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Denotational versus declarative semantics for functional programming

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Computer Science Logic (CSL 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 626))

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Abstract

Denotational semantics is the usual mathematical semantics for functional programming languages. It is higher order (H.O.) in the sense that the semantic domain D includes [D → D] as a subdomain. On the other hand, the usual declarative semantics for logic programs is first order (F.O.) and given by the least Herbrand model. In this paper, we take a restricted kind of H.O. conditional rewriting systems as computational paradigm for functional programming. For these systems, we define both H.O. denotational and F.O. declarative semantics as two particular instances of algebraic semantics over continuous applicative algebras. For the declarative semantics, we prove soundness and completeness of rewriting, as well as an initiality result. We show that both soundness and completeness fail w.r.t. the denotational semantics and we present a natural restriction of rewriting that avoids unsoundness. We conjecture that this restricted rewriting is complete for computing denotation ally valid F.O. results.

Research supported by the PRONTIC project TIC 89/0104.

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Authors and Affiliations

  1. Dpto. L.S.I.I.S., U.P.M., Spain

    Juan Carlos & González Moreno

  2. Dpto. de Informática y Automática, U.C.M., Spain

    Maria Teresa Hortalá González & Mario Rodríguez Artalejo

Authors
  1. Juan Carlos
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  2. González Moreno
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  3. Maria Teresa Hortalá González
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  4. Mario Rodríguez Artalejo
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Editor information

Egon Börger Gerhard Jäger Hans Kleine Büning Michael M. Richter

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© 1992 Springer-Verlag Berlin Heidelberg

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Carlos, J., Moreno, G., González, M.T.H., Artalejo, M.R. (1992). Denotational versus declarative semantics for functional programming. In: Börger, E., Jäger, G., Kleine Büning, H., Richter, M.M. (eds) Computer Science Logic. CSL 1991. Lecture Notes in Computer Science, vol 626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023763

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  • DOI: https://doi.org/10.1007/BFb0023763

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55789-0

  • Online ISBN: 978-3-540-47285-8

  • eBook Packages: Springer Book Archive

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