On Full Abstraction for Pcf : I , Ii And
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Logical Full Abstraction and PCF
We introduce the concept of logical full abstraction, generalising the usual equational notion. We consider the language PCF and two extensions with “parallel” operations. The main result is that, for standard interpretations, logical full abstraction is equivalent to equational full abstraction together with universality; the proof involves constructing enumeration operators. We also consider ...
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It is impossible to add a combinator to PCF to achieve full abstraction for models such asBerry's stable domains in a way analogous to the addition of the \parallel-or" combinatorthat achieves full abstraction for the familiar cpo model. In particular, we de ne a generalnotion of rewriting system of the kind used for evaluating simply typed -terms in Scott'sPCF. Any simply t...
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We examine several extensions and variants of Plotkin’s language PCF, including non-deterministic and probabilistic choice constructs. For each, we give an operational and a denotational semantics, and compare them. In each case, we show soundness and computational adequacy: the two semantics compute the same values at ground types. Beyond this, we establish full abstraction (the observational ...
متن کاملFull abstraction for a Linear PCF
We study S PCF , namely a Turing-complete programming language inspired by a semantic notion of linearity. S PCF is based on a linear core of PCF and some operators providing basic primitives related to exception handling and nondeterministic evaluation. We show that S PCF is fully abstract for a linear model in the category of coherence spaces and linear functions, giving a cogent evidence of ...
متن کاملAxioms for definability and full completeness
Axioms are presented on models of PCF from which full abstraction can be proved. These axioms have been distilled from recent results on definability and full abstraction of game semantics for a number of programming languages. Full completeness for pure simply-typed λ-calculus is also axiomatized.
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تاریخ انتشار 2000