Extensional Constructs in Intensional Type Theory
Extensional Constructs in Intensional Type Theory
TAS - A Generic Window Inference System
TPHOLs '00 Proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Journal of Functional Programming
A computer-verified monadic functional implementation of the integral
Theoretical Computer Science
Proving formally the implementation of an efficient gcd algorithm for polynomials
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
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We propose a simple theory of monotone functions that is the basis for the implementation of a tactic that generalises one step conditional rewriting by “propagating” constraints of the form xRy where the relation R can be weaker than an equivalence relation. The constraints can be propagated only in goals whose conclusion is a syntactic composition of n-ary functions that are monotone in each argument. The tactic has been implemented in the Coq system as a semi-reflexive tactic, which represents a novelty and an improvement over an earlier similar development for NuPRL. A few interesting applications of the tactic are: reasoning in type theory about equivalence classes (by performing rewriting in well-defined goals); reasoning about reductions and properties preserved by reductions; reasoning about partial functions over equivalence classes (by performing rewriting in PERs); propagating inequalities by replacing a term with a smaller (greater) one in a given monotone context.