Variable Binding, Symmetric Monoidal Closed Theories, and Bigraphs
نویسندگان
چکیده
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 this setting, one first specifies an smc theory T , which may express binding operations, in a way reminiscent from higher-order abstract syntax (hoas). 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, in which processes behave linearly, but names do not. This leads to an alternative category of bigraphs, which we compare to the original.
منابع مشابه
Binding bigraphs as symmetric monoidal closed theories
We reconstruct Milner’s [1] category of abstract binding bigraphs Bbg(K) over a signature K as the free (or initial) symmetric monoidal closed (smc) category S(TK) generated by a derived theory TK. The morphisms of S(TK) are essentially proof nets from the Intuitionistic Multiplicative fragment (imll) of Linear Logic [2]. Formally, we construct a faithful, essentially injective on objects funct...
متن کاملThe symmetric monoidal closed category of cpo $M$-sets
In this paper, we show that the category of directed complete posets with bottom elements (cpos) endowed with an action of a monoid $M$ on them forms a monoidal category. It is also proved that this category is symmetric closed.
متن کاملGraphical Presentations of Symmetric Monoidal Closed Theories
We define a notion of symmetric monoidal closed (smc) theory, consisting of a smc signature augmented with equations, and describe the classifying categories of such theories in terms of proof nets.
متن کاملHigher-order Contexts via Games and the Int-construction
Monoidal categories of acyclic graphs capture the notion of multihole context, pervasive in syntax and semantics. Milner’s bigraphs is a recent example. We give a method for generalising such categories to monoidal closed categories of acyclic graphs. The method combines the Int-construction, lifting traced monoidal categories to compact closed ones; the recent formulation of sortings for react...
متن کاملOn Hierarchical Graphs: Reconciling Bigraphs, Gs-monoidal Theories and Gs-graphs
Compositional graph models for global computing systems must account for two relevant dimensions, namely nesting and linking. In Milner’s bigraphs the two dimensions are made explicit and represented as loosely coupled structures: the place graph and the link graph. Here, bigraphs are compared with an earlier model, gs-graphs, based on gs-monoidal theories and originally conceived for modelling...
متن کامل