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arXiv · 0704.2900

Higher-order theories

Andre' Hirschowitz·Marco Maggesi
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Abstract

We extend our approach to abstract syntax (with binding constructions) through modules and linearity. First we give a new general definition of arity, yielding the companion notion of signature. Then we obtain a modularity result as requested by Ghani and Uustalu (2003): in our setting, merging two extensions of syntax corresponds to building an amalgamated sum. Finally we define a natural notion of equation concerning a signature and prove the existence of an initial semantics for a so-called representable signature equipped with a set of equations.

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Andre' Hirschowitz, Marco Maggesi. 2008-09-09. Higher-order theories. https://arxiv.org/abs/0704.2900

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