Results 1 
3 of
3
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 ..."
Abstract

Cited by 12 (4 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
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 ...