A Logical Foundation for Environment Classifiers
Taha and Nielsen have developed a multi-stage calculus {\lambda}{\alpha} with a sound type system using the notion of environment classifiers. They are special identifiers, with which code fragments and variable declarations are annotated, and their scoping mechanism is used to ensure statically tha...
Uloženo v:
| Vydáno v: | Logical methods in computer science Ročník 6, Issue 4 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Logical Methods in Computer Science e.V
01.01.2010
|
| Témata: | |
| ISSN: | 1860-5974, 1860-5974 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Taha and Nielsen have developed a multi-stage calculus {\lambda}{\alpha} with
a sound type system using the notion of environment classifiers. They are
special identifiers, with which code fragments and variable declarations are
annotated, and their scoping mechanism is used to ensure statically that
certain code fragments are closed and safely runnable. In this paper, we
investigate the Curry-Howard isomorphism for environment classifiers by
developing a typed {\lambda}-calculus {\lambda}|>. It corresponds to
multi-modal logic that allows quantification by transition variables---a
counterpart of classifiers---which range over (possibly empty) sequences of
labeled transitions between possible worlds. This interpretation will reduce
the "run" construct---which has a special typing rule in
{\lambda}{\alpha}---and embedding of closed code into other code fragments of
different stages---which would be only realized by the cross-stage persistence
operator in {\lambda}{\alpha}---to merely a special case of classifier
application. {\lambda}|> enjoys not only basic properties including subject
reduction, confluence, and strong normalization but also an important property
as a multi-stage calculus: time-ordered normalization of full reduction. Then,
we develop a big-step evaluation semantics for an ML-like language based on
{\lambda}|> with its type system and prove that the evaluation of a well-typed
{\lambda}|> program is properly staged. We also identify a fragment of the
language, where erasure evaluation is possible. Finally, we show that the proof
system augmented with a classical axiom is sound and complete with respect to a
Kripke semantics of the logic. |
|---|---|
| AbstractList | Taha and Nielsen have developed a multi-stage calculus {\lambda}{\alpha} with
a sound type system using the notion of environment classifiers. They are
special identifiers, with which code fragments and variable declarations are
annotated, and their scoping mechanism is used to ensure statically that
certain code fragments are closed and safely runnable. In this paper, we
investigate the Curry-Howard isomorphism for environment classifiers by
developing a typed {\lambda}-calculus {\lambda}|>. It corresponds to
multi-modal logic that allows quantification by transition variables---a
counterpart of classifiers---which range over (possibly empty) sequences of
labeled transitions between possible worlds. This interpretation will reduce
the "run" construct---which has a special typing rule in
{\lambda}{\alpha}---and embedding of closed code into other code fragments of
different stages---which would be only realized by the cross-stage persistence
operator in {\lambda}{\alpha}---to merely a special case of classifier
application. {\lambda}|> enjoys not only basic properties including subject
