P. de Groote. A CPS-translation of the ¯-calculus. In S. Tison, editor, Proc. CAAP'94. Springer, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....C operator of Felleisen et al. 10] and relating them to classical proofs, there has been a great deal of interest in classical proofs. The following is a tentative (and incomplete) classification: ffl Algorithm extraction, control operators: Griffin [14] Murthy [22] Krivine [21] de Groote [9], Nakano [23] Hirokawa [16] Schwichtenberg and Berger [4] Coquand [6] etc. ffl Formal systems and calculi: Girard [11, 12] Parigot [24] Berardi and Barbanera [2] Danos, Joinet and Schellinx [8] etc. ffl Proofs and semantics of cut elimination: Girard [11] Hofmann [17] Coquand [5] ....

P. de Groote. A CPS-translation of the ¯-calculus. In S. Tison, editor, Proc. CAAP'94. Springer, 1994.

....denotation in linear logic s coherent space semantics. That is, n have the denotation in coherent space semantics. This seems to be overlooked in the field of categorical semantics. 1. 3 Related Works The second part of our work can be seen as a proof theoretical recast of the De Groote s work [4]; He develops a CPS transform of the n . However his method was merely syntactic. What is new to our work is that we adapt this framework to the proof theory. Particularly, we relate the two known constructive classical logic. Our proof theoretical framework are also considered informally by some ....

Phillipe de Groote. A cps-translation of the ¯-calculus. In Proceedings Trees in Algebra and Programming -- CAAP'94, pages 85--99. Springer-Verlag LNCS 787, April 1994.

....in [10] Also DJS themselves gave a guess in the final remark of [3] and in there introduction of [4] about the relation between LKT, negative fragment of LC and Parigot s CND. DeGroote revealed the relation between CBN CPS and Parigot s calculus which is an computational interpretation of CND [5]. Moreover there is a detailed work of Herbelin[13] about term calculus on LJT which is an intuitionistic fragment of LKT. He interpret LJT proofs as programs ( calculus) and cut elimination steps as reduction steps, as we do. We show that calculus is completely included as an intuitionistic ....

....are naturally included in our calculus as a computational step corresponding to permutation of cut. Besides CPS, on the line of classical proofs as programs approach, Parigot s calculus [18 21] is also considered as a standard. DeGroote revealed the relation between CBN CPS and calculus [5]. Moreover, Ong and Stewart (OS) introduce a call by value (CBV) version of calculus in [17] in which they introduce a new reduction rule (iarg ) Parigot proves the computational properties (such as SN and CR) of CBN versions of calculus individually. OS also does the same in CBV case. This ....

Phillipe de Groote. A cps-translation of the ¯-calculus. In Proceedings Trees in Algebra and Programming -- CAAP'94, pages 85--99. Springer-Verlag LNCS 787, April 1994.

....between calculus and ILU in [8] In addition, DJS themselves gave an explanation in their introduction of [3] about the relation between the LKT, the negative fragment of the LC, and Parigot s CND. Specifically, the second part of our work can be seen as a adaptation of the De Groote s work [4]. His investigation is about the CPS translation of the n . However it was merely syntactic. What is new to our work is that we adopt this method to the investigation between the relation of the two style of classical proofs. Herbelin s calculus Herbelin[10] published a detailed work on the ....

Phillipe de Groote. A cps-translation of the ¯-calculus. In Proceedings Trees in Algebra and Programming -- CAAP'94, pages 85--99. Springer-Verlag LNCS 787, April 1994.

....into minimal logic [50] Murthy [18,62,63] and Griffin himself [35] later systematized these ideas by studying different logical embeddings, control operators, and CPS translations. More recently, CPS translations from classical typed calculi to typed calculi were studied by de Groote for [23] and exn [24] by Duba, Harper and MacQueen for the monomorphic fragment of ML (MML) 27] 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 ....

....As a further application of the CPS translation, Griffin [34] used the translation to infer weak normalization of simply typed C terms from strong normalization of simply typed terms. Analogous results were later obtained using a similar argument by de Groote for Parigot s calculus [23], by Duba, Harper and MacQueen for MML [27] and by Harper and Lillibridge for PML [38] and higher order calculus [37] Other authors were also able to deduce strong normalization of a classical calculus from strong normalization of simply typed calculus: Rehof and S rensen for Delta [82] and ....

P. de Groote. A CPS-translation of the ¯-calculus. In S. Tison, editor, Proceedings of CAAP'94, volume 787 of Lecture Notes in Computer Science, pages 85--99. Springer-Verlag, 1994.

