when quoting this document, please refer to the following
URN: urn:nbn:de:0030-drops-2740

Prevosto, Virgile

Certified mathematical hierarchies: the FoCal system

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The focal language (formerly Foc) allows a programmer to incrementally build mathematical structures and to formally prove 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. Inheritance from existing structures allows to reuse their components under some conditions, which are statically checked by the compiler. In this talk, we first present the main constructions of the language. Then we show a shallow embedding of these constructions in the Coq proof assistant, which is used to check the proofs made in Focal. Such a proof can be either an hand-written Coq script, made in an environment set up by the Focal compiler, or a Coq term given the zenon theorem prover, which is partly developped within Focal. Last, we present a formalization of focal structures and show that the Coq embedding is conform to this model.

BibTeX - Entry

  author =	{Virgile Prevosto},
  title =	{Certified mathematical hierarchies: the FoCal system},
  booktitle =	{Mathematics, Algorithms, Proofs},
  year =	{2006},
  editor =	{Thierry Coquand and Henri Lombardi and Marie-Fran{\c{c}}oise Roy},
  number =	{05021},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{},
  annote =	{Keywords: Specifications, proofs, inheritance, refinement, types, Focal, Coq, computer algebra, mathematics}

Keywords: Specifications, proofs, inheritance, refinement, types, Focal, Coq, computer algebra, mathematics
Seminar: 05021 - Mathematics, Algorithms, Proofs
Issue date: 2006
Date of publication: 16.01.2006

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