) k) =
bind (interpWriter h (Vis e✝ k✝)) fun x =>
match x with
| (x, s₁) =>
bind (interpWriter h (k x)) fun x =>
match x with
| (y, s₂) => ret (y, s₁ ++ s₂)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpWriter_bind | [383, 1] | [404, 19] | simp [interp, Bind.bind, WriterT.bindCont, WriterT.mk] | case Vis
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ interp h (bind (Vis e✝ k✝) k) =
bind (interp h (Vis e✝ k✝)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd) | case Vis
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ (bind (h T✝ e✝) fun x => bind (interp h (bind (k✝ x.fst) k)) fun y => ret (y.fst, x.snd ++ y.snd)) =
bind (h T✝ e✝) fun x =>
bind (interp h (k✝ x.fst)) fun x_1 =>
bind (interp h (k x_1.fst)) fun x_2 => ret (x_2.fst, x.snd ++ x_1.snd ++ x_2.snd) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ interp h (bind (Vis e✝ k✝) k) =
bind (interp h (Vis e✝ k✝)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpWriter_bind | [383, 1] | [404, 19] | have h: forall (x y z: String), x ++ (y ++ z) = x ++ y ++ z := by
simp [HAppend.hAppend, Append.append, String.append]
simp [List.append_assoc] | case Vis
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ (bind (h T✝ e✝) fun x => bind (interp h (bind (k✝ x.fst) k)) fun y => ret (y.fst, x.snd ++ y.snd)) =
bind (h T✝ e✝) fun x =>
bind (interp h (k✝ x.fst)) fun x_1 =>
bind (interp h (k x_1.fst)) fun x_2 => ret (x_2.fst, x.snd ++ x_1.snd ++ x_2.snd) | case Vis
E F : Type → Type
T R : Type
h✝ : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h✝ (bind (k✝ a) k) =
bind (interp h✝ (k✝ a)) fun x => bind (interp h✝ (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
h : ∀ (x y z : String), x ++ (y ++ z) = x ++ y ++ z
⊢ (bind (h✝ T✝ e✝) fun x => bind (interp h✝ (bind (k✝ x.fst) k)) fun y => ret (y.fst, x.snd ++ y.snd)) =
bind (h✝ T✝ e✝) fun x =>
bind (interp h✝ (k✝ x.fst)) fun x_1 =>
bind (interp h✝ (k x_1.fst)) fun x_2 => ret (x_2.fst, x.snd ++ x_1.snd ++ x_2.snd) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ (bind (h T✝ e✝) fun x => bind (interp h (bind (k✝ x.fst) k)) fun y => ret (y.fst, x.snd ++ y.snd)) =
bind (h T✝ e✝) fun x =>
bind (interp h (k✝ x.fst)) fun x_1 =>
bind (interp h (k x_1.fst)) fun x_2 => ret (x_2.fst, x.snd ++ x_1.snd ++ x_2.snd)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpWriter_bind | [383, 1] | [404, 19] | simp [ih, h] | case Vis
E F : Type → Type
T R : Type
h✝ : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h✝ (bind (k✝ a) k) =
bind (interp h✝ (k✝ a)) fun x => bind (interp h✝ (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
h : ∀ (x y z : String), x ++ (y ++ z) = x ++ y ++ z
⊢ (bind (h✝ T✝ e✝) fun x => bind (interp h✝ (bind (k✝ x.fst) k)) fun y => ret (y.fst, x.snd ++ y.snd)) =
bind (h✝ T✝ e✝) fun x =>
bind (interp h✝ (k✝ x.fst)) fun x_1 =>
bind (interp h✝ (k x_1.fst)) fun x_2 => ret (x_2.fst, x.snd ++ x_1.snd ++ x_2.snd) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E F : Type → Type
T R : Type
h✝ : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h✝ (bind (k✝ a) k) =
bind (interp h✝ (k✝ a)) fun x => bind (interp h✝ (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
h : ∀ (x y z : String), x ++ (y ++ z) = x ++ y ++ z
⊢ (bind (h✝ T✝ e✝) fun x => bind (interp h✝ (bind (k✝ x.fst) k)) fun y => ret (y.fst, x.snd ++ y.snd)) =
bind (h✝ T✝ e✝) fun x =>
bind (interp h✝ (k✝ x.fst)) fun x_1 =>
bind (interp h✝ (k x_1.fst)) fun x_2 => ret (x_2.fst, x.snd ++ x_1.snd ++ x_2.snd)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpWriter_bind | [383, 1] | [404, 19] | simp [HAppend.hAppend, Append.append, String.append] | E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ ∀ (x y z : String), x ++ (y ++ z) = x ++ y ++ z | E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ ∀ (x y z : String), { data := x.data ++ (y.data ++ z.data) } = { data := x.data ++ y.data ++ z.data } | Please generate a tactic in lean4 to solve the state.