....paper also includes good references for classical control calculi which we omit in this paper. calculus: In addition to CPS calculus, Parigot s calculus [20, 21, 22, 23] is also considered as a standard for classical proofs as programs approach on classical natural deduction (CND) DeGroote [6] revealed the relation between CBN CPS and calculus. Moreover, Ong and Stewart (OS) introduce a call by value (CBV) version of calculus in [18] in which they introduce a new reduction rule (i arg ) Parigot and OS prove the computational properties (such as SN and CR) of (CBN and CBV ....

Phillipe de Groote. A cps-translation of the ¯-calculus. In Proceedings Trees in Algebra and Programming -- CAAP'94, pages 85--99. Springer-Verlag LNCS 787, April 1994.

....a connection between certain terms and control operators in [28] he stated that and (see Example 2.2) have behaviour close to Felleisen s C operator and Scheme callcc respectively but offered no explanation. de Groote was the first to study calculus from a computational viewpoint: in [9] he considered a cps translation. Various researchers e.g. 26, 36] have studied control operators in relation to classical proofs. More recently Bierman [5] has sketched an explanation of in terms of a kind of abstract machine with control environment . In this section we demonstrate the ....

....version and behaves as the identity. Note that (C lift ) in our formulation, is in effect the two axioms (FL ) and (FR ) in [10] taken together. Now let [ n be the theory consisting of equational axioms (fi n ) and (i arg ) de Groote has established the relationship between n and C n in [9]: Proposition 4.1 (de Groote) Let s and s 0 be C terms and t and t 0 terms. Then (i) C n t = t 0 iff [ n ptq = pt 0 q (ii) n s = s 0 iff C n xsy = xs 0 y. The relationship between the respective cbv systems with respect to the same translations is ....

P. de Groote. A CPS-translation of the ¯-calculus. In S. Tison, editor, Proceedings of the 19th International Colloquium on Trees in Algebra and Programming (CAAP'94), pages 85--138. Springer-Verlag, 1994.

....[10] In addition, DJS themselves gave an explanation in their introduction of [4] about the relation between the LKT, the negative fragment of the LC, and Parigot s CND. With regards to isomorphism, DeGroote previously displayed the translation from calculus of Parigot[17] to CBN CPS calculus [5]. Herbelin s calculus Herbelin (1994) published a detailed work on the term calculus of the LJT, which is an intuitionistic fragment of the LKT. He interpreted LJT proofs as programs and cut elimination steps as reduction steps, just as we do here. We show that his system can be totally ....

....terms. That is, it translates ND derivation (as a special case of CND derivation) into LKT and LKQ derivation. We extend his transform to classical one. Remark 4. 2 DeGroote revealed the relation between the CBN CPS and the Parigot s CND and its computational interpretation( calculus) [5]. However our method, which is based on decoration, is far more precise and unifying. Specifically we extended this relation to CBV calculus for the first time. Plotkin shows that a CPS translated term simulates CBN CBV reduction strategy of original term. This justifies our claim CBN CBV ....

Phillipe de Groote. A cps-translation of the ¯-calculus. In Proceedings Trees in Algebra and Programming -- CAAP'94, pages 85--99. Springer-Verlag LNCS 787, April 1994.

....passing syle (CPS) translations, which have been thoroughly studied in calculus [25, 47, 58] becomes Kolmogorov s embedding of classical logic into minimal logic if 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 ....

P. de Groote. A cps-translation of the ¯-calculus. In S. Tison, editor, Colloquium on Trees in Algebra and Programming, volume 787 of Lecture Notes in Computer Science, pages 85--99. Springer-Verlag, 1994.

....On the other hand, since Griffin s influential work[13] on Curry Howard correspondence between classical proofs and programs, there has been a lot of interest on programming in classical proofs. In this line of approach, Parigot s calculus [19] considered to be a standard style. DeGroote[6] presented the relation between call by name(CBN) continuation passing style(CPS) and classical proofs in calculus style. Proof theoretically speaking, this translation induces a logical embedding of classical logic into intuitionistic logic, which is akin to Kolmogorov s negative translation. ....

..... In this formalization, administrative reduction is not needed any more because continuation is not the part of logical system. In relation to calculus ,name has the same role. This equivalence between continuation variable (of CPS) and name variable (of calculus ) was found by DeGroote[6] on CBN case. 5 LKQ term calculus LKQ= Since LKQ LKT inherits computational property of linear logic, it seems reasonable to make it as a subsystem of Proof Net. In this paper, we treat only a term calculus on LKQ which is CBV programming system on classical proofs. We explain how to program ....

Phillipe de Groote. A cps-translation of the ¯-calculus. In Proceedings Trees in Algebra and Programming -- CAAP'94, pages 85--99. Springer-Verlag LNCS 787, April 1994.

