Gilles Barthe, John Hatcliff, and Morten Heine Srensen. CPS translations and applications: the cube and beyond. In O. Danvy, editor, ACM SIGPLAN Workshop on Continuations, number NS-96-13 in BRICS Notes Series, pages 4:1--31, 1997. Cited on page 82.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....classical logic and showed that both Felleisen s CPS translation and its callby name version correspond to well known embeddings of classical logic into intuitionistic logic. Subsequently, typed CPS translations and correctness results have been given for more powerful typed calculi, see, e.g. [27, 28, 8], and applied to the compilation and optimization of typed languages, see, e.g. 19, 44] Grin s discovery initiated a series of studies on the computational content of classical proofs where CPS translations are a frequently employed tool, see, e.g. 13, 33, 38, 39, 34, 12, 4, 42, 24, 25, 35, ....

....to prove that every number theoretic function representable in ; is also representable in ; indicating one possible line of application for CPS translations for (co)inductive types. Third, we study extensions of the suggested translation for more powerful type disciplines. Building on [8], one can show that the translation scales up to systems with dependent types. However, we prove that the translation is extendable neither to small types nor to sum types with dependent case. For the latter, we analyse Geuvers [21] proof of inconsistency of classical logic in the Calculus of ....

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G. Barthe, J. Hatcli, and M. H. Srensen. CPS-translations and applications: the cube and beyond. Higher-Order and Symbolic Computation, 12(2):125-170, 1999.

....classical logic and showed that both Felleisen s CPS translation and its callby name version correspond to well known embeddings of classical logic into intuitionistic logic. Subsequently, typed CPS translations and correctness results have been given for more powerful typed calculi, see, e.g. [27, 28, 8], and applied to the compilation and optimization of typed languages, see, e.g. 19, 44] Grin s discovery initiated a series of studies on the computational content of classical proofs where CPS translations are a frequently employed tool, see, e.g. 13, 33, 38, 39, 34, 12, 4, 42, 24, 25, 35, ....

....to prove that every number theoretic function representable in ; is also representable in ; indicating one possible line of application for CPS translations for (co)inductive types. Third, we study extensions of the suggested translation for more powerful type disciplines. Building on [8], one can show that the translation scales up to systems with dependent types. However, we prove that the translation is extendable neither to small types nor to sum types with dependent case. For the latter, we analyse Geuvers [21] proof of inconsistency of classical logic in the Calculus of ....

[Article contains additional citation context not shown here]

G. Barthe, J. Hatcli, and M. H. Srensen. CPS-translations and applications: the cube and beyond. Higher-Order and Symbolic Computation, 12(2):125-170, 1999.

....: x: ff : x. Our solution to this problem, following Coquand and Herbelin [8] is to define the CPS translation of a term relative to the context in which the terms is considered. Another possibility [14] is to define the translation relative to derivations. These issues are discussed further in [4]. However, even in a fixed context, the type of a term is unique only up to fi equality. This ambiguity is resolved by choosing types in normal form; this is possible since we are dealing with systems where all terms are weakly normalizing. 26 This motivates the following lemma and definition. ....

G. Barthe, J. Hatcliff, and M.H. Srensen. CPS translations and applications: the cube and beyond. In O. Danvy, editor, ACM SIGPLAN Workshop on Continuations, number NS-96-13 in BRICS Notes Series, pages 4:1--31, 1997.

....translates traditional pseudo terms of pure type systems, but relies on a non standard order to be well founded. These results justify dening the CPS translation on domain free pure type systems instead of on traditional pure type systems. The paper is an extended and elaborated version of [6]. 2. The domain free cube This section is a brief introduction to the domain free cube. The rst subsection is devoted to the denition of the systems involved. For readers with no previous 11 knowledge of calculi presented in this style, the second subsection includes a number of examples; ....

G. Barthe, J. Hatclioe, and M.H. S#rensen. CPS-translation and applications: the cube and beyond. In O. Danvy, editor, Proceedings of the Second ACM SIGPLAN Workshop on Continuations, number NS-96-13 in BRICS Notes, pages 4/14/31, 1996.

....principle for Pure Type Systems and use that principle to dene CPS translations and to solve the problem of Expansion Postponement for a large class of Pure Type Systems. Our principle strengthens and generalises similar principles by Dowek, Huet and Werner [12] and Barthe, Hatclioe and S#rensen [6], which have been respectively used to dene j long normal forms and CPS translations for the systems of Barendregt s cube [2, 3] 1 Introduction Pure Type Systems (PTSs) provide a description of typed calculi that is parametric in the notion of type discipline [2, 3, 9, 13, 14, 26] The ....

