Differential interaction nets
We introduce interaction nets for a fragment of the differential lambda-calculus and exhibit in this framework a new symmetry between the of course and the why not modalities of linear logic, which is completely similar to the symmetry between the tensor and par connectives of linear logic. We use a...
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| Veröffentlicht in: | Theoretical computer science 2006-11, Vol.364 (2), p.166-195 |
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| container_end_page | 195 |
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| container_issue | 2 |
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| container_title | Theoretical computer science |
| container_volume | 364 |
| creator | Ehrhard, T. Regnier, L. |
| description | We introduce interaction nets for a fragment of the differential lambda-calculus and exhibit in this framework a new symmetry between the
of course and the
why not modalities of linear logic, which is completely similar to the symmetry between the
tensor and
par connectives of linear logic. We use algebraic intuitions for introducing these nets and their reduction rules, and then we develop two correctness criteria (weak typability and acyclicity) and show that they guarantee strong normalization. Finally, we outline the correspondence between this interaction nets formalism and the resource lambda-calculus. |
| doi_str_mv | 10.1016/j.tcs.2006.08.003 |
| format | Article |
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of course and the
why not modalities of linear logic, which is completely similar to the symmetry between the
tensor and
par connectives of linear logic. We use algebraic intuitions for introducing these nets and their reduction rules, and then we develop two correctness criteria (weak typability and acyclicity) and show that they guarantee strong normalization. Finally, we outline the correspondence between this interaction nets formalism and the resource lambda-calculus.</description><identifier>ISSN: 0304-3975</identifier><identifier>EISSN: 1879-2294</identifier><identifier>DOI: 10.1016/j.tcs.2006.08.003</identifier><identifier>CODEN: TCSCDI</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Applied sciences ; Computer Science ; Computer science; control theory; systems ; Differential lambda-calculus ; Exact sciences and technology ; General logic ; Interaction nets ; Lambda-calculus ; Lambda-calculus with multiplicities ; Linear logic ; Logic and foundations ; Logic in Computer Science ; Mathematical logic, foundations, set theory ; Mathematics ; Programming theory ; Resource lambda-calculus ; Sciences and techniques of general use ; Theoretical computing</subject><ispartof>Theoretical computer science, 2006-11, Vol.364 (2), p.166-195</ispartof><rights>2006</rights><rights>2006 INIST-CNRS</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c361t-bc9950d8ac6f864ebcac588f1a541d5002bd80d11eb367c05b4632ce10304c6b3</citedby><cites>FETCH-LOGICAL-c361t-bc9950d8ac6f864ebcac588f1a541d5002bd80d11eb367c05b4632ce10304c6b3</cites><orcidid>0000-0001-5231-5504 ; 0009-0005-5142-5484</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0304397506005299$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>230,309,310,314,776,780,785,786,881,3537,23909,23910,25118,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=18267491$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://hal.science/hal-00150274$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Ehrhard, T.</creatorcontrib><creatorcontrib>Regnier, L.</creatorcontrib><title>Differential interaction nets</title><title>Theoretical computer science</title><description>We introduce interaction nets for a fragment of the differential lambda-calculus and exhibit in this framework a new symmetry between the
of course and the
why not modalities of linear logic, which is completely similar to the symmetry between the
tensor and
par connectives of linear logic. We use algebraic intuitions for introducing these nets and their reduction rules, and then we develop two correctness criteria (weak typability and acyclicity) and show that they guarantee strong normalization. Finally, we outline the correspondence between this interaction nets formalism and the resource lambda-calculus.</description><subject>Applied sciences</subject><subject>Computer Science</subject><subject>Computer science; control theory; systems</subject><subject>Differential lambda-calculus</subject><subject>Exact sciences and technology</subject><subject>General logic</subject><subject>Interaction nets</subject><subject>Lambda-calculus</subject><subject>Lambda-calculus with multiplicities</subject><subject>Linear logic</subject><subject>Logic and foundations</subject><subject>Logic in Computer Science</subject><subject>Mathematical logic, foundations, set theory</subject><subject>Mathematics</subject><subject>Programming theory</subject><subject>Resource lambda-calculus</subject><subject>Sciences and techniques of general use</subject><subject>Theoretical computing</subject><issn>0304-3975</issn><issn>1879-2294</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMouK7-AA_CXjx4aJ18NsXT4tcKC170HNJpgllquyRhwX9vS0VvzmVgeJ93Zl5CLimUFKi63ZUZU8kAVAm6BOBHZEF1VReM1eKYLICDKHhdyVNyltIOxpKVWpCrh-C9i67PwXar0GcXLeYw9Kve5XROTrztkrv46Uvy_vT4dr8ptq_PL_frbYFc0Vw0WNcSWm1Rea2Ea9Ci1NpTKwVtJQBrWg0tpa7hqkKQjVCcoaPTVagaviQ3s--H7cw-hk8bv8xgg9mst2aaAVAJrBIHOmrprMU4pBSd_wUomCkLszNjFmbKwoAeUT4y1zOztwlt56PtMaQ_UDNViXryvpt1bnz2EFw0CYPr0bUhOsymHcI_W74BIGBx6A</recordid><startdate>20061106</startdate><enddate>20061106</enddate><creator>Ehrhard, T.</creator><creator>Regnier, L.</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0001-5231-5504</orcidid><orcidid>https://orcid.org/0009-0005-5142-5484</orcidid></search><sort><creationdate>20061106</creationdate><title>Differential interaction nets</title><author>Ehrhard, T. ; Regnier, L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c361t-bc9950d8ac6f864ebcac588f1a541d5002bd80d11eb367c05b4632ce10304c6b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Applied sciences</topic><topic>Computer Science</topic><topic>Computer science; control theory; systems</topic><topic>Differential lambda-calculus</topic><topic>Exact sciences and technology</topic><topic>General logic</topic><topic>Interaction nets</topic><topic>Lambda-calculus</topic><topic>Lambda-calculus with multiplicities</topic><topic>Linear logic</topic><topic>Logic and foundations</topic><topic>Logic in Computer Science</topic><topic>Mathematical logic, foundations, set theory</topic><topic>Mathematics</topic><topic>Programming theory</topic><topic>Resource lambda-calculus</topic><topic>Sciences and techniques of general use</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ehrhard, T.</creatorcontrib><creatorcontrib>Regnier, L.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Theoretical computer science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ehrhard, T.</au><au>Regnier, L.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Differential interaction nets</atitle><jtitle>Theoretical computer science</jtitle><date>2006-11-06</date><risdate>2006</risdate><volume>364</volume><issue>2</issue><spage>166</spage><epage>195</epage><pages>166-195</pages><issn>0304-3975</issn><eissn>1879-2294</eissn><coden>TCSCDI</coden><abstract>We introduce interaction nets for a fragment of the differential lambda-calculus and exhibit in this framework a new symmetry between the
of course and the
why not modalities of linear logic, which is completely similar to the symmetry between the
tensor and
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| ispartof | Theoretical computer science, 2006-11, Vol.364 (2), p.166-195 |
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| language | eng |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Applied sciences Computer Science Computer science control theory systems Differential lambda-calculus Exact sciences and technology General logic Interaction nets Lambda-calculus Lambda-calculus with multiplicities Linear logic Logic and foundations Logic in Computer Science Mathematical logic, foundations, set theory Mathematics Programming theory Resource lambda-calculus Sciences and techniques of general use Theoretical computing |
| title | Differential interaction nets |
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