I. Mackie, Lilac --- a functional programming language based on linear logic, Journal of Functional Programming 4 (1993), no. 4, 395--433.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....information flow expressed using logical variables. Walker discusses types supporting more explicit memory management [50] Session types [13] shares the same objective with our mode system. Languages that feature linearity can be found in various programming paradigms. Linear Lisp [4] and Lilac [20] are two examples outside logic programming, while a survey of linear logic programming languages can be found in [23] There is a lot of work on compile time garbage collection other than that based on typing. In logic programming, most of the previous work is based on abstract interpretation ....

Mackie, I., Lilac: A Functional Programming Language Based on Linear Logic. J. Functional Programming, Vol. 4, No. 4 (1994), pp. 1--39.

....computation has an asymmetry between a function s arguments and the value it returns. Logic programming maintains an asymmetry between the program and the goal. Intuitionistic versions of linear logic have been used to explore interesting phenomena in functional computation (see, for example, [18, 1, 6, 28, 15, 2, 5]) logic programming [14] and logical frameworks [9] In this paper, we analyze linear logic in an inherently asymmetric natural deduction formulation following Martin L of s methodology of separating judgments from propositions [19] We require minimal judgmental notions linear hypothetical ....

I. Mackie. Lilac --- a functional programming language based on linear logic. Journal of Functional Programming, 4(4):395--433, 1993.

....analysis of sharing and garbage collection. More concretely, some of the overhead involved in the environment based approach could be avoided by detecting linear usage of variables and directly performing substitutions for such variables. These ideas have led to several abstract machines [16, 17, 18], but all run into diculties with correctly exploiting linearity information. In particular, Wadler [22] and Chirimar et al. 7] tried to give an operational semantics where terms of linear type have exactly one pointer to them. However, their attempts failed mainly because the linearity inherent ....

Ian Mackie. Lilac: A functional programming language based on linear logic. Journal of Functional Programming, 4(4):395-433, 1994.

....Using the Curry Howard isomorphism, we can assign terms to proofs in Intuitionistic Linear Logic. This leads to a refinement of Intuitionistic Logic and the linear version of the hcalculus called the linear term calculus [1] a programming language Lilac based on this idea has been developed [89]. We shall not give the term assignment here. Classical Linear Logic makes a more radical departure from Classical Logic as it is constructive. The term assignment for Classical Linear Logic is shown in the following section. Further Reading The seminal paper by Girard [55] is a must; other ....

I. Mackie. Lilac: A functional programming language based on linear logic. Journal of FunctionaIProgramming, 4(4):1-39, October 1994. (p30)

....in the category. Thus, since we want give a denotational semantics to the rule in the category dI a (via a categorical semantics) we should look for another definition of recursion. The next suggestion is: x 1 : A 1 ; x n : A n ; z : B u : B This rule is actually the one used in [Mac92]. We can now give a denotational semantics with our canonical model dI a , but LTS extended with this rule does not enjoy the Substitution Property. Now, we are trying to extend LTS, where the underlying proof rules 6 for ILL are in Natural Deduction style, with a rule for recursion. LTS would ....

I. Mackie. Lilac : A Functional Programming Language Based on Linear Logic. M.Sc. dissertation, Imperial College, 1992.

....be used to justify program optimisations (one of the motivations for the linear type system of Kobayashi et al. but does not need to be explicitly provided by the programmer. Other linear functional languages have also used type inference to avoid annotating the syntax with linearity information [21, 32]. In the context of session types, it may be that a suitable type inference algorithm could determine which channels correspond to sessions and which to one o communications. We are conscious of the need to produce a syntax which is as simple and exible as possible, in order that the extended ....

I. Mackie. Lilac : A functional programming language based on linear logic. Journal of Functional Programming, 4(4):1-39, October 1994.

....input. The presence of sequential types causes a slight complication: if x : S 2 2 Gamma and x is used in both P and Q, then Tag Gamma (P j Q) must ensure that x is tagged with S 1 in P and with S 1 in Q, or vice versa. Essentially the same problem is encountered in linear type inference [6], and we use the same solution: Tag Gamma (P ) returns a pair (P 0 ; Gamma 0 ) where P 0 is a tagged process and Gamma 0 differs from Gamma only by the possible removal of some usages of sequential types. Then Tag Gamma (P j Q) P 0 j Q 0 ; Gamma 00 ) where Tag Gamma (P ) ....

I. Mackie. Lilac : A functional programming language based on linear logic. Journal of Functional Programming, 4(4):1--39, October 1994.

....can automatically find out which value is linear in the relaxed sense. Promising results were obtained from preliminary experiments with the prototype system. 1 Introduction 1. 1 Linear types A number of type systems based on Girard s linear logic [6] have been proposed for functional languages [1, 3, 13, 21] and concurrent languages [9, 12] They guarantee that certain data structures (called linear values) are accessed just once (or at most once) The distinction between linear values 3 This is a revised version of the technical report TR98 02 from Department of Information Science, University of ....

Ian Mackie. Lilac : A functional programming language based on linear logic. Journal of Functional Programming, 4(4):1--39, October 1994.