....these induction principles prove inadequate, and alternative induction principles must be used. For example, Terlouw [27] uses a dioeerent induction principle to dene a model construction for a class of PTSsstrictly speaking, Terlouw considers a variant of PTSs. The denitions of CPS translations [6] and j long normal forms [12] provide yet other instances where alternative induction principles are required. Both denitions introduce a function f mapping a context Gamma and a term M legal INRIA Sophia Antipolis, 2004 Routes des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France, ....

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G. Barthe, J. Hatclioe, and M.H. S#rensen. CPS-translations and applications: the cube and beyond. Higher-Order and Symbolic Computation, 12:125170, September 1999.

....framework call by value, call byname, and mixed strategy CPS translations for PTSs. The general translation could be instantiated to the translations for F 2 [23] F [22] non dependent PTSs [10] as well as the recent CPS translations for PTSs with dependent types proposed by Barthe et al. [6]. 7 Conclusion and directions for further research The paper introduces monadic type systems, a powerful and flexible framework to capture computational effects in rich (polymorphic, dependent) type systems, and study operational semantics for monadic type systems with dependent types. Much ....

....concerned with the lifting monads. It would be interesting to scale up alternative semantics for notions of computation (see e.g. 43] to the framework of MTSs. Finally, we are interested in exploiting our framework for CPS translation and partial evaluation. Based on the technical results of [6], we are currently extending the results of [28] to MTSs. ....

Gilles Barthe, John Hatcliff, and Morten Heine Sørensen. CPS translations and applications: the cube and beyond. In Olivier Danvy, editor, Proceedings of the Second ACM SIGPLAN Workshop on Continuations, number NS-96-13 in BRICS Notes, pages 4--1--4--31, Paris, France, January 1997. Dept. of Computer Science, Aarhus, Denmark.

....does not require this (and sidesteps the complications regarding the form of A) ffl Simplicity. Domain free type systems are sometimes easier to study than domain full type systems. For example, continuation passing style (CPS) translations are easier to define for domain free type systems see (Barthe et al. 1996). This observation is especially relevant as continuation passing style translations are, apart from their theoretical interest, a fundamental tool in compilation (Appel, 1992) In addition, strong normalization is often easier to prove for domain free type systems than for their (domain full) ....

....details are omitted when the proof proceeds by induction and is similar to the proof for the corresponding result for pure type systems. In the second subsection we present the classification lemma,which is useful in several applications, e.g. to define CPS translations for the domain free cube (Barthe et al. 1996). In the third subsection we consider typechecking issues. We show that although type checking may be undecidable, even for systems of the cube, one can prove a weaker result which allow for DFPTSs to be used in practice. 3.1 Basic properties Throughout this subsection, S denotes a fixed ....

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Barthe, G., Hatcliff, J., & Sørensen, M.H. (1996). CPS-translation and applications: the cube and beyond. Pages 4/1--4/31 of: Danvy, O. (ed), Proceedings of the second ACM SIGPLAN workshop on continuations. BRICS Notes, nos. NS--96--13.

....and by Harper and Lillibridge for ML with polymorphism (PML) 38] and Girard s higher order polymorphic calculus with control operators [37] In the first subsection, we discuss some of the problems related to CPS translations for proof relevant systems. Much of the discussion is taken from [10] where the authors develop CPS translations for logical PTSs and DFPTSs. In the second subsection, we define for every injective logical specification S a CPS translation from DeltaS to S; the translation is inspired from [10] In the third subsection, we use the correctness of the CPS ....

....for proof relevant systems. Much of the discussion is taken from [10] where the authors develop CPS translations for logical PTSs and DFPTSs. In the second subsection, we define for every injective logical specification S a CPS translation from DeltaS to S; the translation is inspired from [10]. In the third subsection, we use the correctness of the CPS translation to derive the consistency of a CPTS from that of its corresponding PTS. Then we generalize our technique to prove consistency of classical arithmetic from consistency of constructive arithmetic. It is possible to go beyond ....

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G. Barthe, J. Hatcliff, and M.H. Sørensen. CPS-translation and applications: the cube and beyond. In O. Danvy, editor, Proceedings of the Second ACM SIGPLAN Workshop on Continuations, number NS-96-13 in BRICS Notes, pages 4/1--4/31, 1996.

....an induction principle for Pure Type Systems and use that principle to define CPS translations and to solve partially the open problem of Expansion Postponement. Our principle strengthens and generalises similar principles by Dowek, Huet and Werner [12] and Barthe, Hatcliff and S rensen [5], which have been respectively used to define j long normal forms and CPS translations for the systems of Barendregt s cube [2, 3] 1 Introduction Pure Type Systems (PTSs) provide a description of typed calculi that is parametric in the notion of type discipline [2, 3, 9, 13, 14, 25] The ....

