Phase A — GolangLean/Core/Eval.lean:
def eval : Nat -> Heap -> Env -> Term -> Option (Value x Heap)
Fuel-bounded recursive evaluator, total over the fuel.
theorem eval_sound: eval succeeds => BigStep holds.
Bridges executable computation to inductive specification.
Phase B — GolangLean/Core/Types.lean:
inductive Ty {unit, int, bool, arrow, ref}
TyEnv := List (String x Ty); BinOp.typeOf
inductive HasType : TyEnv -> Term -> Ty -> Prop
Standard simply-typed lambda calculus + ML-style references.
Phase B — GolangLean/Core/TypeSoundness.lean:
abbrev HeapTy := Array Ty
mutual inductive HasTypeV / HasTypeEnv (value & env typing under heap-typing)
def HasTypeH (heap conforms to heap-typing)
def HeapTy.extends (prefix-extension of heap-typings)
thm HeapTy.extends_refl, extends_trans
thm HasTypeV.weaken, HasTypeEnv.weaken (mutual; under heap-typing extension)
thm HasTypeEnv.lookup_correspondence (well-typed env yields well-typed values)
The preservation theorem itself
HasType /\ HasTypeH /\ HasTypeEnv /\ BigStep
==> ∃ ht', extends /\ HasTypeH' /\ HasTypeV' /\ HasTypeEnv'
is the next deliverable; the infrastructure here is what its proof
case-analysis depends on.
Zero sorries / axioms / admits across the project. Full lake build clean.
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