Normalization in the simply typed -calculus

In this paper, in connection with the program of extending the Curry–Howard isomorphism to classical logic, we study the $\lambda \mu$ -calculus of Parigot emphasizing the difference between the original version of Parigot and the version of de Groote in terms of normalization properties. In order t...

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Veröffentlicht in:	Mathematical structures in computer science Jg. 32; H. 8; S. 1066 - 1098
Hauptverfasser:	Battyányi, Péter, Nour, Karim
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Cambridge Cambridge University Press 01.09.2022
Schlagworte:	Algorithms Calculus Isomorphism Logic Numbers Reduction Syntax
ISSN:	0960-1295, 1469-8072
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Abstract	In this paper, in connection with the program of extending the Curry–Howard isomorphism to classical logic, we study the $\lambda \mu$ -calculus of Parigot emphasizing the difference between the original version of Parigot and the version of de Groote in terms of normalization properties. In order to talk about a satisfactory representation of the integers, besides the usual $\beta$ -, $\mu$ -, and $\mu '$ -reductions, we consider the $\lambda \mu$ -calculus augmented with the reduction rules $\rho$ , $\theta$ and $\varepsilon$ . We show that we need all of these rules for this purpose. Then we prove that, with the syntax of Parigot, the calculus enjoys the strong normalization property even when we add the rules $\rho$ , $\theta$ , and $\epsilon$ , while the $\lambda \mu$ -calculus presented with the more flexible de Groote-style syntax, in contrast, has only the weak normalization property. In particular, we present a normalization algorithm for the $\beta \mu \mu '\rho \theta \varepsilon$ -reduction in the de Groote-style calculus.
AbstractList	In this paper, in connection with the program of extending the Curry–Howard isomorphism to classical logic, we study the $\lambda \mu$ -calculus of Parigot emphasizing the difference between the original version of Parigot and the version of de Groote in terms of normalization properties. In order to talk about a satisfactory representation of the integers, besides the usual $\beta$ -, $\mu$ -, and $\mu '$ -reductions, we consider the $\lambda \mu$ -calculus augmented with the reduction rules $\rho$ , $\theta$ and $\varepsilon$ . We show that we need all of these rules for this purpose. Then we prove that, with the syntax of Parigot, the calculus enjoys the strong normalization property even when we add the rules $\rho$ , $\theta$ , and $\epsilon$ , while the $\lambda \mu$ -calculus presented with the more flexible de Groote-style syntax, in contrast, has only the weak normalization property. In particular, we present a normalization algorithm for the $\beta \mu \mu '\rho \theta \varepsilon$ -reduction in the de Groote-style calculus. In this paper, in connection with the program of extending the Curry–Howard isomorphism to classical logic, we study the $\lambda \mu$-calculus of Parigot emphasizing the difference between the original version of Parigot and the version of de Groote in terms of normalization properties. In order to talk about a satisfactory representation of the integers, besides the usual $\beta$-, $\mu$-, and $\mu '$-reductions, we consider the $\lambda \mu$-calculus augmented with the reduction rules $\rho$, $\theta$ and $\varepsilon$. We show that we need all of these rules for this purpose. Then we prove that, with the syntax of Parigot, the calculus enjoys the strong normalization property even when we add the rules $\rho$, $\theta$, and $\epsilon$, while the $\lambda \mu$-calculus presented with the more flexible de Groote-style syntax, in contrast, has only the weak normalization property. In particular, we present a normalization algorithm for the $\beta \mu \mu '\rho \theta \varepsilon$-reduction in the de Groote-style calculus.
