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A 2-categorical presentation of term graph rewriting

  • A. Corradini
  • F. Gadducci
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1290)

Abstract

It is well-known that a term rewriting system can be faithfully described by a cartesian 2-category, where horizontal arrows represent terms, and cells represent rewriting sequences. In this paper we propose a similar, original 2-categorical presentation for term graph rewriting. Building on a result presented in [8], which shows that term graphs over a given signature are in one-to-one correspondence with arrows of a gs-monoidal category freely generated from the signature, we associate with a term graph rewriting system a gs-monoidal 2-category, and show that cells faithfully represent its rewriting sequences. We exploit the categorical framework to relate term graph rewriting and term rewriting, since gs-monoidal (2-)categories can be regarded as “weak” cartesian (2-) categories, where certain (2-)naturality axioms have been dropped.

Keywords

term graph rewriting directed acyclic graphs categorical models 2-categories 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • A. Corradini
    • 1
  • F. Gadducci
    • 2
  1. 1.CWIAmsterdamThe Netherlands
  2. 2.TUB, Fachbereich 13 InformatikBerlinGermany

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