Semantics of PCF and the full abstraction problem Language, Operational Semantics and Models
نویسنده
چکیده
Language 2 Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 λ-calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Free Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Renaming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Substitution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Syntax of PCF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
منابع مشابه
From Mathematical Functions to Syntax
@article{gdp:lcf-as-pl, author={Plotkin, G. D.}, title={LCF Considered as a Programming Language}, journal={Theoretical Computer Science}, pages={223--255}, year=1977 } Summary: Plotkin investigates the relation between the denotational and the operational semantics of a programming language. As a working example, he picks PCF a language based on Scott’s Logic of Computable Functions. He demons...
متن کاملFrom Mathematical Functions to Programs
@article{gdp:lcf-as-pl, author={Plotkin, G. D.}, title={LCF Considered as a Programming Language}, journal={Theoretical Computer Science}, pages={223--255}, year=1977 } Summary: Plotkin investigates the relation between the denotational and the operational semantics of a programming language. As a working example, he picks PCF a language based on Scott’s Logic of Computable Functions. He demons...
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.
متن کاملFull abstraction for non-deterministic and probabilistic extensions of PCF I: The angelic cases
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 ...
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