An Operational Domain-theoretic Treatment of Recursive Types

Authors:
Weng Kin Ho
Affiliations:
School of Computer Science, The University of Birmingham, Birmingham, United Kingdom
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2006

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Abstract

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.