Higher-Order Proof Construction Based on First-Order Narrowing

Higher-Order Narrowing

We introduce several approaches for solving higher order equational problems by higher order narrow ing and give rst completeness results The results apply to higher order functional logic programming languages and to higher order uni cation modulo a higher order equational theory We lift the general notion of rst order narrow ing to so called higher order patterns and argue that the full highe...

First-Order Proof Tactics in Higher-Order Logic Theorem Provers

In this paper we evaluate the effectiveness of first-order proof procedures when used as tactics for proving subgoals in a higher-order logic interactive theorem prover. We first motivate why such first-order proof tactics are useful, and then describe the core integrating technology: an ‘LCFstyle’ logical kernel for clausal first-order logic. This allows the choice of different logical mapping...

Typed Higher-Order Narrowing without Higher-Order Strategies

We describe a new approach to higher-order narrowing computations in a class of systems suitable for functional logic programming. Our approach is based on a translation of these systems into ordinary (£rst-order) rewrite systems and the subsequent application of conventional narrowing strategies. Our translation is an adaptation to narrowing of Warren’s translation, but unlike similar previous...

A Functional Logic Language Based on Higher Order Narrowing

Functional logic languageshave a syntax like a purely functional language but use narrowing as operational semantics. We present the functional logic language Higher Order Babel which provides higher order unification for parameter passing and solving equations. When searching for a function which solves an equation “polynomial functions” as well as defined functions are taken into account. In ...

Higher-order proof translation