M. Felleisen, D. Friedman, E. Kohlbecker, and B. Duba. Reasoning with continuations. In First Symposium on Logic in Computer Science, pages 131--141. IEEE, June 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... type abstractions comes at considerable cost since it is incompatible with extensions such as mutable data structures and control operators [45, 18, 19] The definitions of these strategies make use of Plotkin s notion of a syntactic value [36] and Felleisen s notion of an evaluation context [11], chosen suitably for each situation. To specify a strategy using this method, we first give a grammar which defines three syntactic categories: V , a set of values, R, a set of redices, and E, a set of evaluation contexts. As an example, the grammar used to specify a call by value strategy for ....

Matthias Felleisen, Daniel Friedman, Eugene Kohlbecker, and Bruce Duba. Reasoning with continuations. In First Symposium on Logic in Computer Science. IEEE, June 1986.

....jumps, and allows for programs that are more efficient than purely functional programs. The formulae as types correspondence presented in this paper is based on a typed version of Idealized Scheme a typed ISWIM containing an operator C similar to call cc developed by Felleisen et al. [3, 2, 4] for reasoning about Scheme programs. Section 2 reviews ISWIM and its extension to Idealized Scheme (IS) with the control operator C of Felleisen et al. Roughly speaking, the evaluation of C(M ) abandons the current control context and applies M to a procedural abstraction of this context. ....

....below. 2 This paper ignores constants and their evaluation. An expression of the form (x:M )V is called a fi v redex. The function eval v produces a result that is equivalent to repeatedly reducing the leftmostoutermost fi v redex not inside the scope of a abstraction. Felleisen et al. [3, 4] have formalized this evaluation order in terms of evaluation contexts. ISWIM evaluation contexts E are defined inductively as E : j EN j V E; where [ represents a hole. If E is an evaluation context, then E[M ] denotes the term that results from placing M in the hole of E. It is ....

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M. Felleisen, D. Friedman, E. Kohlbecker, and B. Duba. Reasoning with continuations. In Proceedings of the First Symposium on Logic in Computer Science, pages 131--141. IEEE, 1986.

....w.r.t. an operational equivalence, was first considered in [Plo75] for call by value and call by name operational equivalence. This approach was later extended, following a similar methodology, to consider other features of computations like nondeterminism (see [Sha84] and sideeffects (see [FFKD86, MT89]) The calculi based only on operational considerations, like the v calculus, are sound and complete w.r.t. the operational semantics, i.e. a program M has a value according to the operational semantics iff it is provably equivalent to a value (not necessarily the same) in the calculus, but they ....

M. Felleisen, D.P. Friedman, E. Kohlbecker, and B. Duba. Reasoning with continuations. In 1st LICS Conf. IEEE, 1986.

....in the second order classical natural deduction. As usual with control operators, the catch throw mechanism is easier to introduce in the framework of abstract stack machines. Indeed, control operators are aimed to handle the continuation (i.e. the rest of the computation to be performed, see Felleisen at al. 1986; 1987) or Reynolds (1993) for a survey) and precisely, in abstract stack machines, the continuation is represented by the stack. In the remainder of this introduction, we will thus consider two simple extensions of Krivine s abstract machine: the machine and the ct machine. The former is ....

Felleisen, M., Friedman, D. P., Kohlbecker, E., & Duba, B. F. (1986). Reasoning with continuations. Pages 131--141 of: First symp. on logic and computer science.

....expressions appearing to the left and which have an extent which is included in T . Third, a continuation can be captured in any context, independently of expressions appearing to their left. 1. 2 Syntactic theories of control Syntactic theories of control were introduced by Felleisen et al. 5] [7], 8] 6] These theories extend the call by value calculus de ned by Plotkin [21] with control operators like C and A. C allows to capture a continuation and A aborts a computation. Felleisen et al. proved these systems to be Church Rosser. This property states that if M reduces to P and M ....

....it is intended to capture its current continuation. This continuation is represented by a functional abstraction of the context which is built step by step by bubbling up [6] callcc applications (using rules C3 and C4) until a callcc reaches the top level. This phase, called the construction phase [7], accumulates all application frames . At this point, rule C8 can be applied (since we suppose that evaluation proceeds in an A application) and a series of v reductions are performed; this phase, called the collection phase [7] concatenates all application frames . After these two phases, we ....