....calculi which we omit in this paper. calculus: In addition to CPS calculus, Parigot s calculus [20, 21, 22, 23] is also considered as a standard for classical proofs as programs approach on classical natural deduction (CND) DeGroote revealed the relation between CBN CPS and calculus [5]. Moreover, Ong and Stewart (OS) introduce a call by value (CBV) version of calculus in [18] in which they introduce a new reduction rule (i arg ) Parigot proves the computational properties (such as SN and CR) of CBN versions of calculus individually. OS also does the same in CBV case. ....

Phillipe de Groote. A cps-translation of the ¯-calculus. In Proceedings Trees in Algebra and Programming -- CAAP'94, pages 85--99. Springer-Verlag LNCS 787, April 1994.

....initiated independently of his work. It is not possible here to explain the aims and achievements of the individual lines of work; it must suffice simply to mention the work of Murthy [14, 59, 60, 61, 62] Barbanera and Berardi [2, 3, 4, 5, 6] Rezus [74, 75] Parigot [66, 67, 68, 69] de Groote [25, 27, 28, 29, 30], Krivine [57] Girard [42] Danos, Joinet, and Schellinx [18] Rehof and S rensen [73] Duba, Harper, and MacQueen[32] Harper and Lillibridge [46, 47] Coquand [15] Berardi, Bezem, and Coquand [11] Ong [65] Underwood [89] and Sato [78] Most of these lines of work study one specific ....

P. de Groote. A CPS-translation of the ¯-calculus. In S. Tison, editor, Colloquium on Trees in Algebra and Programming, volume 787 of Lecture Notes in Computer Science, pages 85--99. Springer-Verlag, 1994.

....between calculus and ILU in [7] In addition, DJS themselves gave an explanation in their introduction of [2] about the relation between the LKT, the negative fragment of the LC, and Parigot s CND. Especially, the second part of our work can be seen as a refinement of the De Groote s work [3]. His investigation is about the CPS translation of the n . However his method was merely syntactic. What is new to our work is that we adopt this method to the proof theory. Herbelin s calculus Herbelin[9] published a detailed work on the term calculus of the LJT, which is an intuitionistic ....

Phillipe de Groote. A cps-translation of the ¯-calculus. In Proceedings Trees in Algebra and Programming -- CAAP'94, pages 85--99. Springer-Verlag LNCS 787, April 1994.

....it does not satisfy, in general, the subject reduction property. The equivalent of ( in the calculus is the following rule: ff: M ) A 0 : An ff: M [ff : f: ff ] f A 0 : An ) which is compatible and satisfies the subject reduction property for any type. However, Ph. de Groote 2 the implementation of this last rule on an environment machine is not straightforward. The difficulty is that the outermost abstraction which occurs in the left hand side of ( does not disappear in its right hand side. Consequently, a straightforward implementation of ( would require ....

....proposition that stands for absurdity, and A ranges over atomic propositions. We also introduce the set of cotypes by saying that is a cotype whenever is a type. y In Section 5, we provide a formal treatment of the notion of free and bound occurences in terms of de Bruijn indices. Ph. de Groote 4 The type system of the calculus is then defined by means of a sequent calculus. The sequents are of the form Gamma Gamma T : where is a type, T is a term, and Gamma is the typing context. Such typing contexts are defined as sets of declarations of the form (x : oe) or (ff : ae ....

[Article contains additional citation context not shown here]

Ph. de Groote. A CPS-translation of the ¯-calculus. In S. Tison, editor, Proceedings of the 19th International Colloquium on Trees in Algebra and Programming (CAAP'94), pages 85-- 99. Lecture Notes in Computer Science, 787, Springer Verlag, 1994.

.... On the proof theoretic side, Parigot has introduced the calculus, an algorithmic interpretation of cut elimination in classical natural deduction [16, 17, 18] From a computer science point of view, the iclassicalj constructs of the calculus may be interpreted in terms of labels and jumps [7]. Independently of Parigot, Rehof and S#rensen have developped a calculus ( Delta ) reminiscent of the calculus [21] They use applications of the form (xM ) instead of named terms. Consequently they may simulate Parigot s structural reduction with usual substitution and fi reduction. In yet ....

Ph. de Groote. A CPS-translation of the ¯-calculus. In S. Tison, editor, Proceedings of the 19th International Colloquium on Trees in Algebra and Programming (CAAP'94), pages 8599. Lecture Notes in Computer Science, 787, Springer Verlag, 1994.

No context found.

Ph. de Groote. A CPS-translation of the ¯-calculus. In Proceedings of the Colloquium on Trees in Algebra and Programming (CAAP'94). Lecture Notes in Computer Science, Springer Verlag, 1994.

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