.... inherited from either BLL or the linear term calculus. 5. 1 Type Reconstruction Algorithm As was noted in Benton et al. 1992) there exists a type reconstruction algorithm which is sound and complete for the term assignment to ILL (without the quantifier rules) based on the algorithm given in Mackie (1991) . In this section, I will show how to extend this algorithm for bounded linear terms. 5.1.1 Bounded Linear Natural Deduction First, it will be necessary to define a system of bounded linear natural deduction (BLND) along with a term assignment system (Figure 5.1) Here, the notation of Mackie ....

....(1991) In this section, I will show how to extend this algorithm for bounded linear terms. 5.1.1 Bounded Linear Natural Deduction First, it will be necessary to define a system of bounded linear natural deduction (BLND) along with a term assignment system (Figure 5. 1) Here, the notation of Mackie (1991) is used: Gammaj Theta t : A stands for Gamman Theta t : A, where Gamma and Theta are multisets and Theta Gamma. Intuitively, Theta represents the unused portion of the type assignments in Gamma, i.e. when giving a type to t using the assumptions in Gamma, the leftover ....

[Article contains additional citation context not shown here]

I. Mackie, Lilac - a functional programming language based on linear logic. Master's Thesis, Imperial College, London, 1991.

.... 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 [30] Interpretations of ....

I. Mackie. Lilac - a functional programming language based on linear logic. Master's Thesis, Imperial College, London, 1991.

....be valuable. We now turn to related work on linear functional programming. The informal connection between imperative like state transformations and linear functions was emphasized from the beginning in linear logic. It formed part of the motivation for a number of linear functional languages [Mackie 1994; Lafont 1988; Holmstrom 1988; Chirimar et al. 1994] where linearity could be used to restrict the number of pointers to functional values and, in some cases, guarantee the safety of destructive array update. This connection was illustrated particularly clearly by Wadler [1990] by translating an ....

Mackie, I. 1994. Lilac : A functional programming language based on linear logic. Journal of Functional Programming 4, 4 (Oct.), 395--433.

....analysis of sharing and garbage collection. More concretely, some of the overhead involved in the environment based approach could be avoided by detecting linear usage of variables and directly performing substitutions for such variables. These ideas have led to several abstract machines [16, 17, 18], but all run into difficulties with correctly exploiting linearity information. In particular, Wadler [22] and Chirimar et al. 7] tried to give an operational semantics where terms of linear type have exactly one pointer to them. However, their attempts failed mainly because the linearity ....

Ian Mackie. Lilac: A functional programming language based on linear logic. Journal of Functional Programming, 4(4):395--433, 1994.

....or input. The presence of session types causes a slight complication: if x : S 2 2 Gamma and x is used in both P and Q, then Tag Gamma (P j Q) must ensure that x is tagged with S 1 in P and with S 1 in Q, or vice versa. Essentially the same problem is encountered in linear type inference [10], and we use the same solution: Tag Gamma (P ) returns a pair (P 0 ; Gamma 0 ) where P 0 is a tagged process and Gamma 0 differs from Gamma only by the possible removal of some usages of session types. Then 12 Tag Gamma (P j Q) P 0 j Q 0 ; Gamma 00 ) where Tag Gamma (P ) ....

I. Mackie. Lilac : A functional programming language based on linear logic. Journal of Functional Programming, 4(4):1--39, October 1994.

....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 is incoherent with Seely s semantics: ....

I. Mackie, Lilac: a functional programming language based on linear logic. Master's Thesis, Imperial College London, 1991.

....point (1) because equalities on C are inherited by . Correctness allows to use as specified in point (2) since is Church Rosser and Strong Normalizing. As far as we know, nobody else gives a solution to both problems expressed in points (1) and (2) once fixed Gamma ILL . In [10] the point (1) is developed for the language A , presented in [1] The syntactical heavyness of A , the need to implement commuting conversions and the non satisfactory operational semantics, makes it difficult to view A as a resource conscious paradigmatic language for every day programming. ....

I. Mackie. Lilac: A functional programming language based on linear logic. Master's thesis, University of London, 1991.

No context found.

I. Mackie, Lilac --- a functional programming language based on linear logic, Journal of Functional Programming 4 (1993), no. 4, 395--433.

No context found.

I. Mackie, Lilac --- a functional programming language based on linear logic, Journal of Functional Programming 4 (1993), no. 4, 395--433.

No context found.

I. Mackie, Lilac --- a functional programming language based on linear logic, Journal of Functional Programming, vol. 4 (1993), no. 4, pp. 395--433.

No context found.

I. Mackie, Lilac --- a functional programming language based on linear logic, Journal of Functional Programming 4 (1993), no. 4, 395--433.

No context found.

I. Mackie, Lilac: a functional programming language based on linear logic. Master's Thesis, Imperial College London, 1991. 21 Maraist et. al.

No context found.

I. Mackie. Lilac : A functional programming language based on linear logic. Journal of Functional Programming, 4(4):1--39, October 1994.

No context found.

Ian Mackie. Lilac: A functional programming language based on linear logic. Journal of Functional Programming, 4(4):395--433, October 1994.

No context found.

I. Mackie, Lilac --- a functional programming language based on linear logic, Journal of Functional Programming 4 (1993), no. 4, 395--433.

No context found.

I. Mackie, Lilac --- a functional programming language based on linear logic, Journal of Functional Programming, vol. 4 (1993), no. 4, pp. 395--433.

No context found.

I. Mackie. Lilac : A functional programming language based on linear logic. Journal of Functional Programming, 4(4):1--39, October 1994.

First 50 documents

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