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Algebraic semantics for functional logic programming with polymorphic order-sorted types

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Algebraic and Logic Programming (ALP 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1139))

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Abstract

In this paper we present the semantics of a functional logic language with parametric and order-sorted polymorphism. Typed programs consist of a polymorphic signature and a set of constructor-based conditional rewriting rules for which we define a semantic calculus. The denotational semantics of the language is based on Scott domains interpreting constructors and functions by monotonic and continuous mappings, respectively, in every instance of the declared type. We prove initiality results for the free ground term algebra. We also prove that the free term algebra with variables is freely generated in the category of models. The semantic calculus is proved to be sound and complete w.r.t. the denotational semantics. As in logic programming, we define the immediate consequence operator, proving that the Hebrand model is the least model of a program.

This work has been supported by the Spanish CICYT (project TIC 95-0433-C03-01 “CPD”).

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Authors and Affiliations

  1. Dpto. Informática y Automática. Fac. Matemáticas, UCM, Av. Complutense s/n, E-28040, Madrid, Spain

    J. M. Almendros-Jiménez, A. Gavilanes-Franco & A. Gil-Luezas

Authors
  1. J. M. Almendros-Jiménez
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  2. A. Gavilanes-Franco
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  3. A. Gil-Luezas
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Michael Hanus Mario Rodríguez-Artalejo

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© 1996 Springer-Verlag Berlin Heidelberg

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Almendros-Jiménez, J.M., Gavilanes-Franco, A., Gil-Luezas, A. (1996). Algebraic semantics for functional logic programming with polymorphic order-sorted types. In: Hanus, M., Rodríguez-Artalejo, M. (eds) Algebraic and Logic Programming. ALP 1996. Lecture Notes in Computer Science, vol 1139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61735-3_20

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  • DOI: https://doi.org/10.1007/3-540-61735-3_20

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  • Print ISBN: 978-3-540-61735-8

  • Online ISBN: 978-3-540-70672-4

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