Abstract

ion for PCF Preliminary Announcement Martin Hyland and Luke Ong 26th July 1993 This note is (intended to be) released in conjunction with a preliminary announcement of Abramsky, Jagadeesan and Malacaria entitled Games and Full Abstraction of PCF. Like Abramsky et al. (but independently), we have found an intensionally fully abstract model for pcf [Plo77]. Our model is a Cartesian closed category of Scott domains all of whose compact elements are definable in pcf. Using Stoughton's Theorem [Sto88], the model can be extensionally collapsed by means of a continuous homomorphism to the least fixpoint, order-extensional, fully abstract model which is shown to be unique by Milner [Mil77]. It is unclear at this stage how our model relates to that of Abramsky et al. Our model of computation is based on a kind of game in which each play consists of a dialogue of questions and answers between two players. This approach is very concrete and in nature goes back to Kleene [Kle78] and Gandy in o...

Citations