Maria Eugenia Occhiuto

Lazy Linear Combinatorial Unification

In this paper we define a two-rule reduction system for the lazy computation of unification on first-order terms. The computation consists of a sequence of reductions which is almost linear with the size of the input. Every reduction transforms the problem into an equivalent one which is a better approximation of the solution. The approach is based on a combinatorial system which provides abstractions for terms and term unification, and does not resort to any specific reduction control strategy. The abstraction on both data and control makes our system suitable in any applicative context where unification is required.

Combinatory Forms for Equational Programming: Instances, Unification and Narrowing

A relevant drawback of current implementations of logic programming languages is represented by the use of substitutions to keep bindings of logical variables, l-variables. Powerful compilation techniques, i.e. translation to combinatory logic, and implementation techniques such as reduction machines, have shown how to overcome this problem in the context of functional languages. The paper addresses a similar approach to equational logic programming: equations are translated into variable-free combinations and correspondingly narrowing is reformulated in terms of a set of reduction rules.