STATE:
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ ∀ (x y z : String), x ++ (y ++ z) = x ++ y ++ z
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpWriter_bind | [383, 1] | [404, 19] | simp [List.append_assoc] | E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ ∀ (x y z : String), { data := x.data ++ (y.data ++ z.data) } = { data := x.data ++ y.data ++ z.data } | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E F : Type → Type
T R : Type
h : E ~> WriterT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x => bind (interp h (k x.fst)) fun x_1 => ret (x_1.fst, x.snd ++ x_1.snd)
⊢ ∀ (x y z : String), { data := x.data ++ (y.data ++ z.data) } = { data := x.data ++ y.data ++ z.data }
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpOption_bind | [406, 1] | [422, 28] | induction t with
| Ret _ => rfl
| Vis _ _ ih =>
simp [interpOption] at *
simp [interp, bind, Bind.bind, OptionT.bind, OptionT.mk]
have fequal2 α β (f g: α → β) x y: f = g → x = y → f x = g y :=
fun h₁ h₂ => by simp [h₁, h₂]
apply fequal2; rfl; funext x
cases x <;> simp [ih] | E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
t : Fitree E T
k : T → Fitree E R
⊢ interpOption h (bind t k) =
bind (interpOption h t) fun x? =>
match x? with
| some x => interpOption h (k x)
| none => ret none | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
t : Fitree E T
k : T → Fitree E R
⊢ interpOption h (bind t k) =
bind (interpOption h t) fun x? =>
match x? with
| some x => interpOption h (k x)
| none => ret none
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpOption_bind | [406, 1] | [422, 28] | rfl | case Ret
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ interpOption h (bind (Ret r✝) k) =
bind (interpOption h (Ret r✝)) fun x? =>
match x? with
| some x => interpOption h (k x)
| none => ret none | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Ret
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ interpOption h (bind (Ret r✝) k) =
bind (interpOption h (Ret r✝)) fun x? =>
match x? with
| some x => interpOption h (k x)
| none => ret none
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpOption_bind | [406, 1] | [422, 28] | simp [interpOption] at * | case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interpOption h (bind (k✝ a) k) =
bind (interpOption h (k✝ a)) fun x? =>
match x? with
| some x => interpOption h (k x)
| none => ret none
⊢ interpOption h (bind (Vis e✝ k✝) k) =
bind (interpOption h (Vis e✝ k✝)) fun x? =>
match x? with
| some x => interpOption h (k x)
| none => ret none | case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
⊢ interp h (bind (Vis e✝ k✝) k) =
bind (interp h (Vis e✝ k✝)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interpOption h (bind (k✝ a) k) =
bind (interpOption h (k✝ a)) fun x? =>
match x? with
| some x => interpOption h (k x)
| none => ret none
⊢ interpOption h (bind (Vis e✝ k✝) k) =
bind (interpOption h (Vis e✝ k✝)) fun x? =>
match x? with
| some x => interpOption h (k x)
| none => ret none
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpOption_bind | [406, 1] | [422, 28] | simp [interp, bind, Bind.bind, OptionT.bind, OptionT.mk] | case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
⊢ interp h (bind (Vis e✝ k✝) k) =
bind (interp h (Vis e✝ k✝)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none | case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
⊢ (bind (h T✝ e✝) fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
⊢ interp h (bind (Vis e✝ k✝) k) =
bind (interp h (Vis e✝ k✝)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpOption_bind | [406, 1] | [422, 28] | have fequal2 α β (f g: α → β) x y: f = g → x = y → f x = g y :=
fun h₁ h₂ => by simp [h₁, h₂] | case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
⊢ (bind (h T✝ e✝) fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none | case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α : Sort ?u.47259) (β : Sort ?u.47260) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (bind (h T✝ e✝) fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
⊢ (bind (h T✝ e✝) fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpOption_bind | [406, 1] | [422, 28] | apply fequal2 | case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α : Sort ?u.47259) (β : Sort ?u.47260) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (bind (h T✝ e✝) fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none | case Vis.a
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ bind (h T✝ e✝) = bind (h T✝ e✝)
case Vis.a
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α : Sort ?u.47259) (β : Sort ?u.47260) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (bind (h T✝ e✝) fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpOption_bind | [406, 1] | [422, 28] | rfl | case Vis.a
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ bind (h T✝ e✝) = bind (h T✝ e✝)
case Vis.a
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none | case Vis.a
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis.a
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ bind (h T✝ e✝) = bind (h T✝ e✝)
case Vis.a
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpOption_bind | [406, 1] | [422, 28] | funext x | case Vis.a
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none | case Vis.a.h
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
x : Option T✝
⊢ (match x with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis.a
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun __do_lift =>
match __do_lift with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
fun x =>
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpOption_bind | [406, 1] | [422, 28] | cases x <;> simp [ih] | case Vis.a.h
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
x : Option T✝
⊢ (match x with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis.a.h
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
x : Option T✝
⊢ (match x with
| some a => interp h (bind (k✝ a) k)
| none => ret none) =
bind
(match x with
| some a => interp h (k✝ a)
| none => ret none)
fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpOption_bind | [406, 1] | [422, 28] | simp [h₁, h₂] | E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
α : Sort ?u.47259
β : Sort ?u.47260
f g : α → β
x y : α
h₁ : f = g
h₂ : x = y
⊢ f x = g y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E F : Type → Type
T R : Type
h : E ~> OptionT (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| some x => interp h (k x)
| none => ret none
α : Sort ?u.47259
β : Sort ?u.47260
f g : α → β
x y : α
h₁ : f = g
h₂ : x = y
⊢ f x = g y
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpExcept_bind | [424, 1] | [441, 28] | induction t with
| Ret _ => rfl
| Vis _ _ ih =>
simp [interpExcept] at *
simp [interp, bind, Bind.bind]
simp [ExceptT.bind, ExceptT.mk, ExceptT.bindCont]
have fequal2 α β (f g: α → β) x y: f = g → x = y → f x = g y :=
fun h₁ h₂ => by simp [h₁, h₂]
apply fequal2; rfl; funext x
cases x <;> simp [ih] | E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
t : Fitree E T
k : T → Fitree E R
⊢ interpExcept h (bind t k) =
bind (interpExcept h t) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interpExcept h (k x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
