Rewriting modulo symmetric monoidal structure
String diagrams are a powerful and intuitive graphical syntax for terms of symmetric monoidal categories (SMCs). They find many applications in computer science and are becoming increasingly relevant in other fields such as physics and control theory. An important role in many such approaches is pla...
Uložené v:
| Vydané v: | Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science s. 710 - 719 |
|---|---|
| Hlavní autori: | , , , , |
| Médium: | Konferenčný príspevok.. |
| Jazyk: | English |
| Vydavateľské údaje: |
New York, NY, USA
ACM
05.07.2016
|
| Edícia: | ACM Conferences |
| Predmet: | |
| ISBN: | 9781450343916, 1450343910 |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | String diagrams are a powerful and intuitive graphical syntax for terms of symmetric monoidal categories (SMCs). They find many applications in computer science and are becoming increasingly relevant in other fields such as physics and control theory.
An important role in many such approaches is played by equational theories of diagrams, typically oriented and applied as rewrite rules. This paper lays a comprehensive foundation for this form of rewriting. We interpret diagrams combinatorially as typed hypergraphs and establish the precise correspondence between diagram rewriting modulo the laws of SMCs on the one hand and double pushout (DPO) rewriting of hypergraphs, subject to a soundness condition called convexity, on the other. This result rests on a more general characterisation theorem in which we show that typed hypergraph DPO rewriting amounts to diagram rewriting modulo the laws of SMCs with a chosen special Frobenius structure.
We illustrate our approach with a proof of termination for the theory of non-commutative bimonoids. |
|---|---|
| AbstractList | String diagrams are a powerful and intuitive graphical syntax for terms of symmetric monoidal categories (SMCs). They find many applications in computer science and are becoming increasingly relevant in other fields such as physics and control theory.
An important role in many such approaches is played by equational theories of diagrams, typically oriented and applied as rewrite rules. This paper lays a comprehensive foundation for this form of rewriting. We interpret diagrams combinatorially as typed hypergraphs and establish the precise correspondence between diagram rewriting modulo the laws of SMCs on the one hand and double pushout (DPO) rewriting of hypergraphs, subject to a soundness condition called convexity, on the other. This result rests on a more general characterisation theorem in which we show that typed hypergraph DPO rewriting amounts to diagram rewriting modulo the laws of SMCs with a chosen special Frobenius structure.
We illustrate our approach with a proof of termination for the theory of non-commutative bimonoids. |
| Author | Gadducci, Fabio Bonchi, Filippo Sobociński, Paweł Kissinger, Aleks Zanasi, Fabio |
| Author_xml | – sequence: 1 givenname: Filippo surname: Bonchi fullname: Bonchi, Filippo email: filippo.bonchi@gmail.com organization: CNRS, ENS Lyon – sequence: 2 givenname: Fabio surname: Gadducci fullname: Gadducci, Fabio email: gadducci@di.unipi.it organization: U. Pisa – sequence: 3 givenname: Aleks surname: Kissinger fullname: Kissinger, Aleks email: aleks@cs.ru.nl organization: Radboud U. Nijmegen – sequence: 4 givenname: Paweł surname: Sobociński fullname: Sobociński, Paweł email: ps@ecs.soton.ac.uk organization: U. Southampton – sequence: 5 givenname: Fabio surname: Zanasi fullname: Zanasi, Fabio email: fzanasi@cs.ru.nl organization: Radboud U. Nijmegen |
| BookMark | eNqNj01LxDAURQMqqGPXbrt00_pePppmKYM6woAgug6vaSLVtoGmRfz3VuwPcHXh3sOFc8lOxzh6xq4RSkSpbrkRQmlVrqkEVicsM7peBxBSGKzOWZbSBwBw1LUBvGDFi_-aurkb3_Mhtksf8_Q9DH6eOrcWY-xa6vM0T4ubl8lfsbNAffLZljv29nD_uj8Ux-fHp_3dsSDO9VwEDkIBDy2Ra5Fk41wFRlacgtMgGg0OvOYkKiUk1rXkLcqAXmsfGjIkduzm75fcYJsYP5NFsL-GdjO0m-GKlv9EbTN1PogfI_tTaA |
