Confluence for classical logic through the distinction between values and computations

We apply an idea originated in the theory of programming languages - monadic meta-language with a distinction between values and computations - in the design of a calculus of cut-elimination for classical logic. The cut-elimination calculus we obtain comprehends the call-by-name and call-by-value fr...

Full description

Saved in:
Bibliographic Details
Published in:Electronic proceedings in theoretical computer science Vol. 164; no. Proc. CL&C 2014; pp. 63 - 77
Main Authors: Espírito Santo, José, Matthes, Ralph, Nakazawa, Koji, Pinto, Luís
Format: Journal Article
Language:English
Published: Open Publishing Association 09.09.2014
ISSN:2075-2180, 2075-2180
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract We apply an idea originated in the theory of programming languages - monadic meta-language with a distinction between values and computations - in the design of a calculus of cut-elimination for classical logic. The cut-elimination calculus we obtain comprehends the call-by-name and call-by-value fragments of Curien-Herbelin's lambda-bar-mu-mu-tilde-calculus without losing confluence, and is based on a distinction of "modes" in the proof expressions and "mode" annotations in types. Modes resemble colors and polarities, but are quite different: we give meaning to them in terms of a monadic meta-language where the distinction between values and computations is fully explored. This meta-language is a refinement of the classical monadic language previously introduced by the authors, and is also developed in the paper.
AbstractList We apply an idea originated in the theory of programming languages - monadic meta-language with a distinction between values and computations - in the design of a calculus of cut-elimination for classical logic. The cut-elimination calculus we obtain comprehends the call-by-name and call-by-value fragments of Curien-Herbelin's lambda-bar-mu-mu-tilde-calculus without losing confluence, and is based on a distinction of "modes" in the proof expressions and "mode" annotations in types. Modes resemble colors and polarities, but are quite different: we give meaning to them in terms of a monadic meta-language where the distinction between values and computations is fully explored. This meta-language is a refinement of the classical monadic language previously introduced by the authors, and is also developed in the paper.
Author Espírito Santo, José
Matthes, Ralph
Nakazawa, Koji
Pinto, Luís
Author_xml – sequence: 1
  givenname: José
  surname: Espírito Santo
  fullname: Espírito Santo, José
– sequence: 2
  givenname: Ralph
  surname: Matthes
  fullname: Matthes, Ralph
– sequence: 3
  givenname: Koji
  surname: Nakazawa
  fullname: Nakazawa, Koji
– sequence: 4
  givenname: Luís
  surname: Pinto
  fullname: Pinto, Luís
BookMark eNpNkMFKAzEQhoNUsNaefIHcZWuSzW42R1mqFgoKVq9hkk3alO2mJFvFt3fbijiXf_iH-Q7fNRp1obMI3VIy44zw-_nrqn6b0ZLPigs0ZkQUGaMVGf3br9A0pS0ZJpeMy3KMPurQufZgO2OxCxGbFlLyBlrchrU3uN_EcFhvhrS48an3nel96LC2_Ze1Hf6E4Tlh6Bpswm5_6OF4Tjfo0kGb7PQ3J-j9cb6qn7Ply9OiflhmJq9Yn2mppTCOcGmk4EA1tWBIUTnghdAVYYLxqsklLRrpaFkyqytHZFMK0OAA8glanLlNgK3aR7-D-K0CeHUqQlwriL03rVW80DnRTLuSaQ66ACZkJRqprbBaAB1Yd2eWiSGlaN0fjxJ1NKxOhtVgWBX5D7DwccY
Cites_doi 10.1145/174675.178053
10.1017/S0960129512000436
10.2307/2275572
10.1016/j.tcs.2006.12.027
10.1145/351240.351262
10.1007/978-3-540-24727-2_30
10.1007/s10990-006-0480-6
10.1016/0890-5401(91)90052-4
10.1016/j.apal.2008.01.001
10.1007/978-3-642-15240-5_13
10.1017/S0960129500001328
10.1007/3-540-58140-5_35
10.1007/978-3-642-04027-6_30
ContentType Journal Article
DBID AAYXX
CITATION
DOA
DOI 10.4204/EPTCS.164.5
DatabaseName CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList
Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
DeliveryMethod fulltext_linktorsrc
Discipline Computer Science
EISSN 2075-2180
EndPage 77
ExternalDocumentID oai_doaj_org_article_45b30b2bf62b4ab5a27987d9be7eb7a1
10_4204_EPTCS_164_5
GroupedDBID 5VS
AAYXX
ADBBV
ALMA_UNASSIGNED_HOLDINGS
BCNDV
CITATION
E3Z
GROUPED_DOAJ
KQ8
M~E
OK1
ID FETCH-LOGICAL-c382t-b9b97cf049c974a1b1eac058fa457b8027248d3915d9f1662eb8f09d67abafaa3
IEDL.DBID DOA
ISICitedReferencesCount 0
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000420008500006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 2075-2180
IngestDate Fri Oct 03 12:39:33 EDT 2025
Sat Nov 29 02:05:24 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed false
IsScholarly true
Issue Proc. CL&C 2014
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c382t-b9b97cf049c974a1b1eac058fa457b8027248d3915d9f1662eb8f09d67abafaa3
OpenAccessLink https://doaj.org/article/45b30b2bf62b4ab5a27987d9be7eb7a1
PageCount 15
ParticipantIDs doaj_primary_oai_doaj_org_article_45b30b2bf62b4ab5a27987d9be7eb7a1
crossref_primary_10_4204_EPTCS_164_5
PublicationCentury 2000
PublicationDate 2014-09-09
PublicationDateYYYYMMDD 2014-09-09
PublicationDate_xml – month: 09
  year: 2014
  text: 2014-09-09
  day: 09
PublicationDecade 2010
PublicationTitle Electronic proceedings in theoretical computer science
PublicationYear 2014
Publisher Open Publishing Association
Publisher_xml – name: Open Publishing Association
References Curien (Curien-Munch-Maccagnoni-ifipTCS10) 2010; 323
van Oostrom (vanOostrom-vanRaamsdonk94) 1994; 813
Polonovski (PolonovskiFOSSACS2004) 2004; 2987
Zeilberger (ZeilbergerAPAL08) 2008; 153
Moggi (Moggi91) 1991; 93
Hatcliff (HatcliffDanvy94) 1994
Levy (LevyHOSC2006) 2006; 19
Girard (GirardMSCS91) 1991; 1
Curien (CurienHerbelinICFP2000) 2000; 35
Dehornoy (Dehornoy-vanOostrom2008) 2008
Girard (GirardLafontTaylor89) 1989
Filinski (FilinskiTCS2007) 2007; 375
Espírito Santo (ourMSCS) 2013; 23
Munch-Maccagnoni (Munch-MaccagnoniCSL09) 2009; 5771
Danos (DanosJoinetSchellinxJSL97) 1997; 62
References_xml – start-page: 458
  volume-title: POPL'94
  year: 1994
  ident: HatcliffDanvy94
  article-title: A generic account of continuation-passing styles
  doi: 10.1145/174675.178053
– volume: 23
  start-page: 1111
  issue: 6
  year: 2013
  ident: ourMSCS
  article-title: Monadic translation of classical sequent calculi
  publication-title: Mathematical Structures in Computer Science
  doi: 10.1017/S0960129512000436
– volume: 62
  start-page: 755
  issue: 3
  year: 1997
  ident: DanosJoinetSchellinxJSL97
  article-title: A New Deconstructive Logic: Linear Logic
  publication-title: J. Symb. Log.
  doi: 10.2307/2275572
– volume-title: Proofs and Types
  year: 1989
  ident: GirardLafontTaylor89
– volume: 375
  start-page: 41
  year: 2007
  ident: FilinskiTCS2007
  article-title: On the relations between monadic semantics
  publication-title: Theor. Comput. Science
  doi: 10.1016/j.tcs.2006.12.027
– volume: 35
  start-page: 233
  volume-title: ICFP '00
  year: 2000
  ident: CurienHerbelinICFP2000
  article-title: The duality of computation
  doi: 10.1145/351240.351262
– volume: 2987
  start-page: 423
  volume-title: FoSSaCS 2004
  year: 2004
  ident: PolonovskiFOSSACS2004
  article-title: Strong normalization oføverline λμtilde07Eμ with explicit substitutions
  doi: 10.1007/978-3-540-24727-2_30
– volume: 19
  start-page: 377
  issue: 4
  year: 2006
  ident: LevyHOSC2006
  article-title: Call-by-push-value: decomposing call-by-value and call-by-name
  publication-title: Higher Order and Symbolic Computation
  doi: 10.1007/s10990-006-0480-6
– volume: 93
  start-page: 55
  issue: 1
  year: 1991
  ident: Moggi91
  article-title: Notions of Computation and Monads
  publication-title: Inf. Comput.