t : Fitree E T
k : T → Fitree E R
⊢ interpExcept h (bind t k) =
bind (interpExcept h t) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interpExcept h (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpExcept_bind | [424, 1] | [441, 28] | rfl | case Ret
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ interpExcept h (bind (Ret r✝) k) =
bind (interpExcept h (Ret r✝)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interpExcept h (k x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Ret
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
r✝ : T
⊢ interpExcept h (bind (Ret r✝) k) =
bind (interpExcept h (Ret r✝)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interpExcept h (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpExcept_bind | [424, 1] | [441, 28] | simp [interpExcept] at * | case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interpExcept h (bind (k✝ a) k) =
bind (interpExcept h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interpExcept h (k x)
⊢ interpExcept h (bind (Vis e✝ k✝) k) =
bind (interpExcept h (Vis e✝ k✝)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interpExcept h (k x) | case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
⊢ interp h (bind (Vis e✝ k✝) k) =
bind (interp h (Vis e✝ k✝)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interpExcept h (bind (k✝ a) k) =
bind (interpExcept h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interpExcept h (k x)
⊢ interpExcept h (bind (Vis e✝ k✝) k) =
bind (interpExcept h (Vis e✝ k✝)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interpExcept h (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpExcept_bind | [424, 1] | [441, 28] | simp [interp, bind, Bind.bind] | case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
⊢ interp h (bind (Vis e✝ k✝) k) =
bind (interp h (Vis e✝ k✝)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x) | case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
⊢ bind (h T✝ e✝) (ExceptT.bindCont fun t => interp h (bind (k✝ t) k)) =
bind (h T✝ e✝) fun x =>
bind (ExceptT.bindCont (fun t => interp h (k✝ t)) x) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
⊢ interp h (bind (Vis e✝ k✝) k) =
bind (interp h (Vis e✝ k✝)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpExcept_bind | [424, 1] | [441, 28] | simp [ExceptT.bind, ExceptT.mk, ExceptT.bindCont] | case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
⊢ bind (h T✝ e✝) (ExceptT.bindCont fun t => interp h (bind (k✝ t) k)) =
bind (h T✝ e✝) fun x =>
bind (ExceptT.bindCont (fun t => interp h (k✝ t)) x) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x) | case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
⊢ (bind (h T✝ e✝) fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
⊢ bind (h T✝ e✝) (ExceptT.bindCont fun t => interp h (bind (k✝ t) k)) =
bind (h T✝ e✝) fun x =>
bind (ExceptT.bindCont (fun t => interp h (k✝ t)) x) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpExcept_bind | [424, 1] | [441, 28] | have fequal2 α β (f g: α → β) x y: f = g → x = y → f x = g y :=
fun h₁ h₂ => by simp [h₁, h₂] | case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
⊢ (bind (h T✝ e✝) fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x) | case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α : Sort ?u.50273) (β : Sort ?u.50274) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (bind (h T✝ e✝) fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
⊢ (bind (h T✝ e✝) fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpExcept_bind | [424, 1] | [441, 28] | apply fequal2 | case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α : Sort ?u.50273) (β : Sort ?u.50274) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (bind (h T✝ e✝) fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x) | case Vis.a
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ bind (h T✝ e✝) = bind (h T✝ e✝)
case Vis.a
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α : Sort ?u.50273) (β : Sort ?u.50274) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (bind (h T✝ e✝) fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
bind (h T✝ e✝) fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpExcept_bind | [424, 1] | [441, 28] | rfl | case Vis.a
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ bind (h T✝ e✝) = bind (h T✝ e✝)
case Vis.a
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x) | case Vis.a
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis.a
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ bind (h T✝ e✝) = bind (h T✝ e✝)
case Vis.a
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpExcept_bind | [424, 1] | [441, 28] | funext x | case Vis.a
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x) | case Vis.a.h
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
x : Except ε T✝
⊢ (match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis.a
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
fun x =>
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpExcept_bind | [424, 1] | [441, 28] | cases x <;> simp [ih] | case Vis.a.h
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
x : Except ε T✝
⊢ (match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis.a.h
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
x : Except ε T✝
⊢ (match x with
| Except.ok a => interp h (bind (k✝ a) k)
| Except.error e => ret (Except.error e)) =
bind
(match x with
| Except.ok a => interp h (k✝ a)
| Except.error e => ret (Except.error e))
fun x? =>
match x? with
| Except.error e => ret (Except.error e)
| Except.ok x => interp h (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/Fitree.lean | Fitree.interpExcept_bind | [424, 1] | [441, 28] | simp [h₁, h₂] | E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
α : Sort ?u.50273
β : Sort ?u.50274
f g : α → β
x y : α
h₁ : f = g
h₂ : x = y
⊢ f x = g y | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
E : Type → Type
ε : Type
F : Type → Type
T R : Type
h : E ~> ExceptT ε (Fitree F)
k : T → Fitree E R
T✝ : Type
e✝ : E T✝
k✝ : T✝ → Fitree E T
ih :
∀ (a : T✝),
interp h (bind (k✝ a) k) =
bind (interp h (k✝ a)) fun x? =>
match x? with
| Except.error ε_1 => ret (Except.error ε_1)
| Except.ok x => interp h (k x)
α : Sort ?u.50273
β : Sort ?u.50274
f g : α → β
x y : α
h₁ : f = g
h₂ : x = y
⊢ f x = g y
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/ToySemantics.lean | double_transpose_correct | [136, 1] | [153, 28] | intros t1 | ⊢ ∀ (t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
run_toy (toy_semantics_region double_transpose)
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 })]) =
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := builtin.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32, snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 })]) | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ run_toy (toy_semantics_region double_transpose)
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 })]) =
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := builtin.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32, snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 })]) | Please generate a tactic in lean4 to solve the state.
