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A normalizing calculus with overloading and subtyping

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Theoretical Aspects of Computer Software (TACS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 789))

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Abstract

Recently, a new calculus with overloading and subtyping was presented by Castagna, Ghelli, and Longo [CGL94]. This calculus, λ&-calculus, is an extension of the simply typed λ-calculus and is promising in that it explains the computational mechanism of object-oriented languages from a new viewpoint. However, in λ&-calculus, the interaction of overloading and subtyping causes some unexpected properties such as non-normalization and the difficulties in constructing a model. In this paper, in order to study this interaction, we present modifications of this calculus so that the exact type of a term is preserved, and investigate their syntactic and semantic properties in detail. We define two calculi λ&C and λ&C * corresponding to two possible meanings of an overloaded type. They have completely different properties though they only differ slightly in reduction rules. Strong normalization holds in λ&C * though it is not the case in λ&C, and transitivity of coercions holds in λ&C though it is not the case in λ&C *. The semantics of λ&C * can be given through the translation to a calculus without subtyping. On the other hand, a semantics of λ&C cannot be given easily because of the circular structure it has.

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Authors and Affiliations

  1. Faculty of Environmental Information, Keio University, 5322 Endoh, Fujisawa, 252, Kanagawa, Japan

    Hideki Tsuiki

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  1. Hideki Tsuiki
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Masami Hagiya John C. Mitchell

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© 1994 Springer-Verlag Berlin Heidelberg

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Tsuiki, H. (1994). A normalizing calculus with overloading and subtyping. In: Hagiya, M., Mitchell, J.C. (eds) Theoretical Aspects of Computer Software. TACS 1994. Lecture Notes in Computer Science, vol 789. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57887-0_100

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  • DOI: https://doi.org/10.1007/3-540-57887-0_100

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57887-1

  • Online ISBN: 978-3-540-48383-0

  • eBook Packages: Springer Book Archive

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