....induction principles prove inadequate, and alternative induction principles must be used. For example, Terlouw [26] uses a different induction principle to define a model construction for a class of PTSs strictly speaking, Terlouw considers a variant of PTSs. The definitions of CPS translations [5] and j long normal forms [12] provide yet other instances where alternative induction principles are required. Both definitions introduce a function f mapping a context Gamma and a term M legal Address: Chalmers Tekniska Hogskola, Institutionen for Datavetenskap, S 412 96 Goteborg, Sweden, ....

[Article contains additional citation context not shown here]

G. Barthe, J. Hatcliff, and M.H. Sørensen. CPS-translations and applications: the cube and beyond. In O. Danvy, editor, Proceedings of the Second ACM SIGPLAN Workshop on Continuations, number NS-96-13 in BRICS Notes, pages 4/1--4/31, 1996.

.... use of abstractions with domain in pure type systems is motivated by history (most type systems have adopted such abstractions) as well as by practical considerations (domain full abstractions are necessary for type checking to be decidable) The paper is an extended and elaborated version of [6]. 2 The domain free cube This section is a brief introduction to the domain free cube. The first subsection is devoted to the definition of the systems involved. For readers with no previous knowledge of calculi presented in this style, the second subsection includes a number of examples; ....

G. Barthe, J. Hatcliff, and M.H. Sørensen. CPS-translation and applications: the cube and beyond. In O. Danvy, editor, Proceedings of the Second ACM SIGPLAN Workshop on Continuations, number NS-96-13 in BRICS Notes, pages 4/1--4/31, 1996.

....we view terms as proofs 1 . In this section, we develop similar results for C 2 . The CPS translation 1 See also [21, 22, 48] more references on control operators and CPS translations appear in [70, 65] and surveys of logical embeddings are presented in [41, 77] 2 Using the results of [11], it is possible to extend the translation to all the systems of the cube and to a much larger class of specifications. We limit ourselves to C for space reasons. Chxi = ae k:x k x if x 2 V otherwise Chsi = s Ch i = Piff: ff Chx:A: M i = ae k:k (x:ChM i) x:ChM i if x:A: M 2 O ....

.... ChM 0 i k) ChM i ChM 0 i if M M 0 2 O otherwise Ch x:A: M i = k:ChMifx : h:h j:i:i (j k)gz:z Ch Pix: A: Bi = Pix: Ch[A]i: Ch[B]i Ch[M ]i = ae : ChM i ChM i if M 2 C otherwise Ch[ i = Ch[ Gamma; x : A]i = Ch[ Gamma]i; x : Ch[A]i Figure 1: CPS translation is inspired from [11] and makes use of domain free pure type systems [12] a variant of pure type systems in which abstractions are of the form x:M , i.e. are not equipped with tags indicating the domain of the argument x 3 . Below denotes the derivability relation for the domain free version of the Calculus of ....

[Article contains additional citation context not shown here]

G. Barthe, J. Hatcliff, and M.H. Sørensen. CPS-translation and applications: the cube and beyond. In O. Danvy, editor, Proceedings of the Second Workshop on Continuations, 1997. To appear. Also available from http://www.cwi.nl/~gilles.

....type systems is not cheating . The second, direct, approach translates traditional pure type systems, requiring a certain order to be well founded. The technique works for Barendregt s cube, but requires rather proof theoretically strong means. The paper is an extended and elaborated version of [4]. 2 The domain free cube In this section we present the domain free cube, taken from [8] For readers with no previous knowledge calculi presented in this style we include in the second subsection below a number of examples; readers familiar with [3] may skip the latter subsection. 2.1 ....

G. Barthe, J. Hatcliff, and M.H. Sørensen. CPS-translation and applications: the cube and beyond. In O. Danvy, editor, Proceedings of the Second ACM SIGPLAN Workshop on Continuations, number NS-96-13 in BRICS Notes, pages 4/1--4/31, 1996.

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Gilles Barthe, John Hatcliff, and Morten Heine Srensen. CPS translations and applications: the cube and beyond. In O. Danvy, editor, ACM SIGPLAN Workshop on Continuations, number NS-96-13 in BRICS Notes Series, pages 4:1--31, 1997. Cited on page 82.

No context found.

G. Barthe, J. Hatcliff, and M. Sorensen. CPS translations and applications: the cube and beyond. Higher Order and Symbolic Computation, 12(2):125--170, September 1999.

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Barthe, G., Hatcli, J., Srensen, M. H. B.: CPS translations and applications: The cube and beyond. Higher-Order and Symbolic Comput. 12(2) (1999) 125-170

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