Categories of partial morphisms and the λp-calculus
Proceedings of a tutorial and workshop on Category theory and computer programming
Full abstraction for sequential algorithms: the state of the art
Algebraic methods in semantics
Advances in Petri nets 1986, part II on Petri nets: applications and relationships to other models of concurrency
Proofs and types
Computational lambda-calculus and monads
Proceedings of the Fourth Annual Symposium on Logic in computer science
A note on inconsistencies caused by fixpoints in a Cartesian closed category
Theoretical Computer Science
Semantics of programming languages: structures and techniques
Semantics of programming languages: structures and techniques
The formal semantics of programming languages: an introduction
The formal semantics of programming languages: an introduction
Handbook of logic in computer science (vol. 1)
A type-theoretical alternative to ISWIM, CUCH, OWHY
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory
Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory
A Simple Adequate Categorical Model for PCF
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
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Usually types of PCF are interpreted as cpos and terms as continuous functions. It is then the case that non-termination of a closed term of ground type corresponds to the interpretation being bottom; we say that the semantics is adequate. We shall here present an axiomatic approach to adequacy for PCF in the sense that we will introduce categorical axioms enabling an adequate semantics to be given. We assume the presence of certain “undefined” maps with the role of being the interpretation of non-terminating terms, but the order-structure is left out. This is different from previous approaches where some kind of order-theoretic structure has been considered as part of an adequate categorical model for PCF. We take the point of view that partiality is the fundamental notion from which order-structure should be derived, which is corroborated by the observation that our categorical model induces an order-theoretic model for PCF in a canonical way.