Unification in an Extensional Lambda Calculus with Ordered Function Sorts and Constant Overloading
نویسندگان
چکیده
The introduction of sorts in rst-order automatic theorem proving has been accompanied by a considerable gain in computational eeciency via reduced search spaces. This suggests that sort information can be employed in higher-order theorem proving with similar results. This paper develops an order-sorted higher-order calculus suitable for automatic theorem proving applications | by extending the extensional simply typed lambda calculus with a higher-order ordered sort concept and constant overloading | and extends Huet's well-known techniques for uniication in the simply typed lambda calculus to arrive at a complete transformation-based uniication algorithm for this sorted calculus. Consideration of an order-sorted logic with functional base sorts and arbitrary term declarations was originally proposed by the second author in a 1991 paper; we give here a corrected calculus which supports constant, rather than arbitrary term, declarations, as well as a corrected uniication algorithm, and prove in this setting results corresponding to those claimed in that earlier work.
منابع مشابه
Uniication in an Extensional Lambda Calculus with Ordered Function Sorts and Constant Overloading
We develop an order-sorted higher-order calculus suitable for automatic theorem proving applications by extending the extensional simply typed lambda calculus with a higher-order ordered sort concept and constant overloading. Huet's well-known techniques for unifying simply typed lambda terms are generalized to arrive at a complete transformation-based uniication algorithm for this sorted calcu...
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