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.
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Appendix B list of references
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A. Veen "The misconstrued semicolon", Ph.D. thesis, Technical University Eindhoven.
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© 1987 Springer-Verlag Berlin Heidelberg
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Meijer, E. (1987). Petri net models for the λ-calculus. In: Rozenberg, G. (eds) Advances in Petri Nets 1987. APN 1986. Lecture Notes in Computer Science, vol 266. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18086-9_25
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DOI: https://doi.org/10.1007/3-540-18086-9_25
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