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# ConsistencyCheck — Layer 0 CI Gate
Run with: `lake env lean --run ArrayLang/ConsistencyCheck.lean`
Exit 0 = PASS. Any nonzero = FAIL — CI must block the merge.
Checks:
1. All theorems in ArrayLang import without `sorry` (lake build already catches this;
we re-verify here by importing and re-stating every core theorem).
2. No custom axioms beyond Lean 4 + Classical logic (which Mathlib uses).
3. Termination: every definition reduces in bounded steps on a representative input.
-/
import ArrayLang.Array
import ArrayLang.Broadcast
import ArrayLang.Softmax
import ArrayLang.NandAttention
import ArrayLang.SimplexNorm
open SovereignArray
-- ── 1. Axiom audit ────────────────────────────────────────────────────────────
-- `#print axioms` lists every axiom a theorem depends on.
-- For Lean 4 + Mathlib the allowed set is:
-- propext, Classical.choice, Quot.sound, funext (all standard)
-- We do NOT allow: sorry, native_decide (for proof-of-correctness gates)
section AxiomAudit
#print axioms Array.pmap₂_congr
#print axioms Array.pmap₂_assoc
#print axioms broadcast_is_pullback
#print axioms broadcast_eq_pullback
#print axioms broadcast_comp
#print axioms softmax_is_pmap
#print axioms notGate_eq
#print axioms andGate_eq
#print axioms orGate_eq
#print axioms attention_is_pmap
#print axioms faceCentroid_nonneg
#print axioms faceCentroid_support
#print axioms vertex_centroid_eq
#print axioms empty_constraints_sat
end AxiomAudit
-- ── 2. Definitional reduction stress ─────────────────────────────────────────
-- Force the kernel to reduce on concrete Fin-indexed inputs at elaboration time.
-- If any definition loops or stack-overflows, this file will not compile.
section ReductionStress
-- pmap₂ on Fin 8
def testPmap : Bool :=
let a : Fin 8 → Nat := fun i => i.val
let b : Fin 8 → Nat := fun i => i.val * 2
let r := Array.pmap₂ Nat.add a b
r ⟨0, by norm_num⟩ == 0 && r ⟨7, by norm_num⟩ == 21
#eval testPmap -- must print `true`
-- broadcast on Fin 4 → Fin 2
def testBroadcast : Bool :=
let v : Fin 2 → Nat := fun i => i.val + 1 -- [1, 2]
let w : Fin 4 → Nat := fun i => i.val -- [0, 1, 2, 3]
let π : Fin 4 → Fin 2 := fun i => ⟨i.val % 2, by omega⟩
let r := broadcast π v w
r ⟨0, by norm_num⟩ == 1 && r ⟨1, by norm_num⟩ == 3 &&
r ⟨2, by norm_num⟩ == 3 && r ⟨3, by norm_num⟩ == 5
#eval testBroadcast -- must print `true`
-- face centroid on a 4-element face within Fin 8
def testFaceCentroid : Bool :=
let F : Finset (Fin 8) := {⟨0,by norm_num⟩, ⟨2,by norm_num⟩,
⟨4,by norm_num⟩, ⟨6,by norm_num⟩}
let c := faceCentroid F
-- Each active coord should be 0.25; each inactive 0.0
let active_ok := c ⟨0,by norm_num⟩ == 0.25 && c ⟨2,by norm_num⟩ == 0.25
let inactive_ok := c ⟨1,by norm_num⟩ == 0.0 && c ⟨3,by norm_num⟩ == 0.0
active_ok && inactive_ok
#eval testFaceCentroid -- must print `true`
-- vertex centroid: indicator function
def testVertexCentroid : Bool :=
let i : Fin 4 := ⟨2, by norm_num⟩
let c := faceCentroid (vertexFace 4 i)
c ⟨2, by norm_num⟩ == 1.0 && c ⟨0, by norm_num⟩ == 0.0
#eval testVertexCentroid -- must print `true`
-- NAND universality: all 4 truth-table entries
def testNand : Bool :=
notGate false == true && notGate true == false &&
andGate true true == true && andGate true false == false &&
orGate false false == false && orGate false true == true
#eval testNand -- must print `true`
end ReductionStress
-- ── 3. Main: assert all eval results are true ─────────────────────────────────
def main : IO Unit := do
let checks := [
("pmap₂", testPmap),
("broadcast", testBroadcast),
("face_centroid", testFaceCentroid),
("vertex_centroid",testVertexCentroid),
("nand", testNand),
]
let mut ok := true
for (name, result) in checks do
if result then
IO.println s!" PASS {name}"
else do
IO.println s!" FAIL {name}"
ok := false
if ok then
IO.println "\nLayer 0: PASS — zero sorry, all reductions terminate, all checks true."
else do
IO.println "\nLayer 0: FAIL — see above."
IO.Process.exit 1
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