Full abstraction for sequential algorithms: the state of the art
Algebraic methods in semantics
Interdefinability of parallel operations in PCF
Theoretical Computer Science - Special issue: Part B: Logic, semantics, and theory of programming
The formal semantics of programming languages: an introduction
The formal semantics of programming languages: an introduction
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
Mathematical theory of domains
Mathematical theory of domains
Handbook of logic in computer science (vol. 3)
A New Characterization of Type-2 Feasibility
SIAM Journal on Computing
A hierarchy of domains with totality, but without density
Computability, enumerability, unsolvability
Foundations of programming languages
Foundations of programming languages
TACS '97 Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software
Refinement types for specification
PROCOMET '98 Proceedings of the IFIP TC2/WG2.2,2.3 International Conference on Programming Concepts and Methods
Resource-bounded continuity and sequentiality for type-two functionals
ACM Transactions on Computational Logic (TOCL)
Exact real number computations relative to hereditarily total functionals
Theoretical Computer Science
Total Functionals and Well-Founded Strategies
TLCA '99 Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications
Continuous Functionals of Dependent Types and Equilogical Spaces
Proceedings of the 14th Annual Conference of the EACSL on Computer Science Logic
Resource-Bounded Continuity and Sequentiality for Type-Two Functionals
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
On sequential functionals of type 3
Mathematical Structures in Computer Science
Operational domain theory and topology of sequential programming languages
Information and Computation
On the Ubiquity of Certain Total Type Structures
Electronic Notes in Theoretical Computer Science (ENTCS)
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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.