Semantics and implementation of an extension of ML for proving programs

Abstract : In recent years, proof assistant have reached an impressive level of maturity. They have led to the certification of complex programs such as compilers and operating systems. Yet, using a proof assistant requires highly specialised skills and it remains very different from standard programming. To bridge this gap, we aim at designing an ML-style programming language with support for proofs of programs, combining in a single tool the flexibility of ML and the fine specification features of a proof assistant. In other words, the system should be suitable both for programming (in the strongly-typed, functional sense) and for gradually increasing the level of guarantees met by programs, on a by-need basis.We thus define and study a call-by-value language whose type system extends higher-order logic with an equality type over untyped programs, a dependent function type, classical logic and subtyping. The combination of call-by-value evaluation, dependent functions and classical logic is known to raise consistency issues. To ensure the correctness of the system (logical consistency and runtime safety), we design a theoretical framework based on Krivine's classical realisability. The construction of the model relies on an essential property linking the different levels of interpretation of types in a novel way.We finally demonstrate the expressive power of our system using our prototype implementation, by proving properties of standard programs like the map function on lists or the insertion sort.
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Rodolphe Lepigre. Semantics and implementation of an extension of ML for proving programs. Programming Languages [cs.PL]. Université Grenoble Alpes, 2017. English. ⟨NNT : 2017GREAM034⟩. ⟨tel-01682908⟩

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