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...
Saved in:
| Published in: | Mathematical structures in computer science Vol. 32; no. 8; pp. 1066 - 1098 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
01.09.2022
|
| Subjects: | |
| ISSN: | 0960-1295, 1469-8072 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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 |
| Author_xml | – sequence: 1 givenname: Péter orcidid: 0000-0001-6703-9661 surname: Battyányi fullname: Battyányi, Péter – sequence: 2 givenname: Karim orcidid: 0000-0003-1943-272X surname: Nour fullname: Nour, Karim |
| BookMark | eNplkE9LxDAUxIOsYHf1A3greJToe8k2TY6y6CoselDBW0jTFLv0n0kLrp_elPXmaeDNjzfDLMmi6ztHyCXCDQLmt6-gBCBTGWMAsMaPE5LgWigqIWcLksw2nf0zsgxhD4AcQSXk-rn3rWnqHzPWfZfWXTp-ujTU7dAc0vEwuDKl1jR2aqZwTk4r0wR38acr8v5w_7Z5pLuX7dPmbkctSv5NS1G4gkmQtsgqJkVm8pJXFrlhvGBWVOBix5yVXPB4V0rKggOLfSyWLkIrcnX8O_j-a3Jh1Pt-8l2M1EzyTCmFLIsUHinr-xC8q_Tg69b4g0bQ8yb63yb8F9V9VCg |
| 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 |
| ContentType | Journal Article |
| Copyright | The Author(s), 2023. Published by Cambridge University Press. This work is licensed under the Creative Commons Attribution License This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited. (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| Copyright_xml | – notice: The Author(s), 2023. Published by Cambridge University Press. This work is licensed under the Creative Commons Attribution License This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited. (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
| DBID | AAYXX CITATION 3V. 7SC 7XB 88I 8AL 8FD 8FE 8FG 8FK ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ JQ2 K7- L6V L7M L~C L~D M0N M2P M7S P5Z P62 PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U |
| DOI | 10.1017/S096012952200041X |
| DatabaseName | CrossRef ProQuest Central (Corporate) Computer and Information Systems Abstracts ProQuest Central (purchase pre-March 2016) Science Database (Alumni Edition) Computing Database (Alumni Edition) Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Technology Collection ProQuest One ProQuest Central ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Computing Database Science Database (via ProQuest SciTech Premium Collection) Engineering Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection ProQuest Central Basic |
| DatabaseTitle | CrossRef Computer Science Database ProQuest Central Student Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts ProQuest Central (Alumni Edition) SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Advanced Technologies Database with Aerospace Engineering Collection Advanced Technologies & Aerospace Collection ProQuest Computing Engineering Database ProQuest Science Journals (Alumni Edition) ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database ProQuest One Academic UKI Edition Materials Science & Engineering Collection ProQuest One Academic ProQuest Central (Alumni) ProQuest One Academic (New) |
| DatabaseTitleList | CrossRef Computer Science Database |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISSN | 1469-8072 |
| EndPage | 1098 |
| ExternalDocumentID | 10_1017_S096012952200041X |
