An algorithm for optimal lambda calculus reduction

We present an algorithm for lambda expression reduction that avoids any copying that could later cause duplication of work. It is optimal in the sense defined by Lévy. The basis of the algorithm is a graphical representation of the kinds of commonality that can arise from substitutions; the idea can be adapted to represent other kinds of expressions besides lambda expressions. The algorithm is also well suited to parallel implementations, consisting of a fixed set of local graph rewrite rules.