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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 ..."
Abstract

Cited by 43 (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.
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...