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Abstract Syntax and Variable Binding (Extended Abstract)
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 ...
An Axiomatisation of Computationally Adequate Domain Theoretic Models of FPC
Categorical models of the metalanguage FPC (a type theory with sums, products, exponentials and recursive types) are defined. Then, domain-theoretic models of FPC are axiomatised and a wide subclass of them —the ...
Complete Cuboidal Sets in Axiomatic Domain Theory (Extended Abstract)
We study the enrichment of models of axiomatic do- main theory. To this end, we introduce a new and broader notion of domain, viz. that of complete cuboidal set, that complies with the axiomatic requirements. We show ...
An Extension of Models of Axiomatic Domain Theory to Models of Synthetic Domain Theory
We relate certain models of Axiomatic Domain Theory (ADT) and Synthetic Domain Theory (SDT). On the one hand, we introduce a class of non-elementary models of SDT and show that the domains in them yield models of ADT. ...