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Matthias Felleisen, Daniel P. Friedman, Eugene E. Kohlbecker, and Bruce Duba. Reasoning with Continuations. In Proceedings of the Symposium on Logic in Computer Science, pages 131-141, Washington DC, June 1986. IEEE Computer Society Press.

....rst and to R(R(A) PAIR [SYMBOL SYMBOL] PAIR [SYMBOL A] NIL] if the outer redex is reduced rst. It is worth noting that the counter example is a program. 4 Related Work While there are a large number of studies of LISP with which we share either our general methodology (e.g. [Gor75, Car76, Mas86, MT89, FFKD86, Fel88]) or our general subject matter (e.g. Pit80, MP80, Smi82] or [Smi84, dRS84, FW84, FW86, DM88, Baw88] we are unfamiliar with any axiomatic treatments of LISP s metalinguistic power. The rst structured operational semantics for LISP was de ned for M expression LISP by Gordon [Gor75] This was ....

....Cartwright, Car76] developed veri cation systems for rstorder S expression like dialects of pure LISP. Mason, Mas86] and later Mason and Talcott, MT89] have provided various axiomatizations of rst order destructive LISP. Our framework is particularly close to that of Felleisen (et al. [FFKD86, Fel88] who provide an operational characterization of Scheme s imperative control features and of assignment. However, our subject matters are di erent: we have not considered either the control features or assignment and they have not considered either pairs or metalinguistic features. The former but ....

M. Felleisen, D. Friedman, E. Kohlbecker, and B. Duba. Reasoning with continuations. In First Annual Symposium on Logic in Computer Science, pages 131-141, 1986.

....w.r.t. an operational equivalence, was rst considered in [Plo75] for call by value and call by name operational equivalence. This approach was later extended, following a similar methodology, to consider other features of computations like nondeterminism (see [Sha84] and sidee ects (see [FFKD86, MT89]) The calculi based only on operational considerations, like the v calculus, are sound and complete w.r.t. the operational semantics, i.e. a program M has a value according to the operational semantics i it is provably equivalent to a value (not necessarily the same) in the calculus, but they ....

M. Felleisen, D.P. Friedman, E. Kohlbecker, and B. Duba. Reasoning with continuations. In 1st LICS Conf. IEEE, 1986.

....an operational equivalence, was rst considered in [Plo75] for call by value and call by name operational equivalence. This approach was later extended, following a similar methodology, to consider other features of computations like nondeterminism (see [Sha84] side e ects and continuations (see [FFKD86, FF89]) The calculi based only on operational considerations, like the v calculus, are sound and complete w.r.t. the operational semantics, i.e. a program M has a value according to the operational semantics i it is provably equivalent to a value (not necessarily the same) in the calculus, but they ....

M. Felleisen, D.P. Friedman, E. Kohlbecker, and B. Duba. Reasoning with continuations. In 1st LICS Conf. IEEE, 1986.

....the usual correspondence between the operational semantics and reify [ 0 v , it is obviously not the case that reify [ 0 v is an extension (conservative or otherwise) of v . 23 5 Related Work While there are many studies of LISP with which we share either our general methodology [Gor75, BM75, Car76, Mas86, MT89, FFKD86, Fel88], or our general subject matter [Pit80, MP80, Smi82, Smi84, RS84, FW84, FW86, DM88, Baw88] we are unfamiliar with any attempts to axiomatize LISP s metalinguistic facilities. We are also unfamiliar with any reference in the literature to the problematic nature of equation (12) in McCarthy s ....

....semantics to R(s) But this is not the case for eval. Moreover, observe that the niceness condition e ectively nulli es the semantic import of the representation decoding: higher order functions. 5. 2 Other Syntactic Studies of LISP Our framework is close to that of Felleisen (et al. [FFKD86, Fel88] who provide an operational characterization of Scheme s imperative control features and of assignment. However, our subject matters are di erent: we have not considered either the control features or assignment and they have not considered either pairs or metalinguistic features. The former but ....

