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Adjoint Rewriting
, 1995
"... This thesis concerns rewriting in the typed calculus. Traditional categorical models of typed calculus use concepts such as functor, adjunction and algebra to model type constructors and their associated introduction and elimination rules, with the natural categorical equations inherent in these s ..."
Abstract

Cited by 24 (11 self)
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This thesis concerns rewriting in the typed calculus. Traditional categorical models of typed calculus use concepts such as functor, adjunction and algebra to model type constructors and their associated introduction and elimination rules, with the natural categorical equations inherent in these structures providing an equational theory for terms. One then seeks a rewrite relation which, by transforming terms into canonical forms, provides a decision procedure for this equational theory. Unfortunately the rewrite relations which have been proposed, apart from for the most simple of calculi, either generate the full equational theory but contain no decision procedure, or contain a decision procedure but only for a subtheory of that required. Our proposal is to unify the semantics and reduction theory of the typed calculus by generalising the notion of model from categorical structures based on term equality to categorical structures based on term reduction. This is accomplished via...