reduction, confluence, and strong normalization but also an important property
as a multi-stage calculus: time-ordered normalization of full reduction. Then,
we develop a big-step evaluation semantics for an ML-like language based on
{\lambda}|> with its type system and prove that the evaluation of a well-typed
{\lambda}|> program is properly staged. We also identify a fragment of the
language, where erasure evaluation is possible. Finally, we show that the proof
system augmented with a classical axiom is sound and complete with respect to a
Kripke semantics of the logic. Taha and Nielsen have developed a multi-stage calculus {\lambda}{\alpha} with a sound type system using the notion of environment classifiers. They are special identifiers, with which code fragments and variable declarations are annotated, and their scoping mechanism is used to ensure statically that certain code fragments are closed and safely runnable. In this paper, we investigate the Curry-Howard isomorphism for environment classifiers by developing a typed {\lambda}-calculus {\lambda}|>. It corresponds to multi-modal logic that allows quantification by transition variables---a counterpart of classifiers---which range over (possibly empty) sequences of labeled transitions between possible worlds. This interpretation will reduce the "run" construct---which has a special typing rule in {\lambda}{\alpha}---and embedding of closed code into other code fragments of different stages---which would be only realized by the cross-stage persistence operator in {\lambda}{\alpha}---to merely a special case of classifier application. {\lambda}|> enjoys not only basic properties including subject reduction, confluence, and strong normalization but also an important property as a multi-stage calculus: time-ordered normalization of full reduction. Then, we develop a big-step evaluation semantics for an ML-like language based on {\lambda}|> with its type system and prove that the evaluation of a well-typed {\lambda}|> program is properly staged. We also identify a fragment of the language, where erasure evaluation is possible. Finally, we show that the proof system augmented with a classical axiom is sound and complete with respect to a Kripke semantics of the logic. |
| Author | Igarashi, Atsushi Tsukada, Takeshi |
| Author_xml | – sequence: 1 givenname: Takeshi surname: Tsukada fullname: Tsukada, Takeshi – sequence: 2 givenname: Atsushi orcidid: 0000-0002-5143-9764 surname: Igarashi fullname: Igarashi, Atsushi |
| BookMark | eNp1kE1LAzEQQIMoWGvPXveoh7XJJjub9VaWVgsVD-o5ZJNJSdluJFkF_739EBHBucww8N7hXZDTPvRIyBWjtwUDOV09Ns85XIs7eVNQRk_IiEmgeVlX4vTXfU4mKW3objhnsoARobNsFdbe6C5bhPfe6sGHPnMhZvP-w8fQb7EfsqbTKXnnMaZLcuZ0l3DyvcfkdTF_aR7y1dP9spmtcsOFHHLHmbPgSgSm24IX2ApEwa0sda2B0baSjqGl0NLKgGyRIW2ZRRBSiBKAj8ny6LVBb9Rb9FsdP1XQXh0eIa6VjoM3HSpWW-lkDRTKSkhjNUeg2DqojNQl1DvX9OgyMaQU0f34GFX7fmrfT4ESSqp9vx1R_iGMHw5thqh99y_3BeEzdZ0 |
| CitedBy_id | crossref_primary_10_1145_3290331 crossref_primary_10_1017_S0956796816000253 |
| Cites_doi | 10.1006/inco.1995.1057 10.1145/1328408.1328430 10.1145/91556.91622 10.1145/1352582.1352591 10.1016/B978-0-934613-04-0.50032-6 10.1016/j.scico.2004.03.011 10.1145/277650.277727 10.1017/S0956796802004598 10.1145/316686.316697 10.1145/1173706.1173709 10.1017/S095679680500568X 10.1145/182409.182483 10.1016/S0304-3975(00)00053-0 10.1016/j.ic.2010.09.008 10.1145/1140335.1140360 10.1145/382780.382785 |
| ContentType | Journal Article |
| DBID | AAYXX CITATION DOA |
