Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-20T05:00:40.892Z Has data issue: false hasContentIssue false

Full abstraction, totality and PCF

Published online by Cambridge University Press:  01 February 1999

Department of Computer Science, University of Edinburgh, King's Buildings, Edinburgh EH9 3JZ, UK. E-mail:


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, 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 that essentially concern whether the sequential and parallel versions of PCF have the same expressive power, in the sense of total equivalence.

Research Article
1999 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)