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Equation solving in conditional AC-theories

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Algebraic and Logic Programming (ALP 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 463))

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Abstract

Conditional Equational Programming is an elegant way to uniformly integrate important features of functional and logic programming. Efficient methods for equation solving are thus of great importance. In this paper, we formulate, and prove sound and complete, an equation solving procedure based on transformation rules. This method achieves a top-down, goal-directed strategy based on decomposition and restructuring, while preserving the advantages of both basic narrowing and normal narrowing. Another new feature, introduced in this paper, is the extension of equation solving to theories with defined functions that are associative and commutative, without using the costly AC-unification operation. This method has been implemented within SUTRA, a theorem proving and equational programming environment based on rewrite techniques and completion.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Illinois, 61801, Urbana, IL, U.S.A.

    Nachum Dershowitz

  2. Department of Computer Science, University of Delaware, 19716, Newark, DE, U.S.A.

    Subrata Mitra & G. Sivakumar

Authors
  1. Nachum Dershowitz
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  2. Subrata Mitra
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  3. G. Sivakumar
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Editor information

Hélène Kirchner Wolfgang Wechler

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© 1990 Springer-Verlag Berlin Heidelberg

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Dershowitz, N., Mitra, S., Sivakumar, G. (1990). Equation solving in conditional AC-theories. In: Kirchner, H., Wechler, W. (eds) Algebraic and Logic Programming. ALP 1990. Lecture Notes in Computer Science, vol 463. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53162-9_46

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  • DOI: https://doi.org/10.1007/3-540-53162-9_46

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53162-3

  • Online ISBN: 978-3-540-46738-0

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