Unification in a sorted λ-calculus with term declarations and function sorts

  • Michael Kohlhase
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 861)

Abstract

The introduction of sorts to first-order automated deduction has brought greater conciseness of representation and a considerable gain in efficiency by reducing search spaces. This suggests that sort information can be employed in higher-order theorem proving with similar results. This paper develops a sorted λ-calculus suitable for automatic theorem proving applications. It extends the simply typed λ-calculus by a higher-order sort concept that includes term declarations and functional base sorts. The term declaration mechanism studied here is powerful enough to subsume subsorting as a derived notion and therefore gives a justification for the special form of subsort inference. We present a set of transformations for sorted (pre-) unification and prove the nondeterministic completeness of the algorithm induced by these transformations.

Keywords

Inference System Partial Function Deduction System Structure Theorem Valid Signature 
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 1994

Authors and Affiliations

  • Michael Kohlhase
    • 1
  1. 1.FB InformatikUniversität des SaarlandesSaarbrückenGermany

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