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- W2471646693 abstract "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 unable to avoid blind alleys in the search space; the unification problems which are generated in the higher-order case are difficult, and most of the computational effort in finding a complete mating is actually spent in unification rather than in enumerating different partial matings. 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. Storing unifiers as graphs also allows us to introduce equality reasoning into higher-order mating search. Component search is capable of handling much larger search spaces than were previously possible with path-enumeration searches, and has produced fully automatic proofs of a number of interesting theorems which were previously intractable." @default.
- W2471646693 created "2016-07-22" @default.
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- W2471646693 date "1999-01-01" @default.
- W2471646693 modified "2023-09-23" @default.
- W2471646693 title "Mating search without path enumeration" @default.
- W2471646693 hasPublicationYear "1999" @default.
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