Intersection Types for the lambda-mu Calculus

We introduce an intersection type system for the lambda-mu calculus that is invariant under subject reduction and expansion. The system is obtained by describing Streicher and Reus's denotational model of continuations in the category of omega-algebraic lattices via Abramsky's domain-logic...

Full description

Saved in:
Bibliographic Details
Published in:Logical methods in computer science Vol. 14, Issue 1
Main Authors: van Bakel, Steffen, Barbanera, Franco, de'Liguoro, Ugo
Format: Journal Article
Language:English
Published: Logical Methods in Computer Science e.V 01.01.2018
Subjects:
computer science - logic in computer science
f.4
f.4.1
ISSN:1860-5974, 1860-5974
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract We introduce an intersection type system for the lambda-mu calculus that is invariant under subject reduction and expansion. The system is obtained by describing Streicher and Reus's denotational model of continuations in the category of omega-algebraic lattices via Abramsky's domain-logic approach. This provides at the same time an interpretation of the type system and a proof of the completeness of the system with respect to the continuation models by means of a filter model construction. We then define a restriction of our system, such that a lambda-mu term is typeable if and only if it is strongly normalising. We also show that Parigot's typing of lambda-mu terms with classically valid propositional formulas can be translated into the restricted system, which then provides an alternative proof of strong normalisability for the typed lambda-mu calculus.
AbstractList We introduce an intersection type system for the lambda-mu calculus that is invariant under subject reduction and expansion. The system is obtained by describing Streicher and Reus's denotational model of continuations in the category of omega-algebraic lattices via Abramsky's domain-logic approach. This provides at the same time an interpretation of the type system and a proof of the completeness of the system with respect to the continuation models by means of a filter model construction. We then define a restriction of our system, such that a lambda-mu term is typeable if and only if it is strongly normalising. We also show that Parigot's typing of lambda-mu terms with classically valid propositional formulas can be translated into the restricted system, which then provides an alternative proof of strong normalisability for the typed lambda-mu calculus.
Author van Bakel, Steffen
de'Liguoro, Ugo
Barbanera, Franco
Author_xml – sequence: 1
  givenname: Steffen
  surname: van Bakel
  fullname: van Bakel, Steffen
– sequence: 2
  givenname: Franco
  surname: Barbanera
  fullname: Barbanera, Franco
– sequence: 3
  givenname: Ugo
  surname: de'Liguoro
  fullname: de'Liguoro, Ugo
BookMark eNpNkE1Lw0AQhhepYK39Ad5y1EN0Z3eTbL1J8KMQ8WA9L5PdWU1Jk7KbHvrvTVsRh4F5GZiH4blkk67viLFr4HdC5lLfV2_lRwrqBh7EreCgz9gUdM7TbFGoyb98weYxrvlYUoIW-ZSly26gEMkOTd8lq_2WYuL7kAzflLS4qR2mm11SYmt37S5esXOPbaT575yxz-enVfmaVu8vy_KxSu34z5DWREJaZVEjKOmtzICUU4I7JQuyuvCO8oXjmmfcIsixHVpEKkSWebRyxpYnrutxbbah2WDYmx4bc1z04ctgGBrbkvGchB9PhUarnIa65tJKKjIuFmA1H1lwYtnQxxjI__GAm6M-c9BnQBkwwhz0yR9pwmSU
ContentType Journal Article
DBID AAYXX
CITATION
DOA
DOI 10.23638/LMCS-14(1:2)2018
DatabaseName CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList
CrossRef
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 1860-5974
