## Unification in a Sorted (lambda)-Calculus with Term Declarations and Function Sorts

• The introduction of sorts to first-order automated deduc-tion has brought greater conciseness of representation and a considerablegain in efficiency by reducing search spaces. This suggests that sort in-formation can be employed in higher-order theorem proving with similarresults. This paper develops a sorted (lambda)-calculus suitable for automatictheorem proving applications. It extends the simply typed (lambda)-calculus by ahigher-order sort concept that includes term declarations and functionalbase sorts. The term declaration mechanism studied here is powerfulenough to subsume subsorting as a derived notion and therefore gives ajustification for the special form of subsort inference. We present a set oftransformations for sorted (pre-) unification and prove the nondetermin-istic completeness of the algorithm induced by these transformations.

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