Josh Berdine, Peter O'Hearn, Uday S. Reddy, and Hayo Thielecke, Linear continuationpassing, Higher-Order and Symbolic Computation 15 (2002), 181--208.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....it can be explained like this: the CPS translation is essentially the composition of two successive (ordinary) CPS translations, and the source language of the second CPS translation is the ordinary call by value lambda calculus without control operators. Therefore, as shown in the literature [5, 4, 15], continuations are used linearly and the target calculus of the second CPS translation can be considered as linear lambda calculus. Continuations in the second CPS translation are metacontinuations in our setting, thus # is linear in the target calculus. The second author exploits this linearity ....

J. Berdine, P. O'Hearn, U. Reddy, and H. Thielecke. Linear Continuation Passing. Higher-Order and Symbolic Computation, pages 181--208, 2002.

....a target language allowing the expression of linearity constraints. More precisely, the CLC calculus is defined to be regular lambda calculus typed with usual types and linear types; this kind of calculus has already been used in work analyzing linearity in CPS translations, e.g. by Berdine et al. [2] and Laird [15] It allows us to give a clear factorization of DJS translation: H H H H LL Linearity of continuations vs. continuation passing. The linearity of CBN continuations should be opposed to the linearity of continuation passing which occurs in CPS translations of the CBV ....

....above is the categorical abstraction of this particular concrete case. 4. CPS Translations As explained in the introduction we use Parigot s lambda mu calculus for encoding classical logic. We use lambda calculus as the target language of the CPStranslations. However, in the spirit of [2], we will design a typing system (a la Curry) which allows to express some linearity constraints; more precisely we add to ordinary intuitionistic types a linear and a non linear negation that are used to type the (translations of) continuations. This typing system may be viewed as a fragment of ....

J. Berdine, P. O'Hearn, U. Reddy, and H. Thielecke. Linear continuation-passing. Higher-Order and Symbolic Computation, 15, 2002.

....the answer is continuation passing style conversion. However, in our linear setting, there are several complications. First, before calling an exception handler, LTAL programs have to dispose of all storage that has been allocated since the handler was installed. Second, as noted in [6], some forms of control ow, such as exceptions and coroutines, can be accomplished using linear CPS translations, whereas other forms such as rst class callcc cannot. Intuitively the reason is that copying continuations requires copying the world . In light of this result, we expect the former ....

Josh Berdine, Peter O'Hearn, Uday S. Reddy, and Hayo Thielecke. Linear continuation-passing. Higher-order and Symbolic Computation, 15(2/3):181-208, 2002.

....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 ....

Josh Berdine, Peter O'Hearn, Uday S. Reddy, and Hayo Thielecke. Linear continuation-passing. HigherOrder and Symbolic Computation, 15:181--208, September 2002.

....Ane CPS Interpretation The source language we consider is the usual call by value, left to right, calculus. One standard cps interpretation is Fischer s continuation rst one [5] in which source procedures are interpreted with the type: D: D R) D R) As investigated by Berdine et.al. [2], this interpretation can be re ned to capture the stylized use of continuations inherent in the procedure call return mechanism: D = D: D R) D R) As usual, toplevel programs are interpreted by answers parameterized by a toplevel continuation: D R) R Functions of ane arrow ....

....making the cps versions of such procedures inexpressible. Now, before we have de ned the translation of terms, we know enough about the cps transformation to characterize its range. 3 Range of CPS First we brie y present an ane variant of the target language of the cps transformation used in [2]. Types are given by the grammar: P : R j A P j P ( P j X j X:P pointed types A : N j P types and the typing judgment is given by the axioms and rules: x : A ; x : A ; x : P x : P ; M : B B = A ; M : A ; x : A ; M : P ; x: M : A P ; M : A P ; ....

J. Berdine, P. W. O'Hearn, U. S. Reddy, and H. Thielecke. Linear continuation-passing. Higher-Order and Symbolic Computation. To appear.

....continuation is passed linearly, so that M can neither discard its current continuation, nor invoke it multiple times. Linear continuation passing is not restricted to languages without control: surprisingly many idioms of control, in which continuations are not first class, adhere to linearity [4]. In the absence of control operators, local answer type polymorphism, naturality and linearity are all easy to see and to prove with a straightforward induction. The addition of call cc to the source language, however, seems to break all these properties beyond repair: in the worst case, no ....

....aim in this section is to use e#ect information to pass continuations linearly whenever there are no control e#ects. The target language with linear typing is defined as in Figure 4. It is essentially the same target language as was used for studying linear continuation passing in earlier work [4], based on Barber and Plotkin s Dual Intuitionistic Linear Logic. In addition to the usual (intuitionistic) application and abstraction, the target language contains linear application, M N , and linear abstraction, #x.M ; the latter will only be used for passing continuations. Continuations ....

[Article contains additional citation context not shown here]

Josh Berdine, Peter W. O'Hearn, Uday Reddy, and Hayo Thielecke. Linear continuation passing. Higher-order and Symbolic Computation, 15(2/3), 2002.

No context found.

Josh Berdine, Peter O'Hearn, Uday S. Reddy, and Hayo Thielecke, Linear continuationpassing, Higher-Order and Symbolic Computation 15 (2002), 181--208.

No context found.

Josh Berdine, Peter O'Hearn, Uday S. Reddy, and Hayo Thielecke, Linear continuationpassing, Higher-Order and Symbolic Computation 15 (2002), 181--208.

No context found.

Josh Berdine, Peter O'Hearn, Uday S. Reddy, and Hayo Thielecke, Linear continuation-passing, Higher-Order and Symbolic Computation, vol. 15 (2002), pp. 181-- 208.

No context found.

Josh Berdine, Peter O'Hearn, Uday S. Reddy, and Hayo Thielecke, Linear continuationpassing, Higher-Order and Symbolic Computation 15 (2002), 181--208.

No context found.

Josh Berdine, Peter O'Hearn, Uday S. Reddy, and Hayo Thielecke, Linear continuationpassing, Higher-Order and Symbolic Computation 15 (2002), 181--208.

No context found.

Josh Berdine, Peter O'Hearn, Uday S. Reddy, and Hayo Thielecke, Linear continuation-passing, Higher-Order and Symbolic Computation, vol. 15 (2002), pp. 181-- 208.

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