Robin Milner. Fully abstract models of typed lambda-calculi. Theoretical Computer Science, 4:1--22, 1977. 59  Home/Search   Document Not in Database   Summary   Related Articles   Check

....outside when one subprogram is replaced by the other. This kind of equality is called observational equality. For simply typed programs, the extensional equality and the observational equality are the same. This is known as the context lemma and has been proved for the first time by R. Milner in [12] for simply typed combinators and call byname evaluation using an analysis of the reductions of terms. In the following we give a proof of the context lemma for simply typed programs that include also recursion. We use the call by value interpretation and the call by name interpretation of the ....

R. Milner. Fully abstract models of typed lambda-calculi. Theoretical Computer Science, 4:1--22, 1977.

....to be transferable, in principle, to object languages. In a later exposition we wish to report how the proposed typed syntax can be a powerful tool for language analysis when coupled with process theoretic reasoning techniques. From the viewpoint of the semantic study of sequentiality [6, 10, 29], our work positions sequentiality as a sub class of the general universe of name passing interactive behaviour. This characterisation allows us to delineate sequentiality against the background of a broad computational universe which, among others, includes concurrency and non determinism, ....

....nite. In particular, for our full abstraction result, we need nite processes which are type wise translatable to (the interpretation of) PCF terms. To this end, we rst show that the congruence = seq can be obtained by only closing terms under j, given an appropriate base (Context Lemma, cf. [29]) Then we use the following result to unfold replication. Proposition 7. open replication) Assume P 1 j P 2 j R where R is a replication with subject x. Then P 1 j P 2 j R = seq (P 1 j R) j ( x) P 2 j R) The proof of Proposition 7 uses a bisimulation induced by the typed transition ....

[Article contains additional citation context not shown here]

Milner, R., Fully abstract models of typed lambda calculi. TCS, 4:1-22, 1977.

....[44] simpli ed Morris style contextual equivalence to weak head reduction and made it a standard notion to reason about program equivalence. However, since it is not very practical to prove contextual equivalence directly, alternative characterizations have been proposed. For instance, Milner [34] introduced his context lemma to reduce the need for fullblown contexts to evaluation contexts. The use of CCS style bisimilarity [35] as a simpler operational method to reason about equivalences in functional programming languages, dates from the early 90s, when Abramsky [1] and Abramsky and Ong ....

....context since region allocations and deallocations do not in uence the termination semantics of the region calculus. A notion of bisimilarity based on all evaluation contexts is called experimental equivalence by Gordon [16,17] and would provide an alternative formulation of Milner s Context Lemma [34]. The transition system has some very useful properties. The following lemma expresses that a well typed converging expression always allows a transition: and e . Then there exists an observation such that the transition (e : exists. Moreover, if Safe ( we have ....

[Article contains additional citation context not shown here]

Robin Milner. Fully abstract models of typed lambda-calculi. Theoretical Computer Science, 4:1-22, 1978.

....or novel. The operational semantics is given as a rewrite relation analogous to operational semantics that have been given for a variety of languages. A good discussion of operational semantics and the relation between operational and denotational semantics can be found in [Plotkin, 1977] or [Milner, 1977]. Although the operational semantics presented here is not novel, it is necessary for a rigorous discussion of lifting transformations. The language defined here serves as a formal model of deterministic compu tation. The language defined in the next section serves as a formal model of ....

Robin Milner. Fully abstract models of typed lambda-calculi. The- oretical Computer Science, 4(1):1-23, 1977.

....languages, The author acknowledges the support of Oxford University Computing Laboratory particularly those with higher types, has proved to be a very subtle and difficult one. The famous Full Abstraction Problem for PCF , raised by Plotkin in 1977 and studied intensively ever since [8, 26, 29, 31], remained open until very recently, when a number of solutions emerged [1, 3, 22, 27, 28] One successful approach was via game semantics, a novel kind of model which includes more intensional information than traditional domain theoretic ones. The correspondence between the strategies used to ....

