Abstract: "New tools are presented for reasoning about properties of recursively defined domains. We work within a general, category- theoretic framework for various notions of 'relation' on domains and for actions of domain constructors on relations. Freyd's analysis of recursiv...

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Bibliographic Details

Main Author:	Pitts, Andrew M. 1956- (Author)
Format:	Book
Language:	English
Published:	Cambridge 1993
Series:	Computer Laboratory <Cambridge>: Technical report 321
Subjects:	Computer software Functional programming (Computer science)
Summary:	Abstract: "New tools are presented for reasoning about properties of recursively defined domains. We work within a general, category- theoretic framework for various notions of 'relation' on domains and for actions of domain constructors on relations. Freyd's analysis of recursive types in terms of a property of mixed initiality /finality is transferred to a corresponding property of invariant relations. The existence of invariant relations is proved under completeness assumptions about the notion of relation. We show how this leads to simpler proofs of the computational adequacy of denotational semantics for functional programming languages with user-declared datatypes We show how the initiality/finality property of invariant relations can be specialized to yield an induction principle for admissible subsets of recursively defined domains, generalizing the principle of structural induction for inductively defined sets. We also show how the initiality/finality property gives rise to the co-induction principle studied by the author (in Cambridge Univ. Computer Laboratory Tech. Rept. No. 252), by which equalities between elements of recursively defined domains may be proved via an appropriate notion of 'bisimulation'.
Physical Description:	38 S.