Wadler, P. 1993. A taste of linear logic. In Mathematical Foundations of Computer Science. Lecture Notes in Computer Science, vol. 711. Springer-Verlag, Gdansk, Poland.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....: 3; halt) in y: 2; halt; D) letlin k = ###. z : 3; halt) in y: 2; k (E) letlin k0 = ###. halt) in Fig. 1. Examples of Information Flow in CPS k is not used in one of the branches, then information about x can be learned by observing z. Linear type systems [2, 13, 33, 34] can express exactly the constraint that k is used in both branches. By making k s linearity explicit, the type system can use the additional information to recover the precision of the source program analysis. Fragment D illustrates our simple approach: In addition to a normal let construct, we ....

Philip Wadler. A taste of linear logic. In Mathematical Foundations of Computer Science, volume 711 of Lecture Notes in Computer Science. Springer-Verlag, 1993.

....b. However, this code is secure; there is no information ow between x and b in B because the continuation k is invoked in both branches. On the other hand, as example C shows, if k is not used in one of the branches, then information about x can be learned by observing b. Linear type systems [2, 19, 43, 44] can express exactly the constraint that k is used in both branches. By making k s linearity explicit, the type system can use the additional information to recover the precision of source program analysis. Fragment D illustrates our simple approach; in addition to a normal let construct, we ....

....similar correctness results for this transformation. 6. Related Work The constraints imposed by linearity can be seen as a form of resource management [19] in this case limiting the set of possible future computations. Linearity has been more widely used in the context of memory consumption [2, 8, 43, 44]. Linear continuations have been studied in terms of their category theoretic semantics [17] and also as a computational interpretation of classical logic [6] Polakow and Pfenning have investigated the connections between ordered linear logic, stack based abstract machines, and CPS [34] Berdine ....

Wadler, P.: 1993, `A Taste of Linear Logic'. In: Mathematical Foundations of Computer Science, Vol. 711 of Lecture Notes in Computer Science. SpringerVerlag, pp. 185-210. 29

....and related systems in which the (multi)sets of formulae occuring in sequents are split into di erent zones. Formulae in some zones are treated classically, whilst those in other zones are treated linearly. Intuitionistic logics inspired by LU have been proposed by Plotkin [Plo93] and Wadler [Wad93]. It is desirable to study the proof and model theory of such systems directly, rather than treating them as syntactic sugar for, for example, ordinary linear logic (if only to verify that it is possible to treat them as such syntactic sugar) The logic of this paper should turn out to be ....

P. Wadler. A taste of linear logic. In A. M. Borzyszkowski and S. Sokolowski, editors, Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science, number 711 in Lecture Notes in Computer Science, pages 185-210, 1993.

....region variables can create aliases, making it impossible to tell by inspection whether any copies exist. 2.3 Alias Control We desire a system for alias control that can easily be enforced by the type system, without expensive and complex program analyses. One possibility is a linear type system [12, 37, 38]. In a linear type system, aliasing would be trivially controlled; any use of a region name would consume that name, ensuring that it could not be used elsewhere. Thus, in a linear type system, the naive rules for allocating and deallocating regions would be sound. Unfortunately, a linear type ....

Philip Wadler. A taste of linear logic. In Mathematical Foundations of Computer Science, volume 711 of LNCS, Gdansk, Poland, August 1993. Springer-Verlag.

....z. However, this code is secure; there is no information flow between x and z in B because the continuation k is invoked in both branches. On the other hand, as example C shows, if k is not used in one of the branches, then information about x can be learned by observing z. Linear type systems [2, 17, 37, 38] can express exactly the constraint that k is used in both branches. By making k s linearity explicit, the type system can use the additional information to recover the precision of source program analysis. Fragment D illustrates our simple approach; in addition to a normal let construct, we ....

....similar correctness results for this transformation. 6. Related Work The constraints imposed by linearity can be seen as a form of resource management [17] in this case limiting the set of possible future computations. Linearity has been more widely used in the context of memory consumption [2, 7, 37, 38]. Linear continuations have been studied in terms of their category theoretic semantics [15] and also as a computational interpretation of classical logic [6] Polakow and Pfenning have investigated the connections between ordered linear logic, stack based abstract machines, and CPS [28] Berdine, ....

Wadler, P.: 1993, `A Taste of Linear Logic'. In: Mathematical Foundations of Computer Science, Vol. 711 of Lecture Notes in Computer Science. pp. 185--210.