| GroupedDBID | -1D -1F -2P -2V -E. -~6 -~N .DC .FH 09C 09E 0E1 0R~ 29M 4.4 5GY 5VS 6~7 74X 74Y 7~V 88I 8FE 8FG 8R4 8R5 9M5 AAAZR AABES AABWE AACJH AAGFV AAKNA AAKTX AAMNQ AANRG AARAB AASVR AAUIS AAUKB AAYXX ABBXD ABBZL ABGDZ ABITZ ABJCF ABJNI ABKKG ABMWE ABQTM ABQWD ABROB ABTCQ ABUWG ABVFV ABVKB ABVZP ABXAU ABXHF ABZCX ACBMC ACDLN ACEJA ACETC ACGFS ACGOD ACIMK ACIWK ACUIJ ACYZP ACZBM ACZUX ACZWT ADCGK ADDNB ADFEC ADKIL ADOVH ADOVT ADVJH AEBAK AEBPU AEHGV AEMTW AENCP AENEX AENGE AFFHD AFFUJ AFKQG AFKRA AFLOS AFLVW AFUTZ AFZFC AGABE AGBYD AGJUD AGLWM AHQXX AHRGI AIGNW AIHIV AIOIP AISIE AJ7 AJCYY AJPFC AJQAS AKMAY AKZCZ ALMA_UNASSIGNED_HOLDINGS ALVPG ALWZO AMVHM ANOYL AQJOH ARABE ARAPS ARZZG ATUCA AUXHV AYIQA AZQEC BBLKV BCGOX BENPR BESQT BGHMG BGLVJ BJBOZ BLZWO BMAJL BPHCQ C0O CAG CBIIA CCPQU CCQAD CCTKK CCUQV CDIZJ CFAFE CFBFF CGQII CHEAL CITATION CJCSC COF CS3 DC4 DOHLZ DU5 DWQXO EBS EGQIC EJD GNUQQ HCIFZ HG- HST HZ~ I.6 I.7 I.9 IH6 IOEEP IOO IS6 I~P J36 J38 J3A JHPGK JQKCU K6V K7- KAFGG KCGVB KFECR L6V L98 LHUNA LW7 M-V M2P M7S M7~ M8. NIKVX NMFBF NZEOI O9- OYBOY P2P P62 PHGZM PHGZT PQGLB PQQKQ PROAC PTHSS PYCCK Q2X RAMDC RCA ROL RR0 S6- S6U SAAAG T9M TN5 UT1 WFFJZ WQ3 WXU WYP ZDLDU ZJOSE ZMEZD ZYDXJ ~V1 3V. 7SC 7XB 8AL 8FD 8FK JQ2 L7M L~C L~D M0N PKEHL PQEST PQUKI PRINS Q9U |
| ID | FETCH-LOGICAL-c183x-d6beb2808cb5f2865a7d3fc13a23b2c6f0e20072d3633fc9988b302310c1dea23 |
| IEDL.DBID | M2P |
| ISSN | 0960-1295 |
| IngestDate | Mon Nov 10 03:07:54 EST 2025 Sat Nov 29 03:56:53 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 8 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c183x-d6beb2808cb5f2865a7d3fc13a23b2c6f0e20072d3633fc9988b302310c1dea23 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0001-6703-9661 0000-0003-1943-272X |
| OpenAccessLink | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/D68E152F29BBF0683FDA756A58C41231/S096012952200041Xa.pdf/div-class-title-normalization-in-the-simply-typed-span-class-inlineformula-span-class-alternatives-img-class-inline-graphic-mathjax-alternative-mathjax-alt-graphic-mathjax-off-data-mimesubtype-png-data-type-src-staticdomain-binary-version-id-urn-cambridge-org-id-binary-20230112085238745-0340-s096012952200041x-s096012952200041x-inline1-png-span-class-mathjax-tex-wrapper-data-mathjax-type-texmath-span-class-tex-math-mathjax-tex-math-mathjax-on-lambda-mu-mu-rho-theta-varepsilon-span-span-span-span-calculus-div.pdf |
| PQID | 2835999125 |
| PQPubID | 33085 |
| PageCount | 33 |
| ParticipantIDs | proquest_journals_2835999125 crossref_primary_10_1017_S096012952200041X |
| PublicationCentury | 2000 |
| PublicationDate | 20220901 |
| PublicationDateYYYYMMDD | 2022-09-01 |
| PublicationDate_xml | – month: 09 year: 2022 text: 20220901 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Cambridge |
| PublicationPlace_xml | – name: Cambridge |
| PublicationSubtitle | MSCS |
| PublicationTitle | Mathematical structures in computer science |
| PublicationYear | 2022 |
| Publisher | Cambridge University Press |
| Publisher_xml | – name: Cambridge University Press |
| 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 |
| SSID | ssj0013109 |
| Score | 2.2616818 |
| 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... |
| SourceID | proquest crossref |
| SourceType | Aggregation Database Index Database |
| StartPage | 1066 |
| SubjectTerms | Algorithms Calculus Isomorphism Logic Numbers Reduction Syntax |
| Title | Normalization in the simply typed -calculus |
| URI | https://www.proquest.com/docview/2835999125 |
