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Proof Contexts with Late Binding


Prevosto,  Virgile
Programming Logics, MPI for Informatics, Max Planck Society;

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Prevosto, V., & Boulmé, S. (2005). Proof Contexts with Late Binding. In Typed Lambda Calculi and Applications: 7th International Conference, TLCA 2005 (pp. 325-339). Berlin, Germany: Springer.

The focal language (formerly Foc) allows one to incrementally build modules and to prove formally their correctness. focal encourages a development process by refinement, deriving step-by-step implementations from specifications. This refinement process is realized using an inheritance mechanism on structures which can mix primitive operations, axioms, algorithms and proofs. Inheriting from existing structures allows to reuse their components under some conditions, statically checked by the compiler. This paper presents two formal semantics for encoding focal constructions in the Coq proof assistant. The first one is a shallow embedding which gives a practical way to use Coq to check proofs in focal libraries. The second one formalizes the focal structures as Coq types (called mixDrecs) and shows that the informal semantics of focal libraries is coherent with respect to Coq logic. In the last part of the paper, we prove that the first embedding is conform to the mixDrecs model.