Introduction to higher order categorical logic
Introduction to higher order categorical logic
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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 ${\mathcal{T}}$, which may express binding operations, in a way reminiscent from higher-order abstract syntax (hoas ). This theory generates an smc category $S ({\mathcal{T}}$ 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.