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An Algebraic Presentation of Term Graphs, via GS-Monoidal Categories

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Abstract

We present a categorical characterization of term graphs (i.e., finite, directed acyclic graphs labeled over a signature) that parallels the well-known characterization of terms as arrows of the algebraic theory of a given signature (i.e., the free Cartesian category generated by it). In particular, we show that term graphs over a signature Σ are one-to-one with the arrows of the free gs-monoidal category generated by Σ. Such a category satisfies all the axioms for Cartesian categories but for the naturality of two transformations (the discharger ! and the duplicator ∇), providing in this way an abstract and clear relationship between terms and term graphs. In particular, the absence of the naturality of ∇ and ! has a precise interpretation in terms of explicit sharing and of loss of implicit garbage collection, respectively.

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Authors and Affiliations

  1. Dipartimento di Informatica, University of Pisa, Corso Italia 40, I-56124, Pisa, Italy. e-mail

    Andrea Corradini

  2. Fachbereich 13 Informatik, Technical University of Berlin, Franklinstraße 28/29, D-10587, Berlin, Germany. e-mail

    Fabio Gadducci

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  1. Andrea Corradini
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Corradini, A., Gadducci, F. An Algebraic Presentation of Term Graphs, via GS-Monoidal Categories. Applied Categorical Structures 7, 299–331 (1999). https://doi.org/10.1023/A:1008647417502

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