Uniication in a Sorted -calculus with Term Declarations and Function Sorts

نویسنده

  • Michael Kohlhase
چکیده

The introduction of sorts to rst-order automated deduction has brought greater conciseness of representation and a considerable gain in eeciency by reducing search spaces. This suggests that sort information can be employed in higher-order theorem proving with similar results. This paper develops a sorted-calculus suitable for automatic theorem proving applications. It extends the simply typed-calculus by a higher-order sort concept that includes term declarations and functional base sorts. The term declaration mechanism studied here is powerful enough to subsume subsorting as a derived notion and therefore gives a justiication for the special form of subsort inference. We present a set of transformations for sorted (pre-) uniication and prove the nondetermin-istic completeness of the algorithm induced by these transformations.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Unification in an Extensional Lambda Calculus with Ordered Function Sorts and Constant Overloading

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 ...

متن کامل

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...

متن کامل

Higher-Order Order-Sorted Resolution

The introduction of sorts to rst-order automated deduction has brought greater conciseness of representation and a considerable gain in eeciency by reducing the search space. It is therefore promising to treat sorts in higher order theorem proving as well. In this paper we present a generalization of Huet's Constrained Resolution to an order-sorted type theory T with term declarations. This sys...

متن کامل

A mechanization of sorted higher-order logic based on the resolution principle

The usage of sorts in first-order automated deduction has brought greater conciseness of representation and a considerable gain in efficiency by reducing the search spaces involved. This suggests that sort information can be employed in higher-order theorem proving with similar results. This thesis develops a sorted higher-order logic ΣHOL suitable for automatic theorem proving applications. ΣH...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1994