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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 ..."
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Cited by 25 (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...
From HindleyMilner types to firstclass structures
 In Proceedings of the Haskell Workshop
, 1995
"... We describe extensions of the HindleyMilner type system to support higherorder polymorphism and firstclass structures with polymorphic components. The combination of these features results in a ‘core language ’ that rivals the expressiveness of the Standard ML module system in some respects and e ..."
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Cited by 14 (0 self)
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We describe extensions of the HindleyMilner type system to support higherorder polymorphism and firstclass structures with polymorphic components. The combination of these features results in a ‘core language ’ that rivals the expressiveness of the Standard ML module system in some respects and exceeds it in others. 1
Eta Expansions in System F
 LIENSDMI, Ecole Normale Superieure
, 1996
"... The use of expansionary jrewrite rules in various typed calculi has become increasingly common in recent years as their advantages over contractive jrewrite rules have become apparent. Not only does one obtain the decidability of fijequality, but rewrite relations based on expansions give a natu ..."
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Cited by 6 (0 self)
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The use of expansionary jrewrite rules in various typed calculi has become increasingly common in recent years as their advantages over contractive jrewrite rules have become apparent. Not only does one obtain the decidability of fijequality, but rewrite relations based on expansions give a natural interpretation of long fijnormal forms, generalise more easily to other type constructors, retain key properties when combined with other rewrite relations, and are supported by a categorical theory of reduction. This paper extends the initial results concerning the simply typed calculus to System F, that is, we prove strong normalisation and confluence for a rewrite relation consisting of traditional fireductions and jexpansions satisfying certain restrictions. Further, we characterise the second order long fijnormal forms as precisely the normal forms of the restricted rewrite relation. These results are an important step towards showing that jexpansions are compatible with the m...