Abstract: "This thesis concerns rewriting in the typed [lambda]- calculus. Traditional categorical models of typed [lambda]-calculus use concepts such as functor, adjunction and algebra to model type constructors and their associated introduction and elimination rules, with the natural categori...

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1. Verfasser:	Ghani, Neil (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Edinburgh Univ. of Edinburgh, Dep. of Computer Science 1995
Schlagworte:	Adjunction theory Categories (Mathematics) Lambda calculus Rewriting systems (Computer science) Hochschulschrift
Zusammenfassung:	Abstract: "This thesis concerns rewriting in the typed [lambda]- calculus. Traditional categorical models of typed [lambda]-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 [lambda]-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 sub-theory of that required Our proposal is to unify the semantics and reduction theory of the typed [lambda]-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 the addition of a pre-order to each of the hom-sets of the category which is used to reflect the reduction of one term to another. Rewrite relations, whose associated equational theory matches that suggested by the traditional semantics, may then be derived from the natural categorical constructions on these ordered categories. Rewrite relations derived in this fashion typically consist of a contractive [beta]-rewrite rule and an expansionary [eta]-rewrite rule for each type constructor. Although confluent, the presence of expansionary [eta]- rewrite rules means the rewrite relation is not strongly normalising and so cannot in itself be used as the basis of a decision procedure Instead, decidability of the equational theory is proved by a variety of term rewriting techniques which will necessarily vary from calculus to calculus. These techniques are developed in three case studies: the simply typed [lambda]-calculus with unit, product and exponential types; the linear [lambda]-calculus containing the tensor from linear logic; and the bicartesian closed calculus obtained by adding coproducts to the simply typed [lambda]-calculus.
Beschreibung:	Zugl.: Edinburgh, Univ., Diss., 1995
Beschreibung:	158 S.