Author	Nour, Karim Battyányi, Péter
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Cites_doi	10.1016/j.apal.2008.10.012 10.1109/SFCS.1983.50 10.1007/978-3-642-54830-7_26 10.2307/2275652 10.1002/1521-3870(200204)48:3<357::AID-MALQ357>3.0.CO;2-L 10.1145/944705.944723 10.1007/s001530050076 10.1007/3-540-57887-0_113 10.1016/0168-0072(94)90047-7 10.1007/BFb0013061 10.1007/978-3-540-32033-3_15 10.1007/3-540-45061-0_68 10.1007/3-540-57887-0_112 10.1007/11417170_13 10.1017/S0960129598002667 10.1007/BFb0022575 10.1145/351240.351262
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References	David (S096012952200041X_ref7) 2007; 77 Saurin (S096012952200041X_ref26) 2008; 5213 Krivine (S096012952200041X_ref12) 1993 Griffin (S096012952200041X_ref11) 1990 de Groote (S096012952200041X_ref9) 1994; 822 S096012952200041X_ref22 S096012952200041X_ref3 S096012952200041X_ref2 Girard (S096012952200041X_ref10) 1989 S096012952200041X_ref23 S096012952200041X_ref5 S096012952200041X_ref21 S096012952200041X_ref6 S096012952200041X_ref24 S096012952200041X_ref25 S096012952200041X_ref8 Sørensen (S096012952200041X_ref28) 2006 Nour (S096012952200041X_ref20) 2017; 13 Battyányi (S096012952200041X_ref4) 2020; 5 S096012952200041X_ref29 S096012952200041X_ref30 Saurin (S096012952200041X_ref27) 2012 S096012952200041X_ref1 S096012952200041X_ref15 S096012952200041X_ref16 S096012952200041X_ref13 S096012952200041X_ref14 S096012952200041X_ref19 S096012952200041X_ref17 S096012952200041X_ref18
References_xml	– ident: S096012952200041X_ref19 doi: 10.1016/j.apal.2008.10.012 – volume: 822 start-page: 31 volume-title: 5th International Conference on Logic Programming and Automated Reasoning, LPAR’94, Lecture Notes in Artificial Intelligence year: 1994 ident: S096012952200041X_ref9 – volume-title: Conference Record of the Seventeenth Annual ACM Symposium on Principles of Programming Languages, POPL’90 year: 1990 ident: S096012952200041X_ref11 – volume-title: Lectures on the Curry-Howard Isomorphism year: 2006 ident: S096012952200041X_ref28 – volume: 5213 start-page: 154 volume-title: 17th EACSL Annual Conference on Computer Science Logic, Lecture Notes in Computer Science year: 2008 ident: S096012952200041X_ref26 – ident: S096012952200041X_ref14 doi: 10.1109/SFCS.1983.50 – ident: S096012952200041X_ref15 doi: 10.1007/978-3-642-54830-7_26 – volume: 13 start-page: 13 1 year: 2017 ident: S096012952200041X_ref20 article-title: A revised completeness result for the simply typed $\lambda \mu$ -calculus using realizability semantics publication-title: Logical Methods in Computer Science – ident: S096012952200041X_ref23 doi: 10.2307/2275652 – volume: 77 start-page: 489 year: 2007 ident: S096012952200041X_ref7 article-title: Arithmetical proofs of strong normalization results for symmetric lambda calculi publication-title: Fundamenta Informaticae – ident: S096012952200041X_ref16 – ident: S096012952200041X_ref18 doi: 10.1002/1521-3870(200204)48:3<357::AID-MALQ357>3.0.CO;2-L – ident: S096012952200041X_ref29 doi: 10.1145/944705.944723 – ident: S096012952200041X_ref17 doi: 10.1007/s001530050076 – ident: S096012952200041X_ref25 doi: 10.1007/3-540-57887-0_113 – ident: S096012952200041X_ref13 doi: 10.1016/0168-0072(94)90047-7 – ident: S096012952200041X_ref21 doi: 10.1007/BFb0013061 – start-page: 435 106 volume-title: Böhm theorem and Böhm trees for the Lambda-mu-calculus year: 2012 ident: S096012952200041X_ref27 – ident: S096012952200041X_ref30 doi: 10.1007/978-3-540-32033-3_15 – volume: 5 start-page: 3702 year: 2020 ident: S096012952200041X_ref4 article-title: Normalization proofs for the un-typed $\mu \mu '$ -calculus publication-title: LICMA’19 Lebanese International Conference on Mathematics and Applications, AIMS Mathematics – ident: S096012952200041X_ref1 doi: 10.1007/3-540-45061-0_68 – ident: S096012952200041X_ref2 doi: 10.1007/3-540-57887-0_112 – ident: S096012952200041X_ref6 doi: 10.1007/11417170_13 – ident: S096012952200041X_ref8 doi: 10.1017/S0960129598002667 – volume-title: Lambda-Calculus Types and Models year: 1993 ident: S096012952200041X_ref12 – ident: S096012952200041X_ref3 – ident: S096012952200041X_ref24 – ident: S096012952200041X_ref22 doi: 10.1007/BFb0022575 – volume-title: Proofs and Types year: 1989 ident: S096012952200041X_ref10 – ident: S096012952200041X_ref5 doi: 10.1145/351240.351262
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Snippet	In this paper, in connection with the program of extending the Curry–Howard isomorphism to classical logic, we study the $\lambda \mu$ -calculus of Parigot... In this paper, in connection with the program of extending the Curry–Howard isomorphism to classical logic, we study the $\lambda \mu$-calculus of Parigot...
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SubjectTerms	Algorithms Calculus Isomorphism Logic Numbers Reduction Syntax
Title	Normalization in the simply typed -calculus
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