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On the reification of semantic linearity

Published online by Cambridge University Press:  10 November 2014

MARCO GABOARDI ,
LUCA PAOLINI  and
MAURO PICCOLO
MARCO GABOARDI
Affiliation:
School of Computing, University of Dundee, Dundee, DD1 4HN, Scotland, U.K.
LUCA PAOLINI
Affiliation:
Dipartimento di Informatica, Università degli Studi di Torino, C.so Svizzera 185, 10149 Torino, Italy Email: paolini@di.unito.it
MAURO PICCOLO
Affiliation:
Dipartimento di Informatica, Università degli Studi di Torino, C.so Svizzera 185, 10149 Torino, Italy Email: paolini@di.unito.it
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Abstract

Linearity is a multi-faceted and ubiquitous notion in the analysis and development of programming language concepts. We study linearity in a denotational perspective by picking out programs that correspond to linear functions between domains.

We propose a PCF-like language imposing linear constraints on the use of variable to program only linear functions. To entail a full abstraction result, we introduce some higher-order operators related to exception handling and parallel evaluation. We study several notions of operational equivalence and show them to coincide with our language. Finally, we present a new operational evaluation of the language that provides the base for a real implementation. It exploits the denotational linearity to provide an efficient evaluation semantics SECD-like, that avoids the use of closures.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 26 , Issue 5 , June 2016 , pp. 829 - 867
Copyright
Copyright © Cambridge University Press 2014 

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