  doi: 10.1016/0890-5401(91)90052-4
– volume: 153
  start-page: 66
  year: 2008
  ident: ZeilbergerAPAL08
  article-title: On the unity of duality
  publication-title: Ann. Pure App. Logic
  doi: 10.1016/j.apal.2008.01.001
– volume-title: Logical Models of Reasoning and Computation (LMRC-08)
  year: 2008
  ident: Dehornoy-vanOostrom2008
  article-title: Z, Proving Confluence by Monotonic Single-Step Upperbound Functions
– volume: 323
  start-page: 165
  volume-title: TCS 2010
  year: 2010
  ident: Curien-Munch-Maccagnoni-ifipTCS10
  article-title: The Duality of Computation under Focus
  doi: 10.1007/978-3-642-15240-5_13
– volume: 1
  start-page: 255
  issue: 3
  year: 1991
  ident: GirardMSCS91
  article-title: A new constructive logic: classic logic
  publication-title: Mathematical Structures in Computer Science
  doi: 10.1017/S0960129500001328
– volume: 813
  start-page: 379
  volume-title: LFCS '94
  year: 1994
  ident: vanOostrom-vanRaamsdonk94
  article-title: Weak orthogonality implies confluence: the higher-order case
  doi: 10.1007/3-540-58140-5_35
– volume: 5771
  start-page: 409
  volume-title: CSL 2009
  year: 2009
  ident: Munch-MaccagnoniCSL09
  article-title: Focalisation and Classical Realisability
  doi: 10.1007/978-3-642-04027-6_30
SSID ssj0000392496
Score 1.9038991
Snippet We apply an idea originated in the theory of programming languages - monadic meta-language with a distinction between values and computations - in the design...
SourceID doaj
crossref
SourceType Open Website
Index Database
StartPage 63
Title Confluence for classical logic through the distinction between values and computations
URI https://doaj.org/article/45b30b2bf62b4ab5a27987d9be7eb7a1
Volume 164
WOSCitedRecordID wos000420008500006&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVAON
  databaseName: DOAJ Directory of Open Access Journals
  customDbUrl:
  eissn: 2075-2180
  dateEnd: 20201231
  omitProxy: false
  ssIdentifier: ssj0000392496
  issn: 2075-2180
  databaseCode: DOA
  dateStart: 20090101
  isFulltext: true
  titleUrlDefault: https://www.doaj.org/
  providerName: Directory of Open Access Journals
– providerCode: PRVHPJ
  databaseName: ROAD: Directory of Open Access Scholarly Resources
  customDbUrl:
  eissn: 2075-2180
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000392496
  issn: 2075-2180
  databaseCode: M~E
  dateStart: 20090101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV09T8MwELVQxcDCN6J8yUNXl3w4sT1C1YoBqkoUxBbdxbbEElBbGPntnJ0UlYmFJZGiyIrexb73Et87xgZgMVfOWIEOlJBplgpt0ImcIozETyltRMv8ezWd6pcXM9to9RX2hLX2wC1w17LAPMEMfZmhBCwgUySTLY2nHCqIwodYz4aYimtwHnRF7CxHOVFQHkva4jyZJfJ6PJuPHockFIbFr3S04dof08tkn-12vJDftM9zwLZcc8j21j0XeDcFj9hzKNFr24pw4pu8Duw3AM3jIsa7vjt0dtyG-dvEwgXe7cfiwdzbLTk0ltdx8PaL3TF7moznozvR9UYQda6zlUCDRtWe-H1NigBSTGkFTQrtQRYKCWKVSW2D-7s1Pi3LzKH2ibGlAgQPkJ-wXvPWuFPGcwCdJlBqW1N6B69totGE37GS8PXQZ4M1RNV7a4FRkXQISFYRyYqQrIo-uw3w_dwSfKvjBYpm1UWz-iuaZ_8xyDnbIVoj404wc8F6q8WHu2Tb9efqdbm4ii8KHR--xt8BPsUF
linkProvider Directory of Open Access Journals
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=Confluence+for+classical+logic+through+the+distinction+between+values+and+computations&rft.jtitle=Electronic+proceedings+in+theoretical+computer+science&rft.au=Esp%C3%ADrito+Santo%2C+Jos%C3%A9&rft.au=Matthes%2C+Ralph&rft.au=Nakazawa%2C+Koji&rft.au=Pinto%2C+Lu%C3%ADs&rft.date=2014-09-09&rft.issn=2075-2180&rft.eissn=2075-2180&rft.volume=164&rft.spage=63&rft.epage=77&rft_id=info:doi/10.4204%2FEPTCS.164.5&rft.externalDBID=n%2Fa&rft.externalDocID=10_4204_EPTCS_164_5
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2075-2180&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2075-2180&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2075-2180&client=summon