# Rewriting on cyclic structures: Equivalence between the operational and the categorical description

Andrea Corradini; Fabio Gadducci

RAIRO - Theoretical Informatics and Applications (2010)

- Volume: 33, Issue: 4-5, page 467-493
- ISSN: 0988-3754

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topCorradini, Andrea, and Gadducci, Fabio. "Rewriting on cyclic structures: Equivalence between the operational and the categorical description." RAIRO - Theoretical Informatics and Applications 33.4-5 (2010): 467-493. <http://eudml.org/doc/222074>.

@article{Corradini2010,

abstract = {
We present a categorical formulation
of the rewriting of possibly cyclic term graphs, based on a
variation of algebraic 2-theories. We show that
this presentation is equivalent to the well-accepted
operational definition proposed by Barendregt et al. – but
for the
case of circular redexes , for which we propose (and
justify formally) a different treatment.
The categorical framework allows us to model in a concise way
also automatic garbage collection
and rules
for sharing/unsharing and folding/unfolding of structures,
and to relate
term graph rewriting to other rewriting formalisms.
},

author = {Corradini, Andrea, Gadducci, Fabio},

journal = {RAIRO - Theoretical Informatics and Applications},

keywords = {Term graphs; directed acyclic graphs; term graph
rewriting; categorical models; traced monoidal categories;
2-categories; algebraic theories; gs-monoidal theories.; cyclic term graphs; algebraic 2-theories; circular redexes; automatic garbage collection; sharing/unsharing; folding/unfolding; term graph rewriting},

language = {eng},

month = {3},

number = {4-5},

pages = {467-493},

publisher = {EDP Sciences},

title = {Rewriting on cyclic structures: Equivalence between the operational and the categorical description},

url = {http://eudml.org/doc/222074},

volume = {33},

year = {2010},

}

TY - JOUR

AU - Corradini, Andrea

AU - Gadducci, Fabio

TI - Rewriting on cyclic structures: Equivalence between the operational and the categorical description

JO - RAIRO - Theoretical Informatics and Applications

DA - 2010/3//

PB - EDP Sciences

VL - 33

IS - 4-5

SP - 467

EP - 493

AB -
We present a categorical formulation
of the rewriting of possibly cyclic term graphs, based on a
variation of algebraic 2-theories. We show that
this presentation is equivalent to the well-accepted
operational definition proposed by Barendregt et al. – but
for the
case of circular redexes , for which we propose (and
justify formally) a different treatment.
The categorical framework allows us to model in a concise way
also automatic garbage collection
and rules
for sharing/unsharing and folding/unfolding of structures,
and to relate
term graph rewriting to other rewriting formalisms.

LA - eng

KW - Term graphs; directed acyclic graphs; term graph
rewriting; categorical models; traced monoidal categories;
2-categories; algebraic theories; gs-monoidal theories.; cyclic term graphs; algebraic 2-theories; circular redexes; automatic garbage collection; sharing/unsharing; folding/unfolding; term graph rewriting

UR - http://eudml.org/doc/222074

ER -

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