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Finitary PCF is not decidable
 Theoretical Computer Science
, 1996
"... The question of the decidability of the observational ordering of finitary PCF was raised [5] to give mathematical content to the full abstraction problem for PCF [9, 14]. We show that the ordering is in fact undecidable. This result places limits on how explicit a representation of the fully abstra ..."
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Cited by 25 (0 self)
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The question of the decidability of the observational ordering of finitary PCF was raised [5] to give mathematical content to the full abstraction problem for PCF [9, 14]. We show that the ordering is in fact undecidable. This result places limits on how explicit a representation of the fully abstract model can be. It also gives a slight strengthening of the author’s earlier result on typed λdefinability [6].
A Relational Account of CallbyValue Sequentiality
 IN: PROC. 12TH SYMP. LOGIC IN COMPUTER SCIENCE
, 1999
"... We construct a model for FPC, a purely functional, sequential, callbyvalue language. The model is built from partial continuous functions, in the style of Plotkin, further constrained to be uniform with respect to a class of logical relations. We prove that the model is fully abstract. ..."
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Cited by 13 (2 self)
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We construct a model for FPC, a purely functional, sequential, callbyvalue language. The model is built from partial continuous functions, in the style of Plotkin, further constrained to be uniform with respect to a class of logical relations. We prove that the model is fully abstract.
Extending Abramsky’s Lazy Lambda Calculus: (Non)Conservativity of Embeddings
, 2013
"... Abstract. Our motivation is the question whether the lazy lambda calculus, a pure lambda calculus with the leftmost outermost rewriting strategy, considered under observational semantics, or extensions thereof, are an adequate model for semantic equivalences in realworld purely functional programmi ..."
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Abstract. Our motivation is the question whether the lazy lambda calculus, a pure lambda calculus with the leftmost outermost rewriting strategy, considered under observational semantics, or extensions thereof, are an adequate model for semantic equivalences in realworld purely functional programming languages, in particular for a pure core language of Haskell. We explore several extensions of the lazy lambda calculus: addition of a seqoperator, addition of data constructors and caseexpressions, and their combination, focusing on conservativity of these extensions. In addition to untyped calculi, we study their monomorphically and polymorphically typed versions. For most of the extensions we obtain nonconservativity which we prove by providing counterexamples. However, we prove conservativity of the extension by data constructors and case in the monomorphically typed scenario. 1