| DOI | 10.2168/LMCS-6(4:8)2010 |
| 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_19d8f896065748cda3e60ebf67c8a569 10_2168_LMCS_6_4_8_2010 |
| GroupedDBID | 29L 2WC 5GY 5VS AAFWJ AAYXX ADBBV ADQAK AENEX AFPKN ALMA_UNASSIGNED_HOLDINGS BCNDV CITATION EBS EJD FRP GROUPED_DOAJ J9A KQ8 M~E OK1 OVT P2P TR2 TUS XSB |
| ID | FETCH-LOGICAL-c348t-f31fd6f5e61ab232eb4ee43d85a9a610b78f1ed06b07c68be1e0b1de648445663 |
| IEDL.DBID | DOA |
| ISICitedReferencesCount | 6 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000287816900008&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 12:32:19 EDT 2025 Sat Nov 29 06:21:50 EST 2025 Tue Nov 18 22:15:00 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-c348t-f31fd6f5e61ab232eb4ee43d85a9a610b78f1ed06b07c68be1e0b1de648445663 |
| ORCID | 0000-0002-5143-9764 |
| OpenAccessLink | https://doaj.org/article/19d8f896065748cda3e60ebf67c8a569 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_19d8f896065748cda3e60ebf67c8a569 crossref_primary_10_2168_LMCS_6_4_8_2010 crossref_citationtrail_10_2168_LMCS_6_4_8_2010 |
| PublicationCentury | 2000 |
| PublicationDate | 2010-01-01 |
| PublicationDateYYYYMMDD | 2010-01-01 |
| PublicationDate_xml | – month: 01 year: 2010 text: 2010-01-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationTitle | Logical methods in computer science |
| PublicationYear | 2010 |
| Publisher | Logical Methods in Computer Science e.V |
| Publisher_xml | – name: Logical Methods in Computer Science e.V |
| References | 10.2168/LMCS-6(4:8)2010_PlotkinStirling86TARK 10.2168/LMCS-6(4:8)2010_NanevskiPfenning05JFP 10.2168/LMCS-6(4:8)2010_KojimaIgarashi10IC 10.2168/LMCS-6(4:8)2010_dynamiclogic 10.2168/LMCS-6(4:8)2010_ConselLawallLeMeur04SCP 10.2168/LMCS-6(4:8)2010_PolettoHsiehEnglerKaashoek99TOPLAS 10.2168/LMCS-6(4:8)2010_TahaSheard00TCS 10.2168/LMCS-6(4:8)2010_GlueckJorgensen95PLILP 10.2168/LMCS-6(4:8)2010_1111060 10.2168/LMCS-6(4:8)2010_KojimaIgarashi08IMLA 10.2168/LMCS-6(4:8)2010_Davies-Atemporallogicappro 10.2168/LMCS-6(4:8)2010_MoggiTahaBenaissaSheard99ESOP 10.2168/LMCS-6(4:8)2010_DBLP:conf/popl/DaviesP96 10.2168/LMCS-6(4:8)2010_ReedPfenning07M4M 10.2168/LMCS-6(4:8)2010_KameyamaKiselyovShan09PEPM 10.2168/LMCS-6(4:8)2010_WicklineLeePfenning98PLDI 10.2168/LMCS-6(4:8)2010_Calcagno2004 10.2168/LMCS-6(4:8)2010_DBLP:journals/iandc/Takahashi95 10.2168/LMCS-6(4:8)2010_VieraPardo06GPCE 10.2168/LMCS-6(4:8)2010_604134 10.2168/LMCS-6(4:8)2010_JonesGomardSestoft93PEbook 10.2168/LMCS-6(4:8)2010_Davies2001 10.2168/LMCS-6(4:8)2010_LawallDanvy94LFP 10.2168/LMCS-6(4:8)2010_Yuse2006 10.2168/LMCS-6(4:8)2010_DanvyFilinski90LFP 10.2168/LMCS-6(4:8)2010_StirlingHandbook 10.2168/LMCS-6(4:8)2010_BenaissaMoggiTahaSheard99IMLA 10.2168/LMCS-6(4:8)2010_NanevskiPfenningPientka08TOCL 10.2168/LMCS-6(4:8)2010_CalcagnoMoggiSheard03JFP 10.2168/LMCS-6(4:8)2010_SatoSakuraiKameyama01JFLP 10.2168/LMCS-6(4:8)2010_hybridlogic |
| References_xml | – ident: 10.2168/LMCS-6(4:8)2010_DBLP:journals/iandc/Takahashi95 doi: 10.1006/inco.1995.1057 – ident: 10.2168/LMCS-6(4:8)2010_KameyamaKiselyovShan09PEPM doi: 10.1145/1328408.1328430 – ident: 10.2168/LMCS-6(4:8)2010_DanvyFilinski90LFP doi: 10.1145/91556.91622 – ident: 10.2168/LMCS-6(4:8)2010_dynamiclogic – ident: 10.2168/LMCS-6(4:8)2010_NanevskiPfenningPientka08TOCL doi: 10.1145/1352582.1352591 – ident: 10.2168/LMCS-6(4:8)2010_604134 – ident: 10.2168/LMCS-6(4:8)2010_1111060 – ident: 10.2168/LMCS-6(4:8)2010_GlueckJorgensen95PLILP – ident: 10.2168/LMCS-6(4:8)2010_hybridlogic – ident: 10.2168/LMCS-6(4:8)2010_PlotkinStirling86TARK doi: 10.1016/B978-0-934613-04-0.50032-6 – ident: 10.2168/LMCS-6(4:8)2010_ConselLawallLeMeur04SCP doi: 10.1016/j.scico.2004.03.011 – ident: 10.2168/LMCS-6(4:8)2010_BenaissaMoggiTahaSheard99IMLA – ident: 10.2168/LMCS-6(4:8)2010_ReedPfenning07M4M – ident: 10.2168/LMCS-6(4:8)2010_WicklineLeePfenning98PLDI doi: 10.1145/277650.277727 – ident: 10.2168/LMCS-6(4:8)2010_CalcagnoMoggiSheard03JFP doi: 10.1017/S0956796802004598 – ident: 10.2168/LMCS-6(4:8)2010_DBLP:conf/popl/DaviesP96 – ident: 10.2168/LMCS-6(4:8)2010_JonesGomardSestoft93PEbook – ident: 10.2168/LMCS-6(4:8)2010_KojimaIgarashi08IMLA – ident: 10.2168/LMCS-6(4:8)2010_Calcagno2004 – ident: 10.2168/LMCS-6(4:8)2010_PolettoHsiehEnglerKaashoek99TOPLAS doi: 10.1145/316686.316697 – ident: 10.2168/LMCS-6(4:8)2010_VieraPardo06GPCE doi: 10.1145/1173706.1173709 – ident: 10.2168/LMCS-6(4:8)2010_NanevskiPfenning05JFP doi: 10.1017/S095679680500568X – ident: 10.2168/LMCS-6(4:8)2010_LawallDanvy94LFP doi: 10.1145/182409.182483 – ident: 10.2168/LMCS-6(4:8)2010_TahaSheard00TCS doi: 10.1016/S0304-3975(00)00053-0 – ident: 10.2168/LMCS-6(4:8)2010_MoggiTahaBenaissaSheard99ESOP – ident: 10.2168/LMCS-6(4:8)2010_KojimaIgarashi10IC doi: 10.1016/j.ic.2010.09.008 – ident: 10.2168/LMCS-6(4:8)2010_StirlingHandbook – ident: 10.2168/LMCS-6(4:8)2010_Yuse2006 doi: 10.1145/1140335.1140360 – ident: 10.2168/LMCS-6(4:8)2010_Davies2001 doi: 10.1145/382780.382785 – ident: 10.2168/LMCS-6(4:8)2010_SatoSakuraiKameyama01JFLP – ident: 10.2168/LMCS-6(4:8)2010_Davies-Atemporallogicappro |
| SSID | ssj0000331826 |
| Score | 1.8924893 |
| Snippet | Taha and Nielsen have developed a multi-stage calculus {\lambda}{\alpha} with
a sound type system using the notion of environment classifiers. They are
special... Taha and Nielsen have developed a multi-stage calculus {\lambda}{\alpha} with a sound type system using the notion of environment classifiers. They are special... |
| SourceID | doaj crossref |
| SourceType | Open Website Enrichment Source Index Database |
| SubjectTerms | computer science - programming languages d.3.3, f.3.3, f.4.1 |
| Title | A Logical Foundation for Environment Classifiers |
| URI | https://doaj.org/article/19d8f896065748cda3e60ebf67c8a569 |
| Volume | 6, Issue 4 |
| WOSCitedRecordID | wos000287816900008&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/eLvHCXMwrV27TsMwFLVQxcDCG_GWB4YyhMa1Y1-zlaoVQ1shAVI3y0-pEiqoFEa-HTtJHwyIhSVD5ETJubHvuXZ8DkJXBfXCuFjkcGPyjBXUZMCkyyyLZNYJQoLUpdmEGI1gPJYPa1Zf6Z-wSh64Aq5FpIMAiWcXgoF1mnqeexO4sKALXm7dy4VcK6bKMZjSRJwrLZ824dAaDLuPGW-yW7hOC8A_0tCaWn-ZVvq7aLvmg7hTPcce2vDTfbSz8FrAddc7QHkHD6pRCq-ckHBknLi32qqGS4vLSUj21ofoud976t5ntdtBZimDeRYoCY6HwnOiTeQ53jDvGXVQaKkjyTECAvEu5yYXloPxxOeGOM8ZsMiCOD1Cjenr1B8jrC0hzsbEE0zCDMCmziudhbawutAn6Gbx8srWUuDJkeJFxZIgoaUSWoorpkAltE5Qc3nBW6WC8XvTu4TmslmSry5PxKCqOqjqr6Ce_sdNztBWtdSf5kvOUWM--_AXaNN-zifvs8vye4nH4VfvG-qJxKs |
| 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=A+Logical+Foundation+for+Environment+Classifiers&rft.jtitle=Logical+methods+in+computer+science&rft.au=Takeshi+Tsukada&rft.au=Atsushi+Igarashi&rft.date=2010-01-01&rft.pub=Logical+Methods+in+Computer+Science+e.V&rft.eissn=1860-5974&rft.volume=6%2C+Issue+4&rft_id=info:doi/10.2168%2FLMCS-6%284%3A8%292010&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_19d8f896065748cda3e60ebf67c8a569 |
| 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 |