Matthias Felleisen, Dan Friedman, Eugene Kohlbecker, and Bruce Duba. Reasoning with continuations. In Proc. 1st Logic in Computer Science, pages 131{ 141, July 1986.

.... the setting of cps conversion, since the cps transform seems fundamental to understanding the other two settings of continuations: a continuation transform forms the basis of many continuation semantics (cf. 24, 26, 30] and is often used to describe the semantics of call cc like operators (cf. [7, 8]. Chapter 2 describes a call by value functional language v and its continuation transform, both of which are the focus of study. In Chapter 3, we describe specific examples that show the failure of reasoning principles based on observational congruence. These examples will have the form M and ....

....transform is that the converse of Corollary 3.1 does not hold: observational congruence on direct terms does not coincide with congruence on continuized terms. Similar anomalies occur in the other two settings. For example, suppose we augment v with the call cc like operators C and A defined in [7, 8]. Terms that are observationally congruent in v may become distinguishable using contexts containing these new operators. In the case of continuation semantics, there are observationally congruent terms that are equivalent in a direct semantics but not equivalent in a continuation semantics. ....

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Matthias Felleisen, Daniel P. Friedman, Eugene Kohlbecker, and Bruce Duba. Reasoning with continuations. In Symp. Logic in Computer Science, pages 131--141, IEEE, 1986.

....of the form fix x 1 (x 2 ) e. We will use x:e as an abbreviation for fix x 0 (x) e when x 0 is not free in e. Note that we restrict let bound expressions to be values for reasons detailed in Section 2.3. A standard call by value operational semantics in the style of Felleisen et al.[5] (see also Wright and Felleisen[16] can be given to Mini ML by defining evaluation contexts (expressions with holes ) and one step reduction rules: E 2 eval context : j hE;ei j hv;Ei j i E j E e j v E ( E[ i hv 1 ;v 2 i] 7 Gamma E[v i ] i = 1; 2) fix v fi) E[ fix x 1 (x 2 ) e) v] ....

M. Felleisen, D. Friedman, E. Kohlbecker, and B. Duba. Reasoning with continuations. In First Symposium on Logic in Computer Science, pages 131--141. IEEE, June 1986.

....and elimination of m cut is administrative one and represents classical computation. Among the administrative reductions, some of them are constrictive morphisms and others are classical(e.g. continuation) calculations. 4. 2 Felleisen s C operator In our CPS calculus, Felleisen s C operator[6] is a cut free derivation of peirce s law. We mechanically calculate them as follows: CBN: C = y:k:y(h:h(k 0 :k 0 (x:l:xk) h:kh) CBV: C = y:k:y(x:l:kx) x:kx) where type of k is :A. Type of y is : A B) A) t (CBN) A B) A) q (CBV) respectively. Remark 3. In CBN, Felleisen ....

Matthias Felleisen, Daniel P. Friedman, Eugene Kohlbecker, and Bruce Duba. Reasoning with continuations. In Proceedings, Symposium on Logic in Computer Science, pages 131--141, Cambridge, Massachusetts, 16--18 June 1986. IEEE Computer Society.

....E 0 [ffl]g) 5 Examples In this section I give a number of examples of PCF programs to give the reader a feel for the computational power of the calculus. In particular, in x5.4, I shall reconsider the examples of encodings given by Ong and Stewart [24] 5. 1 Idealised Scheme Felleisen et al. [8, 9] presented an extension to the (untyped) call by value calculus, called Idealised Scheme. Two new operators are added, written A(M) and C(M ) which are called abort and control, respectively. Both forms are considered to be redexes and their reduction behaviour is given by the following rules. ....

M. Felleisen, D.P. Friedman, E.E. Kohlbecker, and B. Duba. Reasoning with continuations. In Proceedings of Symposium on Logic in Computer Science, pages 131-- 141, June 1986.

....to be expressed in CPS and the pure (and hence freely rearrangable) function computed, in which case we actually get the best of both worlds. 6.3. Control operators From Reynolds s escape to call cc in Scheme, control operators are nicely introduced within the CPS transformation (Reynolds, 1972; Felleisen et al. 1986). However, because CPS appears to constrain expressive power, Felleisen and others have successively proposed new control operators to compose continuations (Felleisen et al. 1987a) and to limit their extent (Felleisen, 1988) As later shown by Sitaram and Felleisen (Sitaram and Felleisen, 1990) ....

