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Domain-Free λµ-Calculus

Published online by Cambridge University Press:  15 April 2002

Ken-Etsu Fujita
Ken-Etsu Fujita*
Affiliation:
Shimane University, Department of Mathematics and Computer Science, Matsue 690-8504, Japan; (fujiken@cis.shimane-u.ac.jp)
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Abstract

We introduce a domain-free λµ-calculus of call-by-valueas a short-hand for the second order Church-style. Our motivation comes from the observation that in Curry-style polymorphic calculi, control operators such as callcc-operators cannot, in general, handle correctly the terms placed on the control operator's left, so that the Curry-style system can fail to prove the subject reduction property. Following the continuation semantics, we also discuss the notion of values in classical system, and propose an extended form of values. It is proved that the CPS-translation is sound with respect to domain-free λ2 (second-order λ-calculus). As a by-product, we obtain the strong normalization propertyfor the second-order λµ-calculus of call-by-value in domain-free style. We also study the problems of type inference, typability, and type checking for the call-by-value system. Finally, we give a brief comparison with standard ML plus callcc,and discuss a natural way to avoid the unsoundness of ML with callcc.

Keywords

λµ-calculusdomain-free stylecall-by-valuepolymorphismsubject reductionCPS-translationstrong normalizationChurch-Rossertype inferencetype checking.

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Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 34 , Issue 6 , November 2000, pp. 433 - 466
Copyright
© EDP Sciences, 2000

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