Marcelo Fiore - Abstract syntax and variable binding

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 both a (binding) algebra and a substitution structure compatible with each other. 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 verifies the semantic substitution lemma. This is joint work with Gordon Plotkin and Daniele Turi, see http://www.dcs.ed.ac.uk/~mf/TYPES/binding.ps .