STATE:
⊢ ∀ (t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
run_toy (toy_semantics_region double_transpose)
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 })]) =
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := builtin.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32, snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 })])
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/ToySemantics.lean | double_transpose_correct | [136, 1] | [153, 28] | simp [double_transpose, toy_semantics_region, toy_semantics_op] | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ run_toy (toy_semantics_region double_transpose)
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 })]) =
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := builtin.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32, snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 })]) | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(interpSSA'
(interpUB'!
(Fitree.bind
(match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.bind (Fitree.trigger (ToyOp.Constant D₁ τ₁ t_lit)) fun t =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) (some res) t
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.bind
(Fitree.trigger
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name))
fun t =>
Fitree.bind (Fitree.trigger (ToyOp.Transpose τ n m t)) fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ))
(some res) t'
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h : τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.bind (Fitree.trigger (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)) fun t =>
Fitree.bind
(Fitree.trigger
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) t))
fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D' τ₂)) (some res)
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) t')
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString ""))
fun x =>
match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.bind (Fitree.trigger (ToyOp.Constant D₁ τ₁ t_lit)) fun t =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) (some res) t
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.bind
(Fitree.trigger
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name))
fun t =>
Fitree.bind (Fitree.trigger (ToyOp.Transpose τ n m t)) fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ))
(some res) t'
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h : τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.bind (Fitree.trigger (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)) fun t =>
Fitree.bind
(Fitree.trigger
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) t))
fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D' τ₂)) (some res)
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) t')
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])) =
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) | Please generate a tactic in lean4 to solve the state.
STATE:
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ run_toy (toy_semantics_region double_transpose)
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 })]) =
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := builtin.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32, snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := builtin.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32, snd := t1 })])
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/ToySemantics.lean | double_transpose_correct | [136, 1] | [153, 28] | simp_itree | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(interpSSA'
(interpUB'!
(Fitree.bind
(match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.bind (Fitree.trigger (ToyOp.Constant D₁ τ₁ t_lit)) fun t =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) (some res) t
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.bind
(Fitree.trigger
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name))
fun t =>
Fitree.bind (Fitree.trigger (ToyOp.Transpose τ n m t)) fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ))
(some res) t'
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h : τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.bind (Fitree.trigger (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)) fun t =>
Fitree.bind
(Fitree.trigger
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) t))
fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D' τ₂)) (some res)
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) t')
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString ""))
fun x =>
match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.bind (Fitree.trigger (ToyOp.Constant D₁ τ₁ t_lit)) fun t =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) (some res) t
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.bind
(Fitree.trigger
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name))
fun t =>
Fitree.bind (Fitree.trigger (ToyOp.Transpose τ n m t)) fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ))
(some res) t'
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h : τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.bind (Fitree.trigger (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)) fun t =>
Fitree.bind
(Fitree.trigger
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) t))
fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D' τ₂)) (some res)
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) t')
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])) =
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(interpSSA'
(interpUB'!
(Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Get
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t1"))))
fun r =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 r))) fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t2") r)))
fun r =>
match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Constant D₁ τ₁ t_lit))) fun r =>
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name)))
fun r =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Transpose τ n m r))) fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h :
τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inr
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) r)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D' τ₂)) res
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) r))))
Fitree.Ret
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) | Please generate a tactic in lean4 to solve the state.
STATE:
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(interpSSA'
(interpUB'!
(Fitree.bind
(match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.bind (Fitree.trigger (ToyOp.Constant D₁ τ₁ t_lit)) fun t =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) (some res) t
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.bind
(Fitree.trigger
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name))
fun t =>
Fitree.bind (Fitree.trigger (ToyOp.Transpose τ n m t)) fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ))
(some res) t'
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h : τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.bind (Fitree.trigger (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)) fun t =>
Fitree.bind
(Fitree.trigger
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) t))
fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D' τ₂)) (some res)
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) t')
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t1",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString ""))
fun x =>
match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.bind (Fitree.trigger (ToyOp.Constant D₁ τ₁ t_lit)) fun t =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) (some res) t
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.bind
(Fitree.trigger
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name))
fun t =>
Fitree.bind (Fitree.trigger (ToyOp.Transpose τ n m t)) fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ))
(some res) t'
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h : τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.bind (Fitree.trigger (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)) fun t =>
Fitree.bind
(Fitree.trigger
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) t))
fun t' =>
SSAEnv.set? (MLIRType.extended (builtin.σ.tensor D' τ₂)) (some res)
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) t')
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])) =
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/ToySemantics.lean | double_transpose_correct | [136, 1] | [153, 28] | simp [interpUB'!] | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(interpSSA'
(interpUB'!
(Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Get
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t1"))))
fun r =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 r))) fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t2") r)))
fun r =>
match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Constant D₁ τ₁ t_lit))) fun r =>
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name)))
fun r =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Transpose τ n m r))) fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h :
τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inr
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) r)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D' τ₂)) res
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) r))))
Fitree.Ret
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(interpSSA'
(Fitree.bind
(Fitree.trigger
(Sum.inl
(SSAEnvE.Get
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t1"))))
fun x =>
Fitree.bind (Fitree.trigger (Sum.inr (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x))) fun x =>
Fitree.bind
(Fitree.trigger
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t2") x)))
fun x =>
Fitree.interp (Fitree.case UBE.handle! fun T => Fitree.trigger)
(match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Constant D₁ τ₁ t_lit))) fun r =>
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name)))
fun r =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Transpose τ n m r))) fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h :
τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inr
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) r)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D' τ₂)) res
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) r))))
Fitree.Ret
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) | Please generate a tactic in lean4 to solve the state.
STATE:
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(interpSSA'
(interpUB'!
(Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Get
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t1"))))
fun r =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 r))) fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t2") r)))
fun r =>
match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Constant D₁ τ₁ t_lit))) fun r =>
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name)))
fun r =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Transpose τ n m r))) fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h :
τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inr
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) r)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D' τ₂)) res
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) r))))
Fitree.Ret
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/ToySemantics.lean | double_transpose_correct | [136, 1] | [153, 28] | simp_itree | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(interpSSA'
(Fitree.bind
(Fitree.trigger
(Sum.inl
(SSAEnvE.Get
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t1"))))
fun x =>
Fitree.bind (Fitree.trigger (Sum.inr (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x))) fun x =>
Fitree.bind
(Fitree.trigger
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t2") x)))
fun x =>
Fitree.interp (Fitree.case UBE.handle! fun T => Fitree.trigger)
(match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Constant D₁ τ₁ t_lit))) fun r =>
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name)))
fun r =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Transpose τ n m r))) fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h :
τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inr
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) r)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D' τ₂)) res
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) r))))
Fitree.Ret
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t1")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) with
| some v =>
Fitree.Ret
(v,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
| none =>
Fitree.Ret
(default,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x.fst) fun x_1 =>
Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd) with
| some v =>
Fitree.Ret
(v,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd)
| none =>
Fitree.Ret
(default,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x.fst) fun x_2 =>
interpSSA' (Fitree.Ret ())
(SSAEnv.set (SSAVal.SSAVal "t3")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
x_2 x.snd)) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) | Please generate a tactic in lean4 to solve the state.
STATE:
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(interpSSA'
(Fitree.bind
(Fitree.trigger
(Sum.inl
(SSAEnvE.Get
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t1"))))
fun x =>
Fitree.bind (Fitree.trigger (Sum.inr (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x))) fun x =>
Fitree.bind
(Fitree.trigger
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAVal.SSAVal "t2") x)))
fun x =>
Fitree.interp (Fitree.case UBE.handle! fun T => Fitree.trigger)
(match
Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk []) with
| Op.mk "toy.constant" [(res, MLIRType.extended (Sum.inl (Sum.inl (D₁, τ₁))))] [] [] attrs =>
match AttrDict.find attrs "value" with
| some (AttrValue.extended { elem := elem, τ_sig := Sum.inl (Sum.inl (D₂, τ₂)) }) =>
match TensorLiteral.ofTensorElem elem D₁ τ₁ with
| none =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| some t_lit =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Constant D₁ τ₁ t_lit))) fun r =>
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D₁ τ₁)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| Op.mk "toy.transpose" [(res, τ₂)] [(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ))))] [] attrs =>
match D with
| [Dimension.Known n, Dimension.Known m] =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor [Dimension.Known n, Dimension.Known m] τ))
t_name)))
fun r =>
Fitree.Vis (Sum.inr (Sum.inr (ToyOp.Transpose τ n m r))) fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set
(MLIRType.extended (builtin.σ.tensor [Dimension.Known m, Dimension.Known n] τ)) res r)))
Fitree.Ret
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
|
Op.mk "toy.reshape" [(res, MLIRType.extended (Sum.inl (Sum.inl (D', τ₂))))]
[(t_name, MLIRType.extended (Sum.inl (Sum.inl (D, τ₁))))] [] attrs =>
if h :
τ₁ = τ₂ ∧ DimList.known D = true ∧ DimList.known D' = true ∧ DimList.prod D' = DimList.prod D then
Fitree.Vis (Sum.inr (Sum.inl (SSAEnvE.Get (MLIRType.extended (builtin.σ.tensor D τ₁)) t_name)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inr
(ToyOp.Reshape τ₁ D D' (_ : DimList.known D = true) (_ : DimList.known D' = true)
(_ : DimList.prod D' = DimList.prod D) r)))
fun r =>
Fitree.Vis
(Sum.inr
(Sum.inl
(SSAEnvE.Set (MLIRType.extended (builtin.σ.tensor D' τ₂)) res
(cast (_ : RankedTensor D' τ₁ = RankedTensor D' τ₂) r))))
Fitree.Ret
else
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")
| x =>
raiseUB
(toString "" ++
toString
(Op.mk "toy.transpose"
