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G. Rosolini

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

2 papers

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I&C Journal 1992 Journal Article

Extensional PERs

P. Freyd
P. Mulry
G. Rosolini
D. Scott

A class of Partial Equivalence Relations (PERs) is described such that the resulting full subcategory of the realizability universe has the expected properties of a good category of CPOs; that is, it is a Cartesian closed category and every endomorphism has a canonical fixed point. Moreover, the reflection functor into the subcategory of strict maps (usually called the “lifting operation”) yields a good notion of “partial map, ” a necessary condition if one wishes to maintain a connection between strict maps and partial maps. It is shown that all functors that arise in practice have canonical invariant objects; hence a host of domain equations are guaranteed to have solutions.

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I&C Journal 1988 Journal Article

Categories of partial maps

E. Robinson
G. Rosolini

This paper attempts to reconcile the various abstract notions of “category of partial maps” which appear in the literature. First a particular algebraic theory (p-categories) is introduced and a representation theorem proved. This gives the authors a coherent framework in which to place the various other definitions. Both algebraic theories and theories which make essential use of the poset-enriched structure of partial maps are discussed. Proofs of equivalence are given where possible and counterexamples where known. The paper concludes with brief sections on the representation of partial maps and on partial algebras.

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