Abstract Syntax and Variable Binding (Extended Abstract)
Fiore, Marcelo P
We develop a theory of abstract syntax with variable binding. To every binding signature we associate a category of models consisting of variable sets endowed with compatible algebra and substitution structures. The syntax generated by the signature is the initial model. This gives a notion of initial algebra semantics encompassing the traditional one; besides compositionality, it automatically veri- fies the semantic substitution lemma.