J. Chirimar, C. A. Gunter, and J. G. Riecke. Linear ML. In Symposium on Lisp and Functional Programming, ACM Press, San Francisco, June 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... functional programming (often involving certain aspects of parallelism) computation is seen as term reduction corresponding to proof reduction (i.e. to the process of cut elimination) Recent work in this area includes Abramsky [1] Benton et al. 6] Gonthier et al. 17, 18] Chirimar et al. [9, 10], and Danos and Regnier [12] On the other hand, in what may be broadly called logic programming (again, often involving concurrency) computation is seen as cut free proof search in certain linear logic theories. From this latter perspective, the cut elimination property is used simply to allow ....

J. Chirimar, C. Gunter, and J. Riecke. Linear ML. In Proc. ACM Symposium on Lisp and Functional Programming, San Francisco. ACM Press, June 1992.

.... in functional programming is in optimization of copying in lazy functional programming language implementation ( singlethreadedness ) studied by Guzm an and Hudak [58] Recent topics involve linear lambda calculus and memory allocation, investigated by Lincoln and Mitchell [70] Chirimar et al. [33, 34], Wadler [90] Mackie [77] and Benton et al. 24] A strong relationship of the multiplicative fragment of linear logic to Petri nets has been demonstrated by Gehlot and Gunter [57, 44, 43] Asperti et al. 12, 14] Engberg and Winskel [41] Marti Oliet and Meseguer [79] and Brown and Gurr ....

J. Chirimar, C. Gunter, and J. Riecke. Linear ML. In Proc. ACM Symposium on Lisp and Functional Programming, San Francisco. ACM Press, June 1992.

....of Girard [Gir87] there is the syntax of Abramsky [Abr90] and there is the semantics of Seely [See89] Each of these has become a standard. Abramsky was inspired by the earlier work of Lafont [Laf88] and Holmstrom [Hol88] and in turn inspired related systems by Chirimar, Gunter, and Riecke [CGR92], Lincoln and Mitchell [LM92] Mackie [Mac91] Troelstra [Tro92] and Wadler [Wad90, Wad91] Seely provided a categorical model, that subsumes other models such as coherence spaces [Gir87] event spaces [Pra91] games [LS91] and the Geometry of Interaction [AJ92] Unfortunately, Abramsky s syntax ....

....B) f u) B Cut Gamma; Delta (t u) B Note the central role played here by Cut. Sequent and natural deduction versions of linear calculus are presented and shown equivalent by Lincoln and Mitchell [LM92] Various mixtures of the two systems have been used by various researchers [BBdPH92, CGR92, Wad90, Wad91]. Id x : A x : A Exchange Gamma; x : A; y : B ; Delta t : C Gamma; y : B ; x : A; Delta t : C Cut Gamma t : A x : A; Delta u : B Gamma; Delta u[t=x ] B Omega R Gamma t : A Delta u : B Gamma; Delta (t ; u) A Omega B) Omega L Gamma; x : A; y : B ....

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J. Chirimar, C. A. Gunter, and J. G. Riecke. Linear ML. In Symposium on Lisp and Functional Programming, ACM Press, San Francisco, June 1992.

....the encoding of linear logic: a variant of Girard s unified logic [10] admits a simpler, more regular treatment than linear logic. This graph system may also serve as a basis for efficient implementations of the various programming languages inspired by linear logic in recent years (e.g. [11, 12, 3]) In fact, work on the calculus [13] suggests an optimality criterion for proof net reduction; our system is optimal in this sense, and so one may even envision optimal implementations of those programming languages. So far we have not succeeded in treating the full linear logic. We seem to have ....

J. Chirimar, C. Gunter, and J. Riecke, "Linear ML." 1991.

.... in which garbage collection was replaced by explicit duplication operations based on linear logic [21] More recent work has attempted to find a linear logical basis for many optimizations in (lazy) functional programming language implementations by concentrating on linear logic as a type system [1, 15, 39, 40, 25, 8, 29, 41]. Other applications include analyzing the control structure of logic programs [7] generalized logic programming [4, 16] and natural language processing [23] A natural characterization of polynomial time computations can be given in a bounded version of linear logic [13] obtained by limiting ....

....the resource sensitivity of linear logic to encode difficult problems in even the propositional fragment of linear logic. Current work is progressing to exploit the unique features of linear logic for use as a type system to study computational complexity [13] and compiler optimization techniques [40, 8, 29, 41, 34, 25], as well as uses in logic programming [16, 3, 4] natural language processing [24, 38] and concurrency [5, 30, 35] These recent contributions are developing linear logic from a theoretical curiosity into a tool that already has practical use within mainstream computer science. ....

J. Chirimar, C. Gunter, and J. Riecke. Linear ML. In Lisp and Functional Programming, 1992. To Appear.

....inference system, here called seq, which is discussed in Section 3.3. Abramsky went on to generalize this system into one incorporating quantifiers and full linear logic, a move which enabled him to interpret linear types in terms of concurrent computations. Recently Chirimar, Gunter, and Riecke [CGR92] have implemented a version of the linear calculus. In this paper we restrict our attention to intuitionistic linear logic. One important property of type systems is subject reduction, which states that if a term t has type A, then any term produced by any number of reduction (evaluation) steps ....

....discard x in 1 The above judgement is provable in seq, nat, and nat2, but after one step of reduction, the judgement becomes x: A 1 which is not provable in any type system discussed in this paper. Chirimar, Gunter, and Riecke have also noticed this failure of subject reduction for open terms [CGR92]. On the other hand, we do have this more general form of subject reduction of the reflexive transitive closure of 0 . That is, we may reduce using 0 anywhere in a term and still preserve the types. With a slight modification of the systems we are working with, an intermediate form of these ....

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J. Chirimar, C. Gunter, and J. Riecke. Linear ML. In Lisp and Functional Programming, 1992. To Appear.

....logic to computing. Early computational models were discussed by Lafont [12] and Holstrom [10] Abramsky wrote a highly influential paper that explored computing applications of both intuitionistic and classical linear logic [1] Other models have been discussed by Chirimar, Gunter, and Riecke [3], Lincoln and Mitchell [13] Reddy [16] and Wadler [21, 22] The particular formulation of linear logic presented here is based on Girard s Logic of Unity, a refinement of linear logic [7] This overcomes some technical problems with other presentations of linear logic, some of which are ....

J. Chirimar, C. A. Gunter, and J. G. Riecke. Linear ML. In Symposium on Lisp and Functional Programming, ACM Press, San Francisco, June 1992.

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J. Chirimar, C. A. Gunter, and J. G. Riecke. Linear ML. In Symposium on Lisp and Functional Programming, ACM Press, San Francisco, June 1992.

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