An operational domain-theoretic treatment of recursive types

We develop a domain theory for treating recursive types with respect to contextual equivalence. The principal approach taken here deviates from classical domain theory in that we do not produce the recursive types via the usual inverse limits constructions- we have it for free by working directly with the operational semantics. By extending type expressions to endofunctors on a ‘syntactic ’ category, we establish algebraic compactness. To do this, we rely on an operational version of the minimal invariance property. In addition, we apply techniques developed herein to reason about FPC programs. Key words: Operational domain theory, recursive types, FPC, realisable functor, algebraic compactness, generic approximation lemma, denotational semantics

An Operational Domain-theoretic Treatment of Recursive Types

We develop an operational domain theory for treating recursive types with respect to contextual equivalence. The principal approach taken here deviates from classical domain theory in that we do not produce the recursive types via usual inverse limits constructions -we have it for free by working directly with the operational semantics. By extending type expressions to functors between some 'syntactic' categories, we establish algebraic compactness. To do this, we rely on an operational version of the minimal invariance property, of which a purely operational proof is given