ProPre A programming language with proofs

Manoury, Pascal; Parigot, Michel; Simonot, Marianna

doi:10.1007/bfb0013095

Cited by 5 publications

(2 citation statements)

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“…Inductive or coinductive types, such as lists or streams, can then be seen as sized types annotated by a large enough (limit) ordinal. 21 In practice, the implementation of PML 2 introduces sizes automatically when typing recursive functions. This means that it replaces (some) inductive and coinductive types, which carry a limit ordinal, with universal quantification over all possible ordinals.…”

Section: Sized Typesmentioning

confidence: 99%

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PML 2 : Integrated Program Verification in ML

Lepigre

2019

Preprint

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We present the PML 2 language, which provides a uniform environment for programming, and for proving properties of programs in an ML-like setting. The language is Curry-style and call-by-value, it provides a control operator (interpreted in terms of classical logic), it supports general recursion and a very general form of (implicit, non-coercive) subtyping. In the system, equational properties of programs are expressed using two new type formers, and they are proved by constructing terminating programs. Although proofs rely heavily on equational reasoning, equalities are exclusively managed by the type-checker. This means that the user only has to choose which equality to use, and not where to use it, as is usually done in mathematical proofs. In the system, writing proofs mostly amounts to applying lemmas (possibly recursive function calls), and to perform case analyses (pattern matchings).

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Section: Sized Typesmentioning

confidence: 99%

“…Several systems have been proposed for verifying ML programs. ProPre [21] relies on a notion of algorithms, corresponding to equational specifications of programs. It is used in conjunction with a type system based on intuitionistic logic.…”

Section: Systems Aimed At Program Verification In MLmentioning

confidence: 99%