Relational Properties of Domains

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Relational Properties of Domains (1996)

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by Andrew M. Pitts

Venue:	Information and Computation
Citations:	112 - 6 self

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@ARTICLE{Pitts96relationalproperties,
    author = {Andrew M. Pitts},
    title = {Relational Properties of Domains},
    journal = {Information and Computation},
    year = {1996},
    volume = {127},
    pages = {66--90}
}

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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-induct...

Keyphrases

relational property invariant relation initiality finality property mixed initiality finality recursive type computational adequacy structural induction completeness assumption corresponding property user-declared datatypes denotational semantics various notion domain constructor new tool admissible subset induction principle functional programming language category-theoretic framework

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