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  3. The Clausal Theory of Types
  • Cited by 45
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    • Publisher:
      Cambridge University Press
      Publication date:
      January 2010
      April 1993
      ISBN:
      9780511569906
      9780521395380
      9780521117906
      DOI:
      https://doi.org/10.1017/CBO9780511569906
      Dimensions:
      (247 x 174 mm)
      Weight & Pages:
      0.406kg, 134 Pages
      Dimensions:
      (244 x 170 mm)
      Weight & Pages:
      0.23kg, 136 Pages
      • Subjects:
      Algorithmics, Complexity, Computer Algebra, Computational Geometry, Computer Science, Programming Languages and Applied Logic
      Series:
      Cambridge Tracts in Theoretical Computer Science (21)
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    Subjects:
    Algorithmics, Complexity, Computer Algebra, Computational Geometry, Computer Science, Programming Languages and Applied Logic
    Series:
    Cambridge Tracts in Theoretical Computer Science (21)
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    Book description

    Logic programming was based on first-order logic. Higher-order logics can also lead to theories of theorem-proving. This book introduces just such a theory, based on a lambda-calculus formulation of a clausal logic with equality, known as the Clausal Theory of Types. By restricting this logic to Horn clauses, a concise form of logic programming that incorporates functional programming is achieved. The book begins by reviewing the fundamental Skolem-Herbrand-Gödel Theorem and resolution, which are then extrapolated to a higher-order setting; this requires introducing higher-order equational unification which builds in higher-order equational theories and uses higher-order rewriting. The logic programming language derived has the unique property of being sound and complete with respect to Henkin-Andrews general models, and consequently of treating equivalent terms as identical. First published in 1993, the book can be used for graduate courses in theorem-proving, but will be of interest to all working in declarative programming.

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