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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.

In the last years, the Java community has been arguing about adding closures to Java in order to improve expressivity. The debate has not yet terminated but all proposals seem to converge towards a notion of Simple Closures which contain only the essential features of anonymous functions. This paper addresses the problem of defining a rigorous semantics for Simple Closures. The technique adopted is well known and has already been used to prove interesting properties of other extensions of Java. A minimal calculus is defined: Featherweight Java extended with Simple Closures. Syntax and semantics of such a calculus are defined and type safety, backward compatibility, and the abstraction property are proved.

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