R. Milner. Fully abstract models of typed lambda-calculi. Theoretical Computer Science, 4:1--22, 1977.

....Abstraction : 48 5 Universality 49 5.1 Recursive Strategies : 50 5. 2 Universal Terms : 51 1 Introduction The Full Abstraction Problem for PCF [Plo77, Mil77, BCL85, Cur92b] is one of the longest standing problems in the semantics of programming languages. There is quite widespread agreement that it is one of the most dicult; there is much less agreement as to what exactly the problem is, or more particularly as to the precise criteria for a solution. The usual ....

....to the precise criteria for a solution. The usual formulation is that one wants a semantic characterization of the fully abstract model (by which we mean the inequationally fully abstract order extensional model, which Milner proved to be uniquely speci ed up to isomorphism by these properties [Mil77]) The problem is to understand what should be meant by a semantic characterization . Our view is that the essential content of the problem, what makes it important, is that it calls for a semantic characterization of sequential, functional computation at higher types. The phrase sequential ....

Robin Milner. Fully abstract models of typed lambda-calculi. Theoretical Computer Science, 4:1-22, 1977.

.... The intricacies arising from the combination of computational features in the language mean that the search for a good, syntax free description of the fully abstract model of Idealized Algol raises significant problems over and above those associated with the full abstraction problem for PCF [20, 29]. In a previous paper [5, 6] we gave the first fully abstract model of Idealized Algol with active, i.e. possibly side effecting, expressions. It is significantly harder to capture the pure version of Idealized Algol originally proposed by Reynolds, in which a sharp distinction is drawn ....

R. Milner. Fully abstract models of typed lambda-calculi. Theoretical Computer Science, 4:1--22, 1977.

.... are present in the language, most notably higher order functions and recursion, the problem of achieving such a construction has proved to be very subtle and difficult; the most basic case is the well known Full Abstraction problem for PCF, which has been studied intensively for some 20 years [9, 18,23, 25]. In a previous paper, game semantics was used as the basis for a solution to this problem [4] namely, a description of the fully abstract model given completely independently of the syntax of PCF. This semantics can be seen as offering an analysis in the light of the results obtained in [1, ....

R. Milner. Fully abstract models of typed lambdacalculi. Theoretical Computer Science, 4:1--22, 1977.

....[41] simplified Morris style contextual equivalence to weak head reduction and made it a standard notion to reason about program equivalence. However, since it is not very practical to prove contextual equivalence directly, alternative characterizations have been proposed. For instance, Milner [32] introduced his context lemma to reduce the need for full blown contexts to evaluation contexts. The use of CCS style bisimilarity [33] as a simpler operational method to reason about equivalences in functional programming languages, dates from the early 90s, when Abramsky [1] and Abramsky and Ong ....

....since region allocations and deallocations do not influence the termination semantics of the region calculus. A notion of bisimilarity based on all evaluation contexts is called experimental equivalence by Gordon [17, 18] and would provide an alternative formulation of Milner s context Lemma [32]. The labeled transition system described above is a superset of the system that is required to define bisimilarity for a polymorphically typed call by value lambda calculus. This suggests that the region calculus enriches a Hindley Milner polymorphic lambda calculus without a#ecting ....

Robin Milner. Fully abstract models of typed lambda-calculi. Theoretical Computer Science, 4:1--22, 1978.

....[41] simpli ed Morris style contextual equivalence to weak head reduction and made it a standard notion to reason about program equivalence. However, since it is not very practical to prove contextual equivalence directly, alternative characterizations have been proposed. For instance, Milner [32] introduced his context lemma to reduce the need for full blown contexts to evaluation contexts. The use of CCS style bisimilarity [33] as a simpler operational method to reason about equivalences in functional programming languages, dates from the early 90s, when Abramsky [1] and Abramsky and Ong ....

