Full abstraction, totality and PCF
نویسنده
چکیده
Inspired by a question of Riecke, we consider the interaction of totality and full abstraction, asking whether full abstraction holds for Scott’s model of cpos and continuous functions if one restricts to total programs and total observations. The answer is negative, as there are distinct operational and denotational notions of totality. However, when two terms are each total in both senses then they are totally equivalent operationally iff they are totally equivalent in the Scott model. Analysing further, we consider sequential and parallel versions of PCF and several models: Scott’s model of continuous functions, Milner’s fully abstract model of PCF and their effective submodels. We investigate how totality differs between these models. Some apparently rather difficult open problems arise, essentially concerning whether the sequential and parallel versions of PCF have the same expressive power, in the sense of total equivalence.
منابع مشابه
Logical Full Abstraction and PCF
We introduce the concept of logical full abstraction, generalising the usual equational notion. We consider the language PCF and two extensions with “parallel” operations. The main result is that, for standard interpretations, logical full abstraction is equivalent to equational full abstraction together with universality; the proof involves constructing enumeration operators. We also consider ...
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عنوان ژورنال:
- Mathematical Structures in Computer Science
دوره 9 شماره
صفحات -
تاریخ انتشار 1999