A type-theoretical alternative to ISWIM, CUCH, OWHY
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
On full abstraction for PCF: I, II, and III
Information and Computation
Information and Computation
On sequential functionals of type 3
Mathematical Structures in Computer Science
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As Dag Normann has recently shown, the fully abstract model for PCF of hereditarily sequential functionals is not ω-complete and therefore not continuous in the traditional terminology (in contrast to the old fully abstract continuous dcpo model of Milner). This is also applicable to a wider class of models such as the recently constructed by the author fully abstract (universal) model for PCF+ = PCF+parallel if. Here we will present an outline of a general approach to this kind of "natural" domains which, although being non-dcpos, allow considering "naturally" continuous functions (with respect to existing directed "pointwise", or "natural" least upper bounds) and also have appropriate version of "naturally" algebraic and "naturally" bounded complete "natural" domains. This is the non-dcpo analogue of the well-known concept of Scott domains, or equivalently, the complete f-spaces of Ershov. In fact, the latter version of natural domains, if considered under "natural" Scott topology, exactly corresponds to the class of f-spaces, not necessarily complete.