[(SSAVal.SSAVal "t3",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4]
(MLIRType.int Signedness.Signless 32)))]
[(SSAVal.SSAVal "t2",
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2]
(MLIRType.int Signedness.Signless 32)))]
[] (AttrDict.mk [])) ++
toString "")))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/ToySemantics.lean | double_transpose_correct | [136, 1] | [153, 28] | simp [interpSSA', Fitree.interpState, SSAEnvE.handle] | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t1")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) with
| some v =>
Fitree.Ret
(v,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
| none =>
Fitree.Ret
(default,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x.fst) fun x_1 =>
Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd) with
| some v =>
Fitree.Ret
(v,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd)
| none =>
Fitree.Ret
(default,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x.fst) fun x_2 =>
interpSSA' (Fitree.Ret ())
(SSAEnv.set (SSAVal.SSAVal "t3")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
x_2 x.snd)) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t1")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) with
| some v =>
Fitree.Ret
(v,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
| none =>
Fitree.Ret
(default,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x.fst) fun x_1 =>
Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd) with
| some v =>
Fitree.Ret
(v,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd)
| none =>
Fitree.Ret
(default,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x.fst) fun x_2 =>
Fitree.interp
(Fitree.case
(fun x e env =>
match x, e with
| .(MLIRType.eval τ), SSAEnvE.Get τ name =>
match SSAEnv.get name τ env with
| some v => Fitree.ret (v, env)
| none => Fitree.ret (default, env)
| .(Unit), SSAEnvE.Set τ name v => Fitree.ret ((), SSAEnv.set name τ v env))
Fitree.liftHandler)
(Fitree.Ret ())
(SSAEnv.set (SSAVal.SSAVal "t3")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
x_2 x.snd)) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) | Please generate a tactic in lean4 to solve the state.
STATE:
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t1")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) with
| some v =>
Fitree.Ret
(v,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
| none =>
Fitree.Ret
(default,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x.fst) fun x_1 =>
Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd) with
| some v =>
Fitree.Ret
(v,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd)
| none =>
Fitree.Ret
(default,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x.fst) fun x_2 =>
interpSSA' (Fitree.Ret ())
(SSAEnv.set (SSAVal.SSAVal "t3")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
x_2 x.snd)) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/ToySemantics.lean | double_transpose_correct | [136, 1] | [153, 28] | simp_itree | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t1")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) with
| some v =>
Fitree.Ret
(v,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
| none =>
Fitree.Ret
(default,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x.fst) fun x_1 =>
Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd) with
| some v =>
Fitree.Ret
(v,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd)
| none =>
Fitree.Ret
(default,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x.fst) fun x_2 =>
Fitree.interp
(Fitree.case
(fun x e env =>
match x, e with
| .(MLIRType.eval τ), SSAEnvE.Get τ name =>
match SSAEnv.get name τ env with
| some v => Fitree.ret (v, env)
| none => Fitree.ret (default, env)
| .(Unit), SSAEnvE.Set τ name v => Fitree.ret ((), SSAEnv.set name τ v env))
Fitree.liftHandler)
(Fitree.Ret ())
(SSAEnv.set (SSAVal.SSAVal "t3")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
x_2 x.snd)) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t1")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) with
| some v =>
Fitree.Ret
(v,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
| none =>
Fitree.Ret
(default,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x.fst) fun x_1 =>
Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd) with
| some v =>
Fitree.Ret
(v,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd)
| none =>
Fitree.Ret
(default,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x.fst) fun x_2 =>
Fitree.Ret
((),
SSAEnv.set (SSAVal.SSAVal "t3")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
x_2 x.snd)) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) | Please generate a tactic in lean4 to solve the state.
STATE:
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t1")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) with
| some v =>
Fitree.Ret
(v,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
| none =>
Fitree.Ret
(default,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x.fst) fun x_1 =>
Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd) with
| some v =>
Fitree.Ret
(v,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd)
| none =>
Fitree.Ret
(default,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x.fst) fun x_2 =>
Fitree.interp
(Fitree.case
(fun x e env =>
match x, e with
| .(MLIRType.eval τ), SSAEnvE.Get τ name =>
match SSAEnv.get name τ env with
| some v => Fitree.ret (v, env)
| none => Fitree.ret (default, env)
| .(Unit), SSAEnvE.Set τ name v => Fitree.ret ((), SSAEnv.set name τ v env))
Fitree.liftHandler)
(Fitree.Ret ())
(SSAEnv.set (SSAVal.SSAVal "t3")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
x_2 x.snd)) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/ToySemantics.lean | double_transpose_correct | [136, 1] | [153, 28] | simp [SSAEnv.get, SSAEnv.getT, SSAEnv.set] | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t1")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) with
| some v =>
Fitree.Ret
(v,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
| none =>
Fitree.Ret
(default,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x.fst) fun x_1 =>
Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd) with
| some v =>
Fitree.Ret
(v,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd)
| none =>
Fitree.Ret
(default,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x.fst) fun x_2 =>
Fitree.Ret
((),
SSAEnv.set (SSAVal.SSAVal "t3")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
x_2 x.snd)) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ (Fitree.bind
(ToyOp.handle (RankedTensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32))
(ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 t1))
fun x =>
Fitree.bind
(ToyOp.handle (RankedTensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32))
(ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x))
fun x_1 =>
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)),
snd := x }),
(SSAVal.SSAVal "t3",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)),
snd := x_1 })])) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) | Please generate a tactic in lean4 to solve the state.
