Conditional Lambda-Theories and the Verification of Static Properties of Programs

Abstract

We present a proof that a simple compiler correctly uses the static properties in its symbol table. We do this by regarding the target code produced by the compiler as a syntactic variant of a λ-term. In general, this λ-term C may not be equal to the semantics S of the source program: they need be equal only when information in the symbol table is valid. We formulate this relation as a conditional λ-judgment Γ ⊃ S = C , where Γ is a formula that represents the invariants implicit in symbol table Γ . We present rules of inference for conditional λ-judgements and prove their soundness. We then use these rules to prove the correctness of a simple compiler that relies on a symbol table. The form of the proof suggests that such proofs may be largely mechanizable.