2007/04/22 by André Hirschowitz, Hirschowitz, Andre', Marco Maggesi +1
Computer Science · #FOS: Computer and information sciences #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.0704.2900
openalex publication_date 2007/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.