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A categorical interpretation of Landin's correspondence principle

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Mathematical Foundations of Programming Semantics (MFPS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 802))

Abstract

Many programming languages can be studied by desugaring them into an intermediate language, namely, the simply-typed λ-calculus. In this manner Landin and Tennent discovered a “correspondence” between the semantics of definition bindings and parameter bindings such that the semantics of free identifiers becomes independent of their mode of definition.

In this paper we consider programming languages with modules and we desugar modules into records. A categorical model for the simply-typed λ-calculus with records is then freely generated. The record construction becomes a tensor product, the lambda abstraction construction becomes a function space, and if the language satisfies the correspondence principle, then the categorical exponentiation diagram commutes. A converse result is also proved. The framework for defining the model is of interest because it defines a hierarchy of call-by-value λ-calculi, of which call-by-name is the weakest form of call-by-value calculus.

Applications to compiling are given.

Part of this work was supported by NSF under grant CCR-9102625.

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Authors and Affiliations

  1. Department of Computing and Information Sciences, Kansas State University, 66506, Manhattan, Kansas, USA

    Anindya Banerjee & David A. Schmidt

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  1. Anindya Banerjee
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  2. David A. Schmidt
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Stephen Brookes Michael Main Austin Melton Michael Mislove David Schmidt

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© 1994 Springer-Verlag Berlin Heidelberg

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Banerjee, A., Schmidt, D.A. (1994). A categorical interpretation of Landin's correspondence principle. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Semantics. MFPS 1993. Lecture Notes in Computer Science, vol 802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58027-1_29

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  • DOI: https://doi.org/10.1007/3-540-58027-1_29

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58027-0

  • Online ISBN: 978-3-540-48419-6

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