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.

Higher-order theories / André, Hirschowitz; Marco, Maggesi. - ELETTRONICO. - (2007), pp. 1-12.

Higher-order theories

Marco Maggesi
2007

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.
2007
André, Hirschowitz; Marco, Maggesi
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1104595
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