Samson Abramsky, Radha Jagadeesan, and Pasquale Malacaria. Full abstraction for PCF. To appear in Information and Computation, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....terms of rigidity, and not in terms of universality. Definition 3 Let A be an object of a category C. X is the set of all finite cliques (sets of points of the web of X) of X, and not of all finite multi cliques (multisets of points of the web of X) In the games considered e.g. in the papers [AJM94, HO94, Nic94], repeated moves are allowed in the interpretation of . 7 These sequential algorithms are not really standard: they are sequential algorithms on sequential data structures (see [Cur94] equipped with a notion of complete plays. This notion can be defined inductively on the construction of ....

Samson Abramsky, Radha Jagadeesan, and Pasquale Malacaria. Full abstraction for PCF. To appear in Information and Computation, 1994.

....t # # u abbreviates #P : # # nat . P t #) # (P u #) Note that the full set theoretic type structure over N# is not a model, because not every set theoretic function N# # N# has a fixed point. However, the usual 11 Scott model based on CPOs (see [Plo77] and the game models of e.g. [AJM96] do provide models of SP # , as do their recursive analogues. The extensional closed term model of PCF also provides a model (which in fact is isomorphic to the recursive game models) 5.3 A constructive pre logical refinement We now describe a constructive refinement from SP to SP # . The basic ....

S. Abramsky, R. Jagadeesan, and P. Malacaria. Full abstraction for PCF. To appear in Information and Computation (1996).

....typically use both Weakening and Contraction. Removing just one of Weakening or Contraction banishes many of these examples. 6. 1 Semantics of Types In the strict parametricity model, types are interpreted as cpo s, i.e. directedcomplete partial orders possessing a least element [Plotkin 1983; Abramsky and Jung 1994]. Level 1 types will always denote countable, flat cpo s, where there is a discretely ordered set of elements arranged just above a least element . More specifically, a type A determines a function [ A] from type environments to cpo s, where a type environment D maps type variables to ....

....to T , which is obtained by distributing Phi over Omega . Our aim is to show that Z and D are isomorphic. To do this, we proceed in four steps. First, we describe the structure of D. This is straightforward, and follows from standard material on recursive domain equations [Plotkin 1983; Abramsky and Jung 1994]. Second, we give the parametricity argument, which relates uses of polymorphic functions to the structure described in the first step. Steps three and four consist of technical results, which use the information from the first two steps to verify that D and Z are isomorphic. Step 1: Structure of ....

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Abramsky, S., Jagadeesan, R., and Malacaria, P. Full abstraction for PCF. To appear in Information and Computation. Abramsky, S. and Jung, A. 1994. Domain theory. In S. Abramsky, D. M. Gabbay, and T. S. E. Maibaum Eds., Handbook of Logic in Computer Science, Volume 3, pp. 1--168. Clarendon Press.

....written as (M; S 0 )# ns , if there exists a value V and a state S 1 such that hM; S 0 i hV; S 1 i. Observational equivalence using program contexts was first defined by [Mor68] It has been studied extensively for call by name and call by value calculus, and its extensions with state [Abr87, AO89, Abr90, Hoa69, MT92, MS88, OT93, Plo76, PS93, SF92]. The definition of observational equivalence for vs is an extension to the definition for v [Mor68] along the lines of [MT92] Definition 4.2 [Observational Equivalence with natural semantics] Let M and N be two vs terms, and ; be the empty state. M is said to be observationally equivalent to ....

S. Abramsky and L. Ong. Full abstraction in the lazy -calculus. Technical report, Imperial College, 1989. To appear in Information and Computation.

....it has allowed various full abstraction results to be obtained, showing that games models capture the behaviour of programs in a precise way. Furthermore, the paradigm is flexible enough to furnish fully abstract models of a wide variety of languages, ranging from purely functional languages [1, 4, 13, 16, 17, 19], to languages with control operators [15] mutable variables [3, 5] and even general references [2] However, despite being grounded on mathematical structures usually associated with concurrency, all of this work has focussed on sequential, deterministic languages. Contribution In this paper we ....

S. Abramsky, R. Jagadeesan, and P. Malacaria. Full abstraction for PCF. To appear in Information and Computation, 199?

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