STATE:
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ Fitree.interp ToyOp.handle
(Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t1")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) with
| some v =>
Fitree.Ret
(v,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
| none =>
Fitree.Ret
(default,
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 x.fst) fun x_1 =>
Fitree.bind
(match
SSAEnv.get (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
(SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd) with
| some v =>
Fitree.Ret
(v,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd)
| none =>
Fitree.Ret
(default,
SSAEnv.set (SSAVal.SSAVal "t2")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)))
x_1 x.snd))
fun x =>
Fitree.Vis (ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x.fst) fun x_2 =>
Fitree.Ret
((),
SSAEnv.set (SSAVal.SSAVal "t3")
(MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)))
x_2 x.snd)) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/ToySemantics.lean | double_transpose_correct | [136, 1] | [153, 28] | simp_itree | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ (Fitree.bind
(ToyOp.handle (RankedTensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32))
(ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 t1))
fun x =>
Fitree.bind
(ToyOp.handle (RankedTensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32))
(ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x))
fun x_1 =>
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)),
snd := x }),
(SSAVal.SSAVal "t3",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)),
snd := x_1 })])) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })]) | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ [(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32), snd := t1 }),
(SSAVal.SSAVal "t2",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)),
snd := transpose (transpose t1) })] =
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32), snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32), snd := t1 })] | Please generate a tactic in lean4 to solve the state.
STATE:
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ (Fitree.bind
(ToyOp.handle (RankedTensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32))
(ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 2 4 t1))
fun x =>
Fitree.bind
(ToyOp.handle (RankedTensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32))
(ToyOp.Transpose (MLIRType.int Signedness.Signless 32) 4 2 x))
fun x_1 =>
Fitree.ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)),
snd := x }),
(SSAVal.SSAVal "t3",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)),
snd := x_1 })])) =
Fitree.Ret
((),
SSAEnv.One
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32),
snd := t1 })])
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Dialects/ToySemantics.lean | double_transpose_correct | [136, 1] | [153, 28] | rw [transpose_involutive] | t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ [(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32), snd := t1 }),
(SSAVal.SSAVal "t2",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)),
snd := transpose (transpose t1) })] =
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32), snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32), snd := t1 })] | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
t1 : RankedTensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32
⊢ [(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32), snd := t1 }),
(SSAVal.SSAVal "t2",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] (MLIRType.int Signedness.Signless 32)),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{
fst :=
MLIRType.extended
(builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] (MLIRType.int Signedness.Signless 32)),
snd := transpose (transpose t1) })] =
[(SSAVal.SSAVal "t1",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32), snd := t1 }),
(SSAVal.SSAVal "t2",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 4, Dimension.Known 2] MLIRType.i32),
snd := transpose t1 }),
(SSAVal.SSAVal "t3",
{ fst := MLIRType.extended (builtin.σ.tensor [Dimension.Known 2, Dimension.Known 4] MLIRType.i32), snd := t1 })]
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/UB.lean | interpUB_bind | [64, 1] | [81, 28] | induction t with
| Ret _ => rfl
| Vis _ _ ih =>
simp [interpUB, Fitree.interpExcept] at *
simp [Fitree.interp, Fitree.bind, Bind.bind]
simp [ExceptT.bind, ExceptT.mk, ExceptT.bindCont]
have fequal2 α β (f g: α → β) x y: f = g → x = y → f x = g y :=
fun h₁ h₂ => by simp [h₁, h₂]
apply fequal2; rfl; funext x
cases x <;> simp [ih] | T R : Type
t : Fitree UBE T
k : T → Fitree UBE R
⊢ interpUB (Fitree.bind t k) =
Fitree.bind (interpUB t) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => interpUB (k x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
T R : Type
t : Fitree UBE T
k : T → Fitree UBE R
⊢ interpUB (Fitree.bind t k) =
Fitree.bind (interpUB t) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => interpUB (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/UB.lean | interpUB_bind | [64, 1] | [81, 28] | rfl | case Ret
T R : Type
k : T → Fitree UBE R
r✝ : T
⊢ interpUB (Fitree.bind (Fitree.Ret r✝) k) =
Fitree.bind (interpUB (Fitree.Ret r✝)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => interpUB (k x) | no goals | Please generate a tactic in lean4 to solve the state.
