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Developing certified programs in the system Coq  The Program tactic
, 1993
"... The system Coq is an environment for proof development based on the Calculus of Constructions extended by inductive definitions. Functional programs can be extracted from constructive proofs written in Coq. The extracted program and its corresponding proof are strongly related. The idea in this p ..."
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Cited by 12 (4 self)
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The system Coq is an environment for proof development based on the Calculus of Constructions extended by inductive definitions. Functional programs can be extracted from constructive proofs written in Coq. The extracted program and its corresponding proof are strongly related. The idea in this paper is to use this link to have another approach: to give a program and to generate automatically the proof from which it could be extracted. Moreover, we introduce a notion of annotated programs.
ContextRelative Syntactic Categories and the Formalization Of Mathematical Text
 TYPES FOR PROOFS AND PROGRAMS
, 1996
"... ..."
A Formalization of Finite and Infinite Sequences in PVS
 Techn. Rep. CSIR9702, Comput. Sci. Inst., Univ. of Nijmegen
, 1997
"... Sequences are often used structures in mathematics and computer science. While working on a formalization of IOautomata theory, we found, as others did before us [4, 15, 14], that a large portion of the lemmas proven concerned sequences. The complexity of the definitions and proofs is increased ..."
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Cited by 2 (1 self)
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Sequences are often used structures in mathematics and computer science. While working on a formalization of IOautomata theory, we found, as others did before us [4, 15, 14], that a large portion of the lemmas proven concerned sequences. The complexity of the definitions and proofs is increased by having sequences of both finite and infinite length in a single type. In this paper a formalization of these kinds of sequences is presented, and it is explained how some problems of other formalizations are circumvented. The formalization is implemented in the Prototype Verification System (PVS) [16]. This paper may be of interest to people in the field of concurrency, mechanical verifications, and to people with an interest in applications of higher order logic. Keywords & Phrases: Mechanical Theorem Proving, the Prototype Verification System (PVS), Sequences, Higherorder Logic. AMS Subject Classification (1991): 03B15 [Mathematical logic and foundations ]: Higherorder logic ...
Synthesizing proofs from programs in the Calculus of Inductive Constructions
, 1994
"... In type theory, a proof can be represented as a typed term [Con86, NPS90]. There exist methods to mark logical parts in proofs and extract their algorithmic contents. The result is a correct program with respect to a specification. This paper focuses on the inverse problem : how to generate a proof ..."
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In type theory, a proof can be represented as a typed term [Con86, NPS90]. There exist methods to mark logical parts in proofs and extract their algorithmic contents. The result is a correct program with respect to a specification. This paper focuses on the inverse problem : how to generate a proof from its specification. The framework is the Calculus of Inductive Constructions [Coq85]. A notion of coherence is introduced between a specification and a program containing types but no logical proofs. This notion is based on the definition of an extraction function called the weak extraction. Such a program can give a method to reconstruct a set of logical properties needed to have a proof of the initial specification. This can be seen either as a method of proving programs or as a method of synthetically describing proofs. Keywords: program proving, extraction, Calculus of Constructions, lambdacalculus R'esum'e En th'eorie des types, une preuve peut etre repr'esent'ee par un terme t...