A Breadth-First Strategy for Mating Search

  • Matthew Bishop
Conference paper

DOI: 10.1007/3-540-48660-7_32

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1632)
Cite this paper as:
Bishop M. (1999) A Breadth-First Strategy for Mating Search. In: Automated Deduction — CADE-16. CADE 1999. Lecture Notes in Computer Science, vol 1632. Springer, Berlin, Heidelberg


Mating search is a very general method for automating proof search; it specifies that one must find a complete mating, without specifying the way in which this is to be achieved. It is the foundation of TPS, an automated theorem-proving system for simply-typed lambda-calculus, and has proven very effective in discovering proofs of higher-order theorems. However, previous implementations of mating search have all relied on essentially the same mating search method: enumerating the paths through a matrix of literals. This is a depth-first strategy which is both computationally expensive and vulnerable to blind alleys in the search space; in addition, the incremental computation of unifiers which is required is, in the higher-order case, very inefficient. We describe a new breadth-first mating search method, called component search, in which matings are constructed by taking unions from a fixed list of smaller matings, whose unifiers are stored and manipulated as directed graphs. Component search is capable of handling much larger search spaces than were possible with path-enumeration search, and has produced fully automatic proofs of a number of interesting theorems which were previously intractable.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Matthew Bishop
    • 1
  1. 1.Department of Mathematical SciencesCarnegie Mellon University PittsburghUSA

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