## An Algebraic Presentation of Term Graphs, via GS-Monoidal Categories (1999)

Venue: | Applied Categorical Structures |

Citations: | 37 - 24 self |

### BibTeX

@ARTICLE{Corradini99analgebraic,

author = {Andrea Corradini and Fabio Gadducci},

title = {An Algebraic Presentation of Term Graphs, via GS-Monoidal Categories},

journal = {Applied Categorical Structures},

year = {1999},

volume = {7},

pages = {7--299}

}

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### OpenURL

### Abstract

. We present a categorical characterisation of term graphs (i.e., finite, directed acyclic graphs labeled over a signature) that parallels the well-known characterisation 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 \Sigma are one-to-one with the arrows of the free gs-monoidal category generated by \Sigma. Such a category satisfies all the axioms for Cartesian categories but for the naturality of two transformations (the discharger ! and the duplicator r), providing in this way an abstract and clear relationship between terms and term graphs. In particular, the absence of the naturality of r and ! has a precise interpretation in terms of explicit sharing and of loss of implicit garbage collection, respectively. Keywords: algebraic theories, directed acyclic graphs, gs-monoidal categories, symmetric monoidal categories, term graphs. Mathematical Subject Clas...