T. Griffin. A formula-as-types notion of control. In Proceedings of the 17th Annual ACM Symposium on Principles of Programming Languages, pages 47-- 58, San Francisco, California, January 17-19 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... Oyster and CLAM [8] and Coq [14] In [27] a computational interpretation of classical natural deduction is discussed, in which lambda terms may be extracted from proofs; this investigation is continued in [28] For other papers dealing with computational interpretations of classical logic see [19], 15] 25] and [26] These systems typically supply a computational interpretation to all classical proofs; in contrast, our system uses classical logic for the part of the proof that does not affect the computation at all. As for logics dealing with fixed points, we can mention the logic for ....

T. Griffin. A formula-as-types notion of control. In Proceedings of the 17th Annual ACM Symposium on Principles of Programming Languages, pages 47-- 58, San Francisco, California, January 17-19 1990.

....insight into eval quote mechanisms. 1 Introduction Let s consider two dual questions. The first is: is there a proofs as programs, formulasas types correspondence for the modal logic S4 There is one between minimal and intuitionistic logics and calculi [How80] and also for classical logic [Gri90] or linear logic [Abr93] so why not S4 As already noted by Davies and Pfenning [DP95] the answer is a kind of calculus augmented with polished versions of Lisp s eval and quote primitives. The second question is: what type system can we graft on eval and quote that would make them usable in ....

Timothy G. Griffin. A formulas-as-types notion of control. In Proceedings of the 17th Annual ACM Symposium on Principles of Programming Languages, pages 47--58, San Francisco, California, January 1990.

....about a typical use of nonlocal control, using a classical typing. Since the original discovery that Felleisen s control operator C could be given a type corresponding to the law of double negation elimination, a great deal of work has been done on the computational meaning of classical proof [2, 3, 6, 24, 33, 36]. However, these ideas have not been exploited in the context of program development or verification. To this end, we have shown how a limited use of classical reasoning in a proof can produce a program extraction which includes a nonlocal control operator. Furthermore, the control operator is ....

....try a = F . The success of backjumping techniques is not limited to such contrived examples, and has been shown in larger problems [40, 43, 1, 5] To get this computational behavior from the proof, we use the fact that call cc can be given the type ( ff fi) ff) ff for any types ff and fi [24, 26]. This is a classical axiom which corresponds to a form of proof by contradiction, particularly when we take fi to be , or falsity. If, from the assumption that ff implies false, we can prove ff, then we have a contradiction so ff must be true. This form of reasoning is not strictly constructive, ....

[Article contains additional citation context not shown here]

T. Griffin. A formulas-as-types notion of control. In Proc. of the Seventeeth Annual Symp. on Principles of Programming Languages, pages 47--58, New York, 1990. Association for Computing Machinery.

.... barriers such as unwind protect [17] Tractable logics for reasoning about program equivalence in the presence of first class continuations in an untyped setting have been developed [9, 10, 39] Recent studies of continuations have addressed the question of their typing in a restricted setting [13, 12, 15] and their impact on full abstraction results [34] This research was supported in part by the Defense Advanced Research Projects Agency (DARPA) under ARPA order 6253. y This research was supported in part by the Defense Advanced Research Projects Agency (DARPA) monitored by the Office of ....

.... result of application of a continuation is now void, we must introduce, in compensation, a map ignore witnessing the inclusion of void into every type : Gamma M : void Gamma ignore M : give up) These two rules have the form of Pierce s Law and false elimination, respectively; see [15] for further discussion. The expression throwM N is now defined as ignore (MN ) For the polymorphic variant, the typing rule for letcc appears in the introduction. The denotational semantics must be changed to reflect the representation of continuations as functions. The domain equation for ....

Timothy Griffin. A formulas-as-types notion of control. In Seventeenth ACM Symposium on Principles of Programming Languages, San Francisco, CA, January 1990, pages 47--58.

....by Davies and Pfenning [DP95] the answer is a kind of calculus augmented with polished versions of Lisp s eval and quote primitives. Our initial motivation for answering this question was intellectual curiosity: if intuitionistic and minimal logics have it [How80] and now classical logic, too [Gri90] why not some modal logics Moreover, the current interest in linear logic, and the fact that the rules of sequent systems for linear logic look like those for S4 a lot, have recently stimulated some researchers [BdP95] into exploring functional interpretations for S4, in the hope of ....

Timothy G. Griffin. A formulas-as-types notion of control. In Proceedings of the 17th Annual ACM Symposium on Principles of Programming Languages, pages 47--58, San Francisco, California, January 1990.

