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Programming with Intersection Types and Bounded Polymorphism
, 1991
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Cited by 68 (4 self)
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representing the official policies, either expressed or implied, of the U.S. Government.
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 37 (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.
Inductive Data Types: Wellordering Types Revisited
 Logical Environments
, 1992
"... We consider MartinLof's wellordering type constructor in the context of an impredicative type theory. We show that the wellordering types can represent various inductive types faithfully in the presence of the fillingup equality rules or jrules. We also discuss various properties of the ..."
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Cited by 8 (1 self)
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We consider MartinLof's wellordering type constructor in the context of an impredicative type theory. We show that the wellordering types can represent various inductive types faithfully in the presence of the fillingup equality rules or jrules. We also discuss various properties of the fillingup rules. 1 Introduction Type theory is on the edge of two disciplines, constructive logic and computer science. Logicians see type theory as interesting because it offers a foundation for constructive mathematics and its formalization. For computer scientists, type theory promises to provide a uniform framework for programs, proofs, specifications, and their development. From each perspective, incorporating a general mechanism for inductively defined data types into type theory is an important next step. Various typetheoretic approaches to inductive data types have been considered in the literature, both in MartinLof's predicative type theories (e.g., [ML84, Acz86, Dyb88, Dyb91, B...
The Virtues of Etaexpansion
, 1993
"... Abstract 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 un ..."
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Abstract 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 &quot;cutting &quot; the loops. 1 Introduction Extensional equality for terms of the simplytyped *calculus requires jconversion, whose interpretation as a reduction rule is usually a contraction *x:f x)f If the type structure contains only arrow and product types, whose jreduction is
Inductive Data Types: Wellordering Types Revisited
"... Abstract We consider MartinL"of's wellordering type constructor in the context of animpredicative type theory. We show that the wellordering types can represent various inductive types faithfully in the presence of the fillingup equality rules or jrules. We also discuss various pr ..."
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Abstract We consider MartinL&quot;of's wellordering type constructor in the context of animpredicative type theory. We show that the wellordering types can represent various inductive types faithfully in the presence of the fillingup equality rules or jrules. We also discuss various properties of the fillingup rules.