| Volume | 32 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVPQU databaseName: Advanced Technologies & Aerospace Database customDbUrl: eissn: 1469-8072 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0013109 issn: 0960-1295 databaseCode: P5Z dateStart: 20010201 isFulltext: true titleUrlDefault: https://search.proquest.com/hightechjournals providerName: ProQuest – providerCode: PRVPQU databaseName: Computer Science Database customDbUrl: eissn: 1469-8072 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0013109 issn: 0960-1295 databaseCode: K7- dateStart: 20010201 isFulltext: true titleUrlDefault: http://search.proquest.com/compscijour providerName: ProQuest – providerCode: PRVPQU databaseName: Engineering Database customDbUrl: eissn: 1469-8072 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0013109 issn: 0960-1295 databaseCode: M7S dateStart: 20010201 isFulltext: true titleUrlDefault: http://search.proquest.com providerName: ProQuest – providerCode: PRVPQU databaseName: ProQuest Central customDbUrl: eissn: 1469-8072 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0013109 issn: 0960-1295 databaseCode: BENPR dateStart: 20010201 isFulltext: true titleUrlDefault: https://www.proquest.com/central providerName: ProQuest – providerCode: PRVPQU databaseName: Science Database (via ProQuest SciTech Premium Collection) customDbUrl: eissn: 1469-8072 dateEnd: 20241209 omitProxy: false ssIdentifier: ssj0013109 issn: 0960-1295 databaseCode: M2P dateStart: 20010201 isFulltext: true titleUrlDefault: https://search.proquest.com/sciencejournals providerName: ProQuest |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1JS8NAFH64Hby4i9Va5iC4wGAzWT2JikVQS3GjSiBklmChprWpooj_3ffShCqCFw-Zw5s5hJm3fPPmLQBbSYIqL5Ye96jInVO3HY6sbLjjmiCm-mQqD8a8u_CbzaDdPmgVDresCKssdWKuqHVPkY98n-qCEZgR7mH_mVPXKHpdLVpoTMI0IhuLQrouRWv8imCNQjwQpXO0a275qpmXjEYi0QTlqjh5ycZvdumnWs5tTWP-v3-5AHMFymRHI7ZYhAmTLsF82cGBFQK9DPdNgqzdIheTdVKGeJBlnad-952Rd1azcOcjRK6ROmbh00v-bX-Gg8ceC3HtEKmv8cD0s063l4a7HI-cHIrZCtw2Tm9OznjRbIErlOo3rj2Jl-ygHijpJpSuGvvaTpRlx8KWQnlJ3ZBbU2jbs5GOt7RAUsMhq64sbXDRKkylvdSsAaOmup4UlrGlRLSFZ278WAitHI2AI_YrsFduddQf1dSIRsFmfvTrXCpQLXc6KsQri8bbvP739AbMCspXyIPCqjA1HLyYTZhRr8NONqjB9PFps3VVg8lzn9dy3qHRv8ax5T58AVBVygw |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1JS-RQEC4aZ0Avo-OC7ajzDooLPOy8pJN4EBmcEcW28aCDQiC-LUxDd7rttBviX_I3TlUWemTAmwcPuVRySepLba_qK4C1JEGTJ5XPfSK58xquxxHKlntNG0riJ9N5M-bvVtBuh5eXu2c1eKlmYaitsrKJuaE2fU018h3iBaNgRjT3BzectkbR6Wq1QqOAxYl9vMeULds7_on6XRfi8Nf5wREvtwpwjfB94MZXmE2GjVCrZkJzmTIwbqIdVwpXCe0nDUv1O2Fc30U5piOhos06TkM7xkoiOkCT_8kjZjFqFRRn41MLp2gpwayAox9tVqeoOUU1CkkmaDbGyyki__GDr91A7tsOpz_aV5mBL2UUzX4UsP8KNZvOwnS1oYKVBmsOrtoUknfLWVPWSRnGuyzr9AbdR0bVZ8OizacI_wplJIt6t_m18RwN__RZhM-OUHonh3aQdbr9NNriCGkqmGbzcPEuL7gAE2k_tYvAaGmwr4RjXaUwmkRM20AKYbRnMKCSQR22K9XGg4IzJC6a6YL4PxzUYbnSbFyajyweq3Xp7dvfYfLo_LQVt47bJ99gStBsRt4AtwwTo-GtXYHP-m7UyYarOVIZXL83CP4CBCsiCA |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Normalization+in+the+simply+typed+-calculus&rft.jtitle=Mathematical+structures+in+computer+science&rft.au=Batty%C3%A1nyi%2C+P%C3%A9ter&rft.au=Nour%2C+Karim&rft.date=2022-09-01&rft.issn=0960-1295&rft.eissn=1469-8072&rft.volume=32&rft.issue=8&rft.spage=1066&rft.epage=1098&rft_id=info:doi/10.1017%2FS096012952200041X&rft.externalDBID=n%2Fa&rft.externalDocID=10_1017_S096012952200041X |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0960-1295&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0960-1295&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0960-1295&client=summon |