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Foundations of equational deduction: A categorical treatment of equational proofs and unification algorithms

  • D. E. Rydeheard
  • J. G. Stell
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 283)

Abstract

We provide a framework for equational deduction based on category theory. Firstly, drawing upon categorical logic, we show how the compositional structure of equational deduction is captured by a 2-category. Using this formulation, algorithms for solving equations are derived from general constructions in category theory. The basic unification algorithm arises from constructions of colimits. We also consider solving equations in the presence of term rewriting systems and the combination of unification algorithms.

Keywords

Category Theory Equational Theory Deductive System Unification Algorithm Automate Deduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • D. E. Rydeheard
    • 1
  • J. G. Stell
    • 1
  1. 1.University of ManchesterUK

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