Abstract
The introduction of sorts to first-order automated deduction has brought a considerable gain in efficiency by reducing the search space. It is therefore promising to treat sorts in higher order theorem proving as well, in order to achieve a similar gain.
In this paper we develop a sorted version of type theory; we extend the syntax and semantics of simple type theory by a higher order sort concept that includes term declarations. In our system the partial ordering on the base sorts induces a partial ordering on the higher types by covariance in the rangesort and the natural inclusion of base function sorts.
We present a set of transformations for sorted (pre-) unification and prove the nondeterministic completeness of the algorithm induced by these transformations.
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© 1992 Springer-Verlag Berlin Heidelberg
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Kohlhase, M. (1992). Unification in order-sorted type theory. In: Voronkov, A. (eds) Logic Programming and Automated Reasoning. LPAR 1992. Lecture Notes in Computer Science, vol 624. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013080
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DOI: https://doi.org/10.1007/BFb0013080
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