| ContentType | Conference Proceeding |
| Copyright | 2016 ACM |
| Copyright_xml | – notice: 2016 ACM |
| DOI | 10.1145/2933575.2935316 |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EndPage | 719 |
| GroupedDBID | 6IE 6IF 6IG 6IL 6IN AAJGR ACM ADPZR ALMA_UNASSIGNED_HOLDINGS APO BEFXN BFFAM BGNUA BKEBE BPEOZ CBEJK GUFHI IEGSK IJVOP OCL RIB RIC RIE RIL RIO |
| ID | FETCH-LOGICAL-a227t-f203502fdaacd1a4bcc609462afc703b70c0e72a3653418842d14f1e77efba9a3 |
| ISBN | 9781450343916 1450343910 |
| ISICitedReferencesCount | 39 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000387609200072&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| IngestDate | Wed Jan 31 06:49:57 EST 2024 Wed Jan 31 06:44:04 EST 2024 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | true |
| Language | English |
| License | Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Permissions@acm.org |
| LinkModel | OpenURL |
| MeetingName | LICS '16: 31st Annual ACM/IEEE Symposium on Logic in Computer Science |
| MergedId | FETCHMERGED-LOGICAL-a227t-f203502fdaacd1a4bcc609462afc703b70c0e72a3653418842d14f1e77efba9a3 |
| PageCount | 10 |
| ParticipantIDs | acm_books_10_1145_2933575_2935316 acm_books_10_1145_2933575_2935316_brief |
| PublicationCentury | 2000 |
| PublicationDate | 20160705 |
| PublicationDateYYYYMMDD | 2016-07-05 |
| PublicationDate_xml | – month: 07 year: 2016 text: 20160705 day: 05 |
| PublicationDecade | 2010 |
| PublicationPlace | New York, NY, USA |
| PublicationPlace_xml | – name: New York, NY, USA |
| PublicationSeriesTitle | ACM Conferences |
| PublicationTitle | Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science |
| PublicationYear | 2016 |
| Publisher | ACM |
| Publisher_xml | – name: ACM |
| SSID | ssj0002178901 |
| Score | 2.2677567 |
| Snippet | String diagrams are a powerful and intuitive graphical syntax for terms of symmetric monoidal categories (SMCs). They find many applications in computer... |
| SourceID | acm |
| SourceType | Publisher |
| StartPage | 710 |
| SubjectTerms | Theory of computation -- Design and analysis of algorithms |
| Title | Rewriting modulo symmetric monoidal structure |
| WOSCitedRecordID | wos000387609200072&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 | |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1La9wwEBab0ENPfaU0bRpcaOhhceuXLPkYloZAumFp0pKb0bMsie1Qr_P49xnJstYJgbaHXrzesZGxvtF4JM03g9BHEmvOYJocJpaSozkJC5GxMKI6ZzmNJLYMuZ_fyPExPTsrFpNJN3Bhri5IXdObm-Lyv0INMgDbUGf_AW7fKAjgHECHI8AOxwce8aMfn4UXtsP-fxq3q6lLpL8_m0PTZoo3PbmtTMhWV5kNA1NzWfQUwL7MwzDqxzr1XV2bHEj1L1NAp7topu1tVZmSXAIEdbOUPfmkE0Oekj4QsRa2cvD0wKzdXDY-5AeMXidEf4nxpb9wBMpgVxsdA-fc-_0nDQdl2pvhPZq5gtsLdq2soLe2potVCxo2H5EZ761txLmNg8UjbZzfm-7GGY5SSxUemVziwmKV-1c8_mHITA4N8G1S8E8_wy_YnnwDbRAS96Q_vzAHczQKTpIlAbrH-dxgw-NdjigQfHnQpHFyRDVyUU6fo631-wZrJXiBJqp-iZ4NsAYO1lco9GgGPZqBRzMY0Aw8mlvox8HX09lh6IpnhCxJyCrUidkzTrRkTMiYZVyIHKbyecK0ACvPSSQiRRKW5hgcGUqzRMaZjhUhCkZvwdLXaLNuavUGBUxjJYsi4VgV0A6nhv2BFScSU8ql3EYf4J1LMwbasie649L1S-n6ZRt9-uM9JQcN0W__orV36OlaXXbQJvSFeo-eiKvVsv29a_G8Aw6QXmM |
| linkProvider | IEEE |
| 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%3Abook&rft.genre=proceeding&rft.title=Proceedings+of+the+31st+Annual+ACM%2FIEEE+Symposium+on+Logic+in+Computer+Science&rft.atitle=Rewriting+modulo+symmetric+monoidal+structure&rft.au=Bonchi%2C+Filippo&rft.au=Gadducci%2C+Fabio&rft.au=Kissinger%2C+Aleks&rft.au=Soboci%C5%84ski%2C+Pawe%C5%82&rft.series=ACM+Conferences&rft.date=2016-07-05&rft.pub=ACM&rft.isbn=9781450343916&rft.spage=710&rft.epage=719&rft_id=info:doi/10.1145%2F2933575.2935316 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=9781450343916/lc.gif&client=summon&freeimage=true |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=9781450343916/mc.gif&client=summon&freeimage=true |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=9781450343916/sc.gif&client=summon&freeimage=true |