....since region allocations and deallocations do not in uence the termination semantics of the region calculus. A notion of bisimilarity based on all evaluation contexts is called experimental equivalence by Gordon [17, 18] and would provide an alternative formulation of Milner s context Lemma [32]. The labeled transition system described above is a superset of the system that is required to de ne bisimilarity for a polymorphically typed call by value lambda calculus. This suggests that the region calculus enriches a Hindley Milner polymorphic lambda calculus without a ecting ....

Robin Milner. Fully abstract models of typed lambda-calculi. Theoretical Computer Science, 4:1-22, 1978.

....to satisfy: N ( M x:M 1 ) 9N 1 : N y:N 1 8P 2 : M 1 [P=x] N 1 [P=y] Further details are given in the next section. The applicative bisimulation relation can be described in a more traditional way (from the point of view of calculus) as a Morris style contextual congruence [Mor68, Plo77, Mil77, Bar84]. De nition 2.4 The relation . on is de ned by N 8C[ 2 : C[M ] C[N ] This is extended to in the same way as . Proposition 2.5 . This is a special case of a result we will prove later. Our proof will make essential use of domain logic, despite the fact that ....

....language semantics, this is not very useful. In the next section, we shall study full abstraction in a syntax directed framework, using our domain logic as a tool. 26 6 Lambda Transition Systems considered as Programming Languages The classical discussion of full abstraction in the calculus [Plo77, Mil77] is set in the typed calculus with ground data. As remarked in the Introduction, this material has not to date been transferred successfully to the pure untyped calculus. To see why this is so, let us recall some basic notions from [Plo77, Mil77] Firstly, there is a natural notion of ....

[Article contains additional citation context not shown here]

R. Milner. Fully abstract models of typed lambda-calculi. Theoretical Computer

....order extensional models; a model is orderextensional if elements of the function spaces are ordered according to the pointwise order. If we limit attention to extensional models, that is models where denotations correspond to functions between input and output values, then from Milner s results [12] it is known that any extensional model of PCF which is fully abstract is necessarily order extensional. Here we focus on stable bistructure models of PCF, as a means to obtain order extensional models which at the same time take some account of the way a function is computed. Stable bistructures ....

Milner, A.R.G., Fully abstract models of typed lambda-calculi. Theoretical Computer Science 4(1), pp. 1-23, 1977.

No context found.

Robin Milner. Fully abstract models of typed lambda-calculi. Theoretical Computer Science, 4:1--22, 1977. 59

No context found.

Milner, R. (1977). Fully abstract models of typed lambda-calculi. TCS 4, 1-22.

No context found.

R. Milner. Fully abstract models of typed lambda-calculi. Theoretical Computer Science, 4:1--23, 1977.

No context found.

R. Milner. Fully abstract models of typed lambda-calculi. Theoretical Computer Science, 4(1):1--22, 1977.

No context found.

R. Milner. Fully abstract models of typed lambda-calculi. Theoretical Computer Science, 4(1):1--22, 1977.

No context found.

Milner, R., Fully abstract models of typed lambda calculi. TCS, 4:1-22, 1977.

No context found.

R. Milner. Fully abstract models of typed lambda-calculi. Theoretical Computer Science, 4:1--22, 1977.

No context found.

R. Milner. Fully abstract models of typed lambda-calculi. Theoretical Computer Science, 4:1--22, 1977.

No context found.

Milner, R., Fully Abstract Models of Typed Lambda-Calculi, Theoretical Computer Science, volume 4 (1977), 1-22, 1997.

No context found.

Milner, R., Fully abstract models of typed lambda calculi. TCS, 4:1-22, 1977.

No context found.

Milner, R., Fully abstract models of typed lambda calculi. TCS, 4:1-22, 1977.

No context found.

R. Milner, Fully abstract models of typed lambda-calculi, Theoretical Computer Science 4, 1-23 (1977).

No context found.

Robin Milner. Fully abstract models of typed lambda calculi. Theoretical Computer Science, 4(1), 1977.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC