A. Stoughton. Equationally fully abstract models of PCF. In Proc. 5th Int. Conf. Mathematical Foundations of Programming Semantics, pages 271--283. LNCS Vol. 442, Springer-Verlag, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....model was constructed from which it is just a matter of lopping the top element off to arrive at Milner s unique fully abstract model. Refinements We conclude this subection by mentioning some recent refinements of the classical results of Plotkin and Milner by Stoughton [ Stoughton, 1991c; Stoughton, 1991a ] ffl There is only one extensional, continuous model for pcfp; it is precisely the unique fully abstract model. ffl There is an equationally fully abstract model for pcfp distinct from the unique order extensional, continuous, inequationally fully abstract model. More recently, Sieber [ ....

A. Stoughton. Equationally fully abstract models of PCF. In Proc. 5th Int. Conf. Mathematical Foundations of Programming Semantics, pages 271--283. LNCS Vol. 442, Springer-Verlag, 1991.

....is based on partial orders, and if denotational approximation coincides with operational approximation, where M operationally approximates N if in any context C[ Delta] such that C[M ] and C[N ] have base type, if C[M ] reduces to a final answer, then C[N ] returns the same final answer. See [Sto90] for a discussion of equationally fully abstract models) Milner constructed the model using a sophisticated inverse limit, where the finite models were built from operational equivalence classes of terms. Nevertheless, it still tells us little independent of the operational equivalence ....

A. Stoughton. Equationally fully abstract models of PCF. In M. Main, A. Melton, M. Mislove, and D. Schmidt, editors, Mathematical Foundations of Programming Semantics, volume 442 of Lecture Notes in Computer Science, pages 271--283. Springer Verlag, 1990.

....the domain. In this paper, we use prove f.e. completeness for our positive results, and lack of full abstraction in our negative results, thus proving the stronger result in each case. We remark that for extensional models of PCF, full abstraction and f.e. completeness are known to be equivalent [Mi77,St90]. There are non extensional algebraic models of PCF that are f.e. complete but not fully abstract. 5 FP and FP1 are not fully abstract Our goal in this section is to prove that neither FP nor FP1 is fully abstract. We actually prove that FPA is not fully abstract, where FPA is the extension of FP ....

A. Stoughton, Equationally fully abstract models of PCF, Proc. 5th MFPS, Lecture Notes in Computer Science No. 442, Springer-Verlag (1990).

....operationally equivalent. ii) The stable function model, which is neither order extensional nor equationally fully abstract [Ber] BCL] iii) The terminal object of the category of equationally fully abstract, extensional models, which is inequationally fully abstract and order extensional [Mil][Sto2]. A model is inequationally fully abstract iff one term is less than another in the model exactly when the first is operationally less defined than the second. iv) The initial object of the above category, which is neither inequationally fully abstract nor order extensional [Sto2] In contrast, ....

....[Mil] Sto2] A model is inequationally fully abstract iff one term is less than another in the model exactly when the first is operationally less defined than the second. iv) The initial object of the above category, which is neither inequationally fully abstract nor order extensional [Sto2]. In contrast, the only known extensional model of parallel PCF, i.e. PCF augmented with the parallel or operation, is the continuous function model, which is inequationally fully abstract and order extensional [Plo] In fact, a result of Plotkin Milner Berry s shows that this model is the ....

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A. Stoughton. Equationally fully abstract models of PCF. Proceedings of the 5th International Conference on the Mathematical Foundations of Programming Semantics, Lecture Notes in Computer Science, vol. 442, Springer-Verlag, 1990, pp. 271--283.

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