ExternalDocumentID oai_doaj_org_article_f0e2faae28ac4d81bb03c3e750291c80
10_23638_LMCS_14_1_2_2018
GroupedDBID .4S
.DC
29L
2WC
5GY
5VS
AAFWJ
AAYXX
ADBBV
ADMLS
ADQAK
AENEX
AFPKN
ALMA_UNASSIGNED_HOLDINGS
ARCSS
BCNDV
CITATION
EBS
EJD
FRP
GROUPED_DOAJ
J9A
KQ8
MK~
ML~
M~E
OK1
OVT
P2P
TR2
TUS
XSB
ID FETCH-LOGICAL-c236t-bee23c4ca8a143fc351e4d420d437ec87fde69d08050ca13a13dacaae7255fac3
IEDL.DBID DOA
ISICitedReferencesCount 3
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000426512000011&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 1860-5974
IngestDate Fri Oct 03 12:52:27 EDT 2025
Sat Nov 29 08:04:21 EST 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Language English
License https://arxiv.org/licenses/nonexclusive-distrib/1.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c236t-bee23c4ca8a143fc351e4d420d437ec87fde69d08050ca13a13dacaae7255fac3
OpenAccessLink https://doaj.org/article/f0e2faae28ac4d81bb03c3e750291c80
ParticipantIDs doaj_primary_oai_doaj_org_article_f0e2faae28ac4d81bb03c3e750291c80
crossref_primary_10_23638_LMCS_14_1_2_2018
PublicationCentury 2000
PublicationDate 2018-01-01
PublicationDateYYYYMMDD 2018-01-01
PublicationDate_xml – month: 01
  year: 2018
  text: 2018-01-01
  day: 01
PublicationDecade 2010
PublicationTitle Logical methods in computer science
PublicationYear 2018
Publisher Logical Methods in Computer Science e.V
Publisher_xml – name: Logical Methods in Computer Science e.V
SSID ssj0000331826
Score 2.0889087
Snippet We introduce an intersection type system for the lambda-mu calculus that is invariant under subject reduction and expansion. The system is obtained by...
SourceID doaj
crossref
SourceType Open Website
Index Database
SubjectTerms computer science - logic in computer science
f.4
f.4.1
Title Intersection Types for the lambda-mu Calculus
URI https://doaj.org/article/f0e2faae28ac4d81bb03c3e750291c80
Volume 14, Issue 1
WOSCitedRecordID wos000426512000011&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: 1860-5974
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000331826
  issn: 1860-5974
  databaseCode: DOA
  dateStart: 20040101
  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: 1860-5974
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0000331826
  issn: 1860-5974
  databaseCode: M~E
  dateStart: 20040101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LS8NAEF5EPHjxLdYXe_CgwtJ9xWy8aWnx0BbBB70tm32AoFGa1qO_3dlNKvXkRQg5hBBmv8lkvm-yzCB05rilgVJPuPKxqTYrIKQUIyErMy8UdzQN7Xse5uOxmkyK-6VRX3FPWNMeuAGuG6jnwRjPlbHSAckqqbDCQ6LjBbMqqXVgPUtiKn2DhYjEufmNyQW8ZN3hqPdAmDxn1_wCsp76lYiW-vWnxDLYQhstI8Q3jSXbaMVXO2hzMW0Bt8G3i0gq3tVp61SFo36sMTBODAwOg1tLZ8jbHPfMayzo1XvoadB_7N2RdtgBsWDfjJTec2GlNcoAhQlWZMxLJzl1UuTeqjw4f1U4WGpGrWECDmcsAJODKAjGin20Wr1X_gBhYVXmM144V5YS-E4hvFIBgs-USklBO-hysXL90fS00KAFEkw6wgR6QDPNdYSpg24jNj83xnbU6QI4SbdO0n856fA_HnKE1qNBTf3jGK3OpnN_gtbs5-ylnp4m_8N59NX_BgaJtRA
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=Intersection+Types+for+the+lambda-mu+Calculus&rft.jtitle=Logical+methods+in+computer+science&rft.au=van+Bakel%2C+Steffen&rft.au=Barbanera%2C+Franco&rft.au=de%27Liguoro%2C+Ugo&rft.date=2018-01-01&rft.issn=1860-5974&rft.eissn=1860-5974&rft.volume=14%2C+Issue+1&rft_id=info:doi/10.23638%2FLMCS-14%281%3A2%292018&rft.externalDBID=n%2Fa&rft.externalDocID=10_23638_LMCS_14_1_2_2018
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1860-5974&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1860-5974&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1860-5974&client=summon