A Semi-reflexive Tactic for (Sub-)Equational Reasoning

  • Claudio Sacerdoti Coen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3839)


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 x R y 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.


Monotone Function Natural Deduction Sequent Calculus Applicative Context Proof Search 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Claudio Sacerdoti Coen
    • 1
  1. 1.Project PCRI, CNRS, École Polytechnique, INRIAUniversité Paris-Sud 

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