....present in the area. Thirdly, on showing that the restrictions on # abstraction in substructural logics has useful parallels in computation where resources may be consumed by computation. Wadler and colleagues show that this kind of term system has connections with functional programming [160, 278, 279, 281, 280, 282, 283]. 2.11 Structurally Free Logic A very recent innovation in the proof theory of substructural logics is the advent of structurally free logic. The idea is not new it comes from a 1976 essay by Bob Meyer [171] However, the detailed exposition is new, dating from 1997 [42, 41, 93] The ....

PHILIP WADLER. "A Taste of Linear Logic". In Mathematical Foundations of Computer Science, volume 711 of Lecture Notes in Computer Science, Gdansk, Poland, August 1993. Springer-Verlag.

....##) in letlin k2 = #k. z : 2; k ##) in if x then letlin k = ###. k1 k0) in k2 k else letlin k = ###. k2 k0) in k1 k Fig. 1. Examples of Information Flow in CPS k is not used in one of the branches, then information about x can be learned by observing z. Linear type systems [2, 13, 33, 34] can express exactly the constraint that k is used in both branches. By making k s linearity explicit, the type system can use the additional information to recover the precision of the source program analysis. Fragment D illustrates our simple approach; in addition to a normal let construct, we ....

Philip Wadler. A taste of linear logic. In Mathematical Foundations of Computer Science, volume 711 of Lecture Notes in Computer Science. Springer-Verlag, 1993.

....to stateful programming. These sections are primarily interested in the static semantics of LTT and treat its operational semantics only informally. We then present the framework for modular development of operational semantics in Section 6. This paper assumes familiarity with linear logic [6, 18] and with the propositions as types correspondence [9] Additional familiarity with LF and logical frameworks in general will be helpful, but is not required. 2 Intuitionistic LTT The LTT type theory consists of two parts: a proof sub language, and a computational programming language built ....

Philip Wadler. A taste of linear logic. In Mathematical Foundations of Computer Science, volume 711 of Lecture Notes in Computer Science. Springer-Verlag, 1993.

....x 1 , x 2 , and x are all aliases for the same location, even though they have different types. Consequently, the initialization flags do not prevent a field from being initialized twice. It is possible to use monads [Wadler 1990a; Launchbury and Peyton Jones 1995] or linear types [Girard 1987; Wadler 1990b; 1993] to ensure that a tuple is initialized exactly once, but we have avoided these approaches in the interest of a simpler type system. The presence of uninitialized values also raises some garbage collection issues; in Section 8 we discuss how our implementation deals with these issues. 6.1 ....

Wadler, P. 1993. A taste of linear logic. In Mathematical Foundations of Computer Science. Lecture Notes in Computer Science, vol. 711. Springer-Verlag, Gdansk, Poland.

....using standard programming language techniques [VSI96] Heintze and Riecke [HR98] have shown that security labels can be applied to a the typed lambda calculus with reference types.Agat shows how to blind certain eliminate covert timing channels [Aga00] by translation. Linear language constructs [Wad90, Wad93, Abr93] have been used to regulate resource consumption. Linear continuations have been introduced earlier, but in order to study their categorytheoretic semantics [Fil92] Riely et al. have developed a notion of partial typing that allows statements to be made about type correctness in a distributed ....

Philip Wadler. A taste of linear logic. In Mathematical Foundations of Computer Science, volume 711 of Lecture Notes in Computer Science. Springer-Verlag, August-September 1993.

....reader. Also most fragments of Linear Logic are undecidable. This makes the reachability problem for LLPNs based on such fragment undecidable. 2 Chapter 7 Bibliographic Remarks Introductions to Linear logic apart from Girard s original paper [Gir87] are available in [Sce93] Tro93] Tro92] and [Wad93]. For a thorough treatment of decidability and complexity issues of the various fragments of Linear Logic we refer the reader to [LSS92] An abridged version of this paper has been published as [Far98] 30 Bibliography [Bro89] C. Brown. Relating Petri Nets to Formulae of Linear Logic. Technical ....

P. Wadler. A Taste of Linear Logic. In Mathematical Foundations of Computer Science, pages 185-210. Springer-Verlag, 1993.

....when this is acceptable. Many people have paid particular attention to the issue of update in place and associated efficiences of implementation. Examples include the unique types of Clean [11] Guzman and Hudak s single threaded lambda calculus [26] and numerous applications of linear logic [5, 29, 41, 136, 137]. This work gives useful insights into the way functional languages make use of the store available to them; it is however quite distinct from the aim of this dissertation, which is to look at names and references as convenient and powerful 126 CHAPTER 6. CONCLUSION programming constructs in ....

