Variable binding, symmetric monoidal closed theories, and bigraphs

Richard Garner (1) , Tom Hirschowitz (2) , Aurélien Pardon (3)

1 DPMMS - Department of Pure Mathematics and Mathematical Statistics
2 LAMA - Laboratoire de Mathématiques
3 LIP - Laboratoire de l'Informatique du Parallélisme

This paper investigates the use of symmetric monoidal closed (SMC) structure for representing syntax with variable binding, in particular for languages with linear aspects. In our setting, one first specifies an SMC theory T, which may express binding operations, in a way reminiscent from higher-order abstract syntax. This theory generates an SMC category S(T) whose morphisms are, in a sense, terms in the desired syntax. We apply our approach to Jensen and Milner's (abstract binding) bigraphs, which are linear w.r.t. processes. This leads to an alternative category of bigraphs, which we compare to the original.

Mots clés: Symmetric monoidal closed categories; Linear Logic; Variable binding; Bigraphs

Domaines: Logique en informatique [cs.LO]; Catégories et ensembles [math.CT]; Langage de programmation [cs.PL]

Richard Garner, Tom Hirschowitz, Aurélien Pardon. Variable binding, symmetric monoidal closed theories, and bigraphs. CONCUR 2009, 2009, Bologna, Italy. pp.321-337, ⟨10.1007/978-3-642-04081-8_22⟩. ⟨hal-00388100⟩