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The Virtues of Etaexpansion
, 1993
"... Interpreting jconversion as an expansion rule in the simplytyped calculus maintains the confluence of reduction in a richer type structure. This use of expansions is supported by categorical models of reduction, where ficontraction, as the local counit, and jexpansion, as the local unit, are li ..."
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Cited by 36 (4 self)
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Interpreting jconversion as an expansion rule in the simplytyped calculus maintains the confluence of reduction in a richer type structure. This use of expansions is supported by categorical models of reduction, where ficontraction, as the local counit, and jexpansion, as the local unit, are linked by local triangle laws. The latter form reduction loops, but strong normalisation (to the long fijnormal forms) can be recovered by "cutting" the loops.
Monads and Modular Term Rewriting
, 1997
"... . Monads can be used to model term rewriting systems by generalising the wellknown equivalence between universal algebra and monads on the category Set. In [Lu96], the usefulness of this semantics was demonstrated by giving a purely categorical proof of the modularity of confluence for the disjoint ..."
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Cited by 20 (13 self)
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. Monads can be used to model term rewriting systems by generalising the wellknown equivalence between universal algebra and monads on the category Set. In [Lu96], the usefulness of this semantics was demonstrated by giving a purely categorical proof of the modularity of confluence for the disjoint union of term rewriting systems (Toyama's theorem). This paper provides further support for the use of monads in term rewriting by giving a categorical proof of the most general theorem concerning the modularity of strong normalisation. In the process, we also improve upon some technical aspects of the earlier work. 1 Introduction Term rewriting systems (TRSs) are widely used throughout computer science as they provide an abstract model of computation while retaining a relatively simple syntax and semantics. Reasoning about large term rewriting systems can be very difficult and an alternative is to define structuring operations which build large term rewriting systems from smaller ones. Of...
A Semantics for Static Type Inference
 Information and Computation
, 1993
"... Curry's system for Fdeducibility is the basis for static type inference algorithms for programming languages such as ML. If a natural "preservation of types by conversion" rule is added to Curry's system, it becomes undecidable, but complete relative to a variety of model classes. We show compl ..."
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Cited by 9 (0 self)
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Curry's system for Fdeducibility is the basis for static type inference algorithms for programming languages such as ML. If a natural "preservation of types by conversion" rule is added to Curry's system, it becomes undecidable, but complete relative to a variety of model classes. We show completeness for Curry's system itself, relative to an extended notion of model that validates reduction but not conversion.
betaetaEquality for Coproducts
 In Typed calculus and Applications, number 902 in Lecture Notes in Computer Science
, 1995
"... . Recently several researchers have investigated fijequality for the simply typed calculus with exponentials, products and unit types. In these works, jconversion was interpreted as an expansion with syntactic restrictions imposed to prevent the expansion of introduction terms or terms which for ..."
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. Recently several researchers have investigated fijequality for the simply typed calculus with exponentials, products and unit types. In these works, jconversion was interpreted as an expansion with syntactic restrictions imposed to prevent the expansion of introduction terms or terms which form the major premise of elimination rules. The resulting rewrite relation was shown confluent and strongly normalising to the long fijnormal forms. Thus reduction to normal form provides a decision procedure for fijequality. This paper extends these methods to sum types. Although this extension was originally thought to be straight forward, the proposed jrule for the sum is substantially more complex than that for the exponent or product and contains features not present in the previous systems. Not only is there a facility for expanding terms of sum type analogous to that for product and exponential, but also the ability to permute the order in which different subterms of sum type are e...
Monads and Modular Term Rewriting
, 1997
"... . Monads can be used to model term rewriting systems by generalising the wellknown equivalence between universal algebra and monads on the category Set. In [Lu96], this semantics was used to give a purely categorical proof of the modularity of confluence for the disjoint union of term rewriting sys ..."
Abstract
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. Monads can be used to model term rewriting systems by generalising the wellknown equivalence between universal algebra and monads on the category Set. In [Lu96], this semantics was used to give a purely categorical proof of the modularity of confluence for the disjoint union of term rewriting systems. This paper provides further support for monadic semantics of rewriting by giving a categorical proof of the most general theorem concerning the modularity of strong normalisation. In the process, we improve upon the technical aspects of earlier work. 1 Introduction Term rewriting systems (TRSs) are widely used throughout computer science as they provide an abstract model of computation while retaining a relatively simple syntax and semantics. Reasoning about large term rewriting systems can be very difficult and an alternative is to define structuring operations which build large term rewriting systems from smaller ones. Of particular interest is whether key properties are modular, th...