....defines an embedding of the calculus, with fi reduction, inside SKInT. It is unknown at the moment whether this embedding is conservative. As far as typing is concerned, it is well known that M 7 Pn (M) gives rise to typings obtained by double negation transformations in the style of Kolmogorov (Griffin, 1990; Murthy, 1991) Let denote any type, let :A denote A ) define Pn (A) as : A) 0 , where (A) 0 is defined by: o) 0 = df o (o 2 O) A ) B) 0 = df Pn (A) Pn (B) We extend these notations to contexts Pn ( Gamma) and let Pn (x 1 :A 1 ; xn :An ) denote x 1 :Pn (A 1 ) xn :Pn ....

Griffin, T. G. (1990). A formulas-as-types notion of control. In Conference record of the 17th Annual ACM Symposium on Principles of Programming Languages (POPL'90), pages 47--58, San Francisco, California.

.... interpretation of classical logic in terms of a valuation semantic has been given by the authors in [1] However, one of the most appealing directions for the computer scientist, not only the theoretical one, is that which has begun being developed with works by Griffin To Roberta Gottardi [8] and Murthy [10] indeed it was these works that made raise the interest for the topic we are speaking about) In these works a strong relation has been established between classical logic and the control operators usually added in functional programming languages in order to have in them some of ....

Timothy G. Griffin. A formulas-as-types notion of control. In "Conference Record of the Seventeenth Annual ACM Symposium on Principles of Programming Languages ", 1990.

....about a typical use of nonlocal control, using a classical typing. Since the original discovery that Felleisen s control operator C could be given a type corresponding to the law of double negation elimination, a great deal of work has been done on the computational meaning of classical proof [2, 3, 6, 22, 30, 33]. However, these ideas have not been exploited in the context of program development or verification. To this end, we have shown how a limited use of classical reasoning in a proof can produce a program extraction which includes a nonlocal control operator. Furthermore, the control operator is ....

....try a = F . The success of backjumping techniques is not limited to such contrived examples, and has been shown in larger problems [36, 39, 1, 5] To get this computational behavior from the proof, we use the fact that call cc can be given the type ( ff fi) ff) ff for any types ff and fi [22, 24]. This is a classical axiom which corresponds to a form of proof by contradiction, particularly when we take fi to be , or falsity. If, from the assumption that ff implies false, we can prove ff, then we have a contradiction so ff must be true. This form of reasoning is not strictly constructive, ....

[Article contains additional citation context not shown here]

T. Griffin. A formulas-as-types notion of control. In Proc. of the Seventeeth Annual Symp. on Principles of Programming Languages, pages 47--58, 1990.

....loop control variables are restored and the program starts again where it left off. Persistent disjunction can also serve as an approximation to classical disjunction. For discussion, see [30] For research on connections between classical logic and procedural programming mechanisms, to start see [21] and [26] The 2LP interpreter, which supports both linear constraints and persistent disjunction, is based on two fundamental technologies. The type continuous is maintained by means of an incremental linear programming solver based on the revised simplex method. The backtracking and choice point ....

T. Griffin, A formulas-as-type notion of control, in Proceedings of the 17th ACM Symposium on Principles of Programming Languages, 1990.

.... run time support for multiple threads of control [40, 27] Tractable logics for reasoning about program equivalence in the presence of first class continuations in an untyped setting have been developed [8, 9, 38] Recent studies have focused on questions of typing for first class continuations [12, 11, 14] and their impact on full abstraction results [32] The subject of this paper is the extension of Standard ML with primitives for first class continuations similar to those found in Scheme. The two new primitives are callcc, for call with current continuation, which takes a function as ....

.... result of application of a continuation is now void, we must introduce, in compensation, a map ignore witnessing the inclusion of void into every type : Gamma M : void Gamma ignore M : give up) These two rules have the form of Pierce s Law and false elimination, respectively; see [14] for further discussion. The expression throwM N is now defined as ignore (MN ) For the polymorphic variant, the typing rule for letcc appears in the introduction. The denotational semantics must be changed to reflect the representation of continuations as functions. The domain equation for ....

Timothy Griffin. A formulas-as-types notion of control. In Seventeenth ACM Symposium on Principles of Programming Languages, San Francisco, CA, January 1990, pages 47--58.

....assignment is inconsistent, we return immediately to this point by applying the continuation to the evidence of inconsistency, in the form of a conflict set. To get this computational behaviour from the proof, we use the fact that call cc can be given the type ( ff ) ff) ff for any type ff [11, 17, 16, 23]. This corresponds to a form a proof by contradiction; if, from the assumption that ff is false, we can prove ff, then we have a contradiction so ff must be true. This form of reasoning is not strictly constructive, but in this case we still have a computational meaning for it. Although a ....

T. Griffin. A formulas-as-types notion of control. In Proc. of the Seventeeth Annual Symp. on Principles of Programming Languages, pages 47--58, 1990.

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