Isomorphisms of types: from &lgr;-calculus to information retrieval and language design
Isomorphisms of types: from &lgr;-calculus to information retrieval and language design
A Metalanguage for interactive proof in LCF
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
A survey of software reuse libraries
Annals of Software Engineering
Type Isomorphisms for Module Signatures
PLILP '96 Proceedings of the 8th International Symposium on Programming Languages: Implementations, Logics, and Programs
MKM '03 Proceedings of the Second International Conference on Mathematical Knowledge Management
A foundational view on integration problems
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
A content based mathematical search engine: whelp
TYPES'04 Proceedings of the 2004 international conference on Types for Proofs and Programs
Complete completion using types and weights
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
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We propose a method to search for a lemma in a Coq proof library by using the lemma type as a key. The method is based on the concept of type isomorphism developed within the functional programming framework. We introduce a theory which is a generalization of the axiomatization for the simply typed λ-calculus (associated with Closed Cartesian Categories) to an Extended Calculus of Constructions with a more Extensional conversion rule. We show a soundness theorem for this theory but we notice that it is not contextual and requires "ad hoc" contextual rules. Thus, we see how we must adapt this theory for Coq and we define an approximation of the contextual part of this theory, which is implemented in a decision procedure.