STATE:
case Ret
T R : Type
k : T → Fitree UBE R
r✝ : T
⊢ interpUB (Fitree.bind (Fitree.Ret r✝) k) =
Fitree.bind (interpUB (Fitree.Ret r✝)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => interpUB (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/UB.lean | interpUB_bind | [64, 1] | [81, 28] | simp [interpUB, Fitree.interpExcept] at * | case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
interpUB (Fitree.bind (k✝ a) k) =
Fitree.bind (interpUB (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => interpUB (k x)
⊢ interpUB (Fitree.bind (Fitree.Vis e✝ k✝) k) =
Fitree.bind (interpUB (Fitree.Vis e✝ k✝)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => interpUB (k x) | case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
⊢ Fitree.interp UBE.handle (Fitree.bind (Fitree.Vis e✝ k✝) k) =
Fitree.bind (Fitree.interp UBE.handle (Fitree.Vis e✝ k✝)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
interpUB (Fitree.bind (k✝ a) k) =
Fitree.bind (interpUB (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => interpUB (k x)
⊢ interpUB (Fitree.bind (Fitree.Vis e✝ k✝) k) =
Fitree.bind (interpUB (Fitree.Vis e✝ k✝)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => interpUB (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/UB.lean | interpUB_bind | [64, 1] | [81, 28] | simp [Fitree.interp, Fitree.bind, Bind.bind] | case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
⊢ Fitree.interp UBE.handle (Fitree.bind (Fitree.Vis e✝ k✝) k) =
Fitree.bind (Fitree.interp UBE.handle (Fitree.Vis e✝ k✝)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x) | case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
⊢ Fitree.bind (UBE.handle T✝ e✝) (ExceptT.bindCont fun t => Fitree.interp UBE.handle (Fitree.bind (k✝ t) k)) =
Fitree.bind (UBE.handle T✝ e✝) fun x =>
Fitree.bind (ExceptT.bindCont (fun t => Fitree.interp UBE.handle (k✝ t)) x) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
⊢ Fitree.interp UBE.handle (Fitree.bind (Fitree.Vis e✝ k✝) k) =
Fitree.bind (Fitree.interp UBE.handle (Fitree.Vis e✝ k✝)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/UB.lean | interpUB_bind | [64, 1] | [81, 28] | simp [ExceptT.bind, ExceptT.mk, ExceptT.bindCont] | case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
⊢ Fitree.bind (UBE.handle T✝ e✝) (ExceptT.bindCont fun t => Fitree.interp UBE.handle (Fitree.bind (k✝ t) k)) =
Fitree.bind (UBE.handle T✝ e✝) fun x =>
Fitree.bind (ExceptT.bindCont (fun t => Fitree.interp UBE.handle (k✝ t)) x) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x) | case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
⊢ (Fitree.bind (UBE.handle T✝ e✝) fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
Fitree.bind (UBE.handle T✝ e✝) fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
⊢ Fitree.bind (UBE.handle T✝ e✝) (ExceptT.bindCont fun t => Fitree.interp UBE.handle (Fitree.bind (k✝ t) k)) =
Fitree.bind (UBE.handle T✝ e✝) fun x =>
Fitree.bind (ExceptT.bindCont (fun t => Fitree.interp UBE.handle (k✝ t)) x) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/UB.lean | interpUB_bind | [64, 1] | [81, 28] | have fequal2 α β (f g: α → β) x y: f = g → x = y → f x = g y :=
fun h₁ h₂ => by simp [h₁, h₂] | case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
⊢ (Fitree.bind (UBE.handle T✝ e✝) fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
Fitree.bind (UBE.handle T✝ e✝) fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x) | case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α : Sort ?u.7562) (β : Sort ?u.7563) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (Fitree.bind (UBE.handle T✝ e✝) fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
Fitree.bind (UBE.handle T✝ e✝) fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
⊢ (Fitree.bind (UBE.handle T✝ e✝) fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
Fitree.bind (UBE.handle T✝ e✝) fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/UB.lean | interpUB_bind | [64, 1] | [81, 28] | apply fequal2 | case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α : Sort ?u.7562) (β : Sort ?u.7563) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (Fitree.bind (UBE.handle T✝ e✝) fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
Fitree.bind (UBE.handle T✝ e✝) fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x) | case Vis.a
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ Fitree.bind (UBE.handle T✝ e✝) = Fitree.bind (UBE.handle T✝ e✝)
case Vis.a
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α : Sort ?u.7562) (β : Sort ?u.7563) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (Fitree.bind (UBE.handle T✝ e✝) fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
Fitree.bind (UBE.handle T✝ e✝) fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/UB.lean | interpUB_bind | [64, 1] | [81, 28] | rfl | case Vis.a
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ Fitree.bind (UBE.handle T✝ e✝) = Fitree.bind (UBE.handle T✝ e✝)
case Vis.a
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x) | case Vis.a
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis.a
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ Fitree.bind (UBE.handle T✝ e✝) = Fitree.bind (UBE.handle T✝ e✝)
case Vis.a
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x)
TACTIC:
|
https://github.com/opencompl/lean-mlir.git | e43d21592801e5e40477b14b7a554e356060c40c | MLIR/Semantics/UB.lean | interpUB_bind | [64, 1] | [81, 28] | funext x | case Vis.a
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x) | case Vis.a.h
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
x : Except String T✝
⊢ (match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x) | Please generate a tactic in lean4 to solve the state.
STATE:
case Vis.a
T R : Type
k : T → Fitree UBE R
T✝ : Type
e✝ : UBE T✝
k✝ : T✝ → Fitree UBE T
ih :
∀ (a : T✝),
Fitree.interp UBE.handle (Fitree.bind (k✝ a) k) =
Fitree.bind (Fitree.interp UBE.handle (k✝ a)) fun x =>
match x with
| Except.error ε => Fitree.ret (Except.error ε)
| Except.ok x => Fitree.interp UBE.handle (k x)
fequal2 : ∀ (α β : Type 1) (f g : α → β) (x y : α), f = g → x = y → f x = g y
⊢ (fun x =>
match x with
| Except.ok a => Fitree.interp UBE.handle (Fitree.bind (k✝ a) k)
| Except.error e => Fitree.ret (Except.error e)) =
fun x =>
Fitree.bind
(match x with
| Except.ok a => Fitree.interp UBE.handle (k✝ a)
| Except.error e => Fitree.ret (Except.error e))
fun x =>
match x with
| Except.error e => Fitree.ret (Except.error e)
| Except.ok x => Fitree.interp UBE.handle (k x)
TACTIC:
|
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