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International Conference on Typed Lambda Calculi and Applications

TLCA 1999: Typed Lambda Calculi and Applications pp 162–177Cite as

Explicitly Typed λμ-Calculus for Polymorphism and Call-by-Value

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1581))

Abstract

We introduce an explicitly typed λμ-calculus of call-by-value as a short-hand for the 2nd order Church-style. Our motivation comes from the observation that in Curry-style polymorphic calculi, control operators such as callcc or μ-operators cannot, in general, treat the terms placed on the control operator’s left. Following the continuation semantics, we also discuss the notion of values in classical system, and propose an extended form of values. It is shown that the CPS-translation is sound with respect to λ2 (2nd order λ-calculus). Next, we provide an explicitly and an implicitly typed Damas-Milner systems with μ-operators. Finally, we give a brief comparison with standard ML plus callcc, and discuss a natural way to avoid the unsoundness of ML with callcc.

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Author information

Authors and Affiliations

  1. Kyushu Institute of Technology, Iizuka, 820-8502, Japan

    Ken-etsu Fujita

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  1. Ken-etsu Fujita
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Editors and Affiliations

  1. CNRS - UPR9016, Institut de Mathématiques de Luminy, 163 Avenue de Luminy, case 907, F-13288, Marseille cedex 9, France

    Jean-Yves Girard

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Fujita, Ke. (1999). Explicitly Typed λμ-Calculus for Polymorphism and Call-by-Value. In: Girard, JY. (eds) Typed Lambda Calculi and Applications. TLCA 1999. Lecture Notes in Computer Science, vol 1581. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48959-2_13

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  • DOI: https://doi.org/10.1007/3-540-48959-2_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65763-7

  • Online ISBN: 978-3-540-48959-7

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