A Colored Version of the -

Rippling is a technique developed for inductive theorem proving which uses syntactic diierences of terms to guide the proof search. Annotations (like colors) to terms are used to maintain this information. This technique has several advantages, e.g. it is highly goal oriented and involves little search. In this paper we give a general formalisation of coloring terms in a higher-order setting. We introduce a simply-typed lambda calculus with color annotations and present algorithms for uni-cation, pre-uniication and pattern uniication. Our work is a formal basis to the implementation of rippling in a higher-order setting which is required e.g. in case of middle-out reasoning. Another application is in the construction of natural language semantics, where the color annotations rule out linguistically invalid readings that are possible using standard higher-order uniication.