Felleisen, M., Friedman, D. P., Kohlbecker, E., and Duba, B. (1986). Reasoning with continuations.

.... firstclass continuations in a functional language, all tracing back to Reynolds s escape operator [19] or, less directly, to Landin s J operator [14] In general, we need an operator C such that an expression CM invokes the procedure M with a representation K of the evaluation context [6] surrounding CM . If M ever invokes K with a value V , the then current context of evaluation is abandoned, and control returns to the context represented by K, as if CM had just returned V . For example, 2 C (k: 3 k 4) Gamma 6 The difference from exceptions is that the entire captured ....

....behavior, which makes it superior in many ways to exceptions both for both theoretical and practical purposes. For concreteness in the following, we will adopt Griffin s simply typed formulation of first class continuations [9] which uses essentially a typed variant of Felleisen s C operator [6]; the actual choice is not critical, however. We will generally emphasize applications of continuations as k ffl v. Similarly, we will write ffl x: M for the syntactic representation of a continuation. And finally, we will use the notation :ff for the type of ff accepting continuations. To ....

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Felleisen, M., Friedman, D. P., Kohlbecker, E., and Duba, B. Reasoning with continuations. In Proceedings of Symposium on Logic in Computer Science, IEEE, Cambridge, Massachusetts (June 1986) 131--141.

.... 40] for providing asynchronous signal handlers [29] and for implementing non blind backtracking [15] and dynamic barriers such as unwind protect [21] Tractable logics for reasoning about program equivalence in the presence of first class continuations in an untyped setting have been developed [11, 12, 37]. Recent studies of continuations have addressed the question of their typing in a restricted setting [13, 14, 16] 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 ....

Matthias Felleisen, Daniel Friedman, Eugene Kohlbecker, and Bruce Duba. Reasoning with continuations. In First Symposium on Logic in Computer Science. IEEE, June 1986.

.... 6] for providing asynchronous signal handlers [30] and for implementing non blind backtracking [14] and dynamic 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 ....

Matthias Felleisen, Daniel Friedman, Eugene Kohlbecker, and Bruce Duba. Reasoning with continuations. In First Symposium on Logic in Computer Science. IEEE, June 1986.

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M. Felleisen, D. Friedman, E. Kohlbecker, and B. Duba. Reasoning with continuations. In First Symposium on Logic in Computer Science, pages 131--141. IEEE, June 1986.

No context found.

Matthias Felleisen, Daniel Friedman, Eugene Kohlbecker, and Bruce Duba. Reasoning with continuations. In First Symposium on Logic in Computer Science. IEEE, June 1986.

No context found.

Matthias Felleisen, Daniel P. Friedman, Eugene E. Kohlbecker, and Bruce Duba. Reasoning with continuations. In Proceedings of the Symposium on Logic in Computer Science, pages 131--141, Washington DC, June 1986. IEEE Computer Society Press.

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Matthias Felleisen, Daniel P. Friedman, Eugene E. Kohlbecker, and Bruce Duba. Reasoning with continuations. Proceedings of the Symposium on Logic in Computer Science, pages 131--141, 1986.

No context found.

Matthias Felleisen, Daniel P. Friedman, Eugene Kohlbecker, and Bruce Duba. Reasoning with continuations. In Proceedings of the IEEE Symposium on Logic in Computer Science (LICS'86), pages 131--141, Cambridge, MA, June 1986. IEEE Computer Society.

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Matthias Felleisen, Daniel P. Friedman, Eugene Kohlbecker, and Bruce Duba. Reasoning with continuations. In Proceedings of the Symposium on Logic in Computer Science, pages 131--141. IEEE Computer Society Press, Washigton DC, 1986.

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Felleisen, M., Friedman, D., Kohlbecker, E., Duba, B., Reasoning with continuations, in Proceedings of the First Annual ACM Symposium on Principles of Programming Languages, 180-190, 1986.

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M. Felleisen, D.P. Friedman, E. Kohlbecker, and B. Duba. Reasoning with continuations. In Symposium on login in computer science, 1986.

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