Petri net models for the λ-calculus

Abstract

In [Kluge & Schlütter 83] a Petri net model was presented for the reduction of expressions in a λ-calculus like language. The λ-plan model outlined here, tries to deal with two problems left open by the authors of that paper namely that they model only applicative order string-reduction and do not allow higher order functions. We will try to solve this by using a two-level approach.

In order to model the reduction of a given λ-term, an execution plan for the reduction of the term is generated. Execution of that λ-plan implies two levels of activity. On the control-flow level, transitions send each other messages (tokens) in order to detect redexes. Once a redex has been found a local change is made to the data-flow level where the structure of the plan is transformed according to the reduction rules of λ-calculus.

Although this paper is concerned only with string-reduction, an extension of the model to incorporate graph-reduction is straightforward. The plan model can also be adapted to model other rewriting systems as well.