P. Wadler. A taste of linear logic. In MFCS '93 [58]. (p. 125)

....x 1 , x 2 , and x are all aliases for the same location, even though they have di#erent types. Consequently, the initialization flags do not prevent a field from being initialized twice. It is possible to use monads [Wadler 1990a; Launchbury and Peyton Jones 1995] or linear types [Girard 1987; Wadler 1990b; 1993] to ensure that a tuple is initialized exactly once, but we have avoided these approaches in the interest of a simpler type system. The presence of uninitialized values also raises some garbage collection issues; in Section 8 we discuss how our implementation deals with these issues. From System ....

Wadler, P. 1993. A taste of linear logic. In Mathematical Foundations of Computer Science.

....region variables can create aliases, making it impossible to tell by inspection whether any copies exist. 2.3 Alias Control We desire a system for alias control that can easily be enforced by the type system, without expensive and complex program analyses. One possibility is a linear type system [12, 37, 38]. In a linear type system, aliasing would be trivially controlled; any use of a region name would consume that name, ensuring that it could not be used elsewhere. Thus, in a linear type system, the naive rules for allocating and deallocating regions would be sound. Unfortunately, a linear type ....

Philip Wadler. A taste of linear logic. In Mathematical Foundations of Computer Science, volume 711 of LNCS, Gdansk, Poland, August 1993. Springer-Verlag.

....thus at the end of the sequence, x 0 , x 1 , and x are all aliases for the same location, even though they have di#erent (but compatible) types. Consequently, the initialization flags do not prevent a field from being 16 initialized twice. It is possible to use monads [44, 22] or linear types [18, 45, 46] to ensure that a tuple is initialized exactly once, but we have avoided these approaches in the interest of a simpler type system. The static semantics for # A are given in Figure 14. Figure 15 presents the type translation from # H to # A . All that happens is that initialization flags ....

Philip Wadler. A taste of linear logic. In Mathematical Foundations of Computer Science, volume 711 of LNCS, Gdansk, Poland, August 1993. Springer-Verlag.

....are important for models of reference counting implementations, but are unnecessary here since our operational semantics is formulated at a slightly higher level of abstraction where we do not keep explicit reference counts. Other closely related formulations of linear logic can be found in [Wad93, BBdPH93, MOTW95]. 2.1 Syntax Definition 2.1 describes the syntax of terms. We differ from Plotkin in that we distinguish between two kinds of variables: non linear variables (ranged over by x, y and z) which may be freely duplicated or discarded, and linear variables (ranged over by a, b, c and d) which must ....

Philip Wadler. A taste of linear logic. In Mathematic Foundations of Computing Science, number 711 in LNCS. Springer-Verlag, August 1993.

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Wadler, P. 1993. A taste of linear logic. In Mathematical Foundations of Computer Science. Lecture Notes in Computer Science, vol. 711. Springer-Verlag, Gdansk, Poland.

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Wadler, P. 1993. A taste of linear logic. In Mathematical Foundations of Computer Science. Lecture Notes in Computer Science, vol. 711. Springer-Verlag, Gdansk, Poland.

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Wadler, P. 1993. A taste of linear logic. In Mathematical Foundations of Computing Science (MFCS'93) (Gdansk, Aug. 1993), pp. 185--210. Springer-Verlag LNCS 711. Invited Talk.

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Philip Wadler. A taste of linear logic. In Mathematical Foundations of Computer Science,volume 711 of LNCS, Gdansk, Poland, August 1993. Springer-Verlag.

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Philip Wadler. A taste of linear logic. In Mathematical Foundations of Computer Science, volume 711 of Lecture Notes in Computer Science. Springer-Verlag, August-September 1993.

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Philip Wadler. A taste of linear logic. In Mathematical Foundations of Computing Science, Gdansk, August 1993. Springer-Verlag LNCS 711. Invited Talk. 49

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P. Wadler. A taste of linear logic. In MFCS '93 [58]. (p. 125)

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P. Wadler. A taste of linear logic. In Mathematical Foundations of Computing Science, 1993. LNCS 711.

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P. Wadler. A taste of linear logic. In Mathematical Foundations of Computing Science, Gdansk, Poland, August 1993. Springer Verlag LNCS 711.

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