Skip to Main content Skip to Navigation
Journal articles

Subset Coercions in Coq

Abstract : We propose a new language for writing programs with dependent types on top of the Coq proof assistant. This language permits to establish a phase distinction between writing and proving algorithms in the Coq environment. Concretely, this means allowing to write algorithms as easily as in a practical functional programming language whilst giving them as rich a specification as desired and proving that the code meets the specification using the whole Coq proof apparatus. This is achieved by extending conversion to an equivalence which relates types and subsets based on them, a technique originating from the "Predicate subtyping" feature of PVS and following mathematical convention. The typing judgements can be translated to the (CIC) by means of an interpretation which inserts coercions at the appropriate places. These coercions can contain existential variables representing the propositional parts of the final term, corresponding to proof obligations (or PVS type-checking conditions). A prototype implementation of this process is integrated with the Coq environment.
Document type :
Journal articles
Complete list of metadata

https://hal.inria.fr/inria-00628869
Contributor : Matthieu Sozeau Connect in order to contact the contributor
Submitted on : Tuesday, October 4, 2011 - 2:01:44 PM
Last modification on : Sunday, June 26, 2022 - 11:54:34 AM

Links full text

Identifiers

Collections

Citation

Matthieu Sozeau. Subset Coercions in Coq. Lecture Notes in Computer Science, Springer, 2007, pp.237-252. ⟨10.1007/978-3-540-74464-1_16⟩. ⟨inria-00628869⟩

Share

Metrics

Record views

61