On Full Abstraction for PCF: I, II, and III

On Full Abstraction for PCF: I, II, and III

We present an order-extensional, order (or inequationally) fully abstract model for Scott's language pcf. The approach we have taken is very concrete and in nature goes back to S. C Kleene (1978, in ``General Recursion Theory II, Proceedings of the 1977 Oslo Symposium,'' NorthHolland, Amsterdam) and R. O. Gandy (1993, ``Dialogues, Blass Games, Sequentiality for Objects of Finite Type,'' unpubli...

On Full Abstraction for Pcf : I , Ii And

Full Abstraction for PCF

An intensional model for the programming language PCF is described, in which the types of PCF are interpreted by games, and the terms by certain “history-free” strategies. This model is shown to capture definability in PCF. More precisely, every compact strategy in the model is definable in a certain simple extension of PCF. We then introduce an intrinsic preorder on strategies, and show that i...

Full abstraction for probabilistic PCF

We present a probabilistic version of PCF, a well-known simply typed universal functional language. The type hierarchy is based on a single ground type of natural numbers. Even if the language is globally call-byname, we allow a call-by-value evaluation for ground type arguments in order to provide the language with a suitable algorithmic expressiveness. We describe a denotational semantics bas...

Full abstraction, totality and PCF

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 the...