Linear logic: Difference between revisions

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Linear distributions are fundamental in the proof theory of linear logic. The consequences of this map were first investigated in {{sfn|Cockett| & Seely| (1997}}) and called a "weak distribution".{{sfn|Cockett|Seely|1997}} In subsequent work it was renamed to "linear distribution" to reflect the fundamental connection to linear logic.

; Other implications :

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*{{Cite journal|last=Bimbó|first=Katalin|author-link=Katalin Bimbó|date=2015-09-13|title=The decidability of the intensional fragment of classical linear logic|journal=Theoretical Computer Science|volume=597|pages=1–17|doi=10.1016/j.tcs.2015.06.019|issn=0304-3975|doi-access=free}}

*{{cite journal|last1=Cockett|first1=J. Robin|author1-link=Robin Cockett|last2=Seely|first2=Robert|year=1997|title=Weakly distributive categories|journal=Journal of Pure and Applied Algebra|volume=114|issue=2|pages=133–173|doi=10.1016/0022-4049(95)00160-3 }}

*{{cite book|last=Di Cosmo|first=Roberto|year=1996|title=The Linear Logic Primer|type=Course notes|chapter=2|url=http://www.dicosmo.org/CourseNotes/LinLog/}}

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==Further reading==

* {{cite web |title=Introduction to Linear Logic |last=BraunerBraüner| first=Torben|url=http://www.brics.dk/LS/96/6/BRICS-LS-96-6.pdf |date=December 1996|publisher=Basic Research in Computer Science (BRICS)|volume=LS-96/6|series=BRICS Lecture Series |access-date=2025-05-20}}

* {{cite book |last1=Di Cosmo |first1=Roberto |last2=Danos |first2=Vincent |year=1992|title=The Linear Logic Primer |url=https://www.dicosmo.org/CourseNotes/LinLog/ }}

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*{{cite SEP|title=Linear Logic|url-id=logic-linear|date=2023-09-16|edition=Fall 2023|author-last=Di Cosmo|author-first=Roberto|author-last2=Miller|author-first2=Dale |author-link2=Dale Miller (academic)}}

* {{cite book |last1=Girard |first1=Jean-Yves |last2=Lafont |first2=Yves |last3=Taylor |first3=Paul |year=1989 |title=Proofs and Types |publisher=Cambridge University Press |url=http://www.cs.man.ac.uk/~pt/stable/Proofs+Types.html |archive-url=https://web.archive.org/web/20160704202340/http://www.cs.man.ac.uk/~pt/stable/Proofs+Types.html |archive-date=4 July 2016 }}

* {{cite book |last=Hoare |first=C. A. R. |year=1985 |title=Communicating Sequential Processes |publisher=Prentice-Hall International |isbn=0-13-153271-5 }}

*{{cite conference | last = Lafont | first = Yves | year = 1993 | title = Introduction to Linear Logic | book-title = TEMPUS Summer School on Algebraic and Categorical Methods in Computer Science | ___location = Brno, Czech Republic | type = Lecture notes}}

* {{cite book|last=Miller |first=Dale |year=2004 |chapter=Overview of Linear Logic Programming |title=Linear Logic in Computer Science |editor1-last=Ehrhard |editor2-last=Girard |editor3-last=Ruet |editor4-last=Scott |publisher=Cambridge University Press |series=London Mathematical Society Lecture Notes |volume=316 |url=http://www.lix.polytechnique.fr/Labo/Dale.Miller/papers/llp.pdf }}

* {{cite web |title=Introduction to Linear Logic |last=Lincoln |first=Patrick|url=http://www.csl.sri.com/~lincoln/papers/sigact92.ps |format=Postscript }}

* {{cite book|last=Miller |first=Dale |year=2004 |chapter=Overview of Linear Logic Programming |title=Linear Logic in Computer Science |editor1-last=Ehrhard |editor2-last=Girard |editor3-last=Ruet |editor4-last=Scott |publisher=Cambridge University Press |series=London Mathematical Society Lecture Notes |volume=316 |url=http://www.lix.polytechnique.fr/Labo/Dale.Miller/papers/llp.pdf }}

* {{cite web |title=Linear Logic Wiki |url=http://llwiki.ens-lyon.fr/ }}

* {{cite book | last = Troelstra | first = A. S. | author-link = Anne Sjerp Troelstra | year = 1992 | title = Lectures on Linear Logic | publisher = CSLI Publications | ___location = Stanford | series = CSLI Lecture Notes | volume = 29 |publisher isbn =Stanford 978-0937073773 }}

* {{cite book |last1=Troelstra |first1=A. S.| author1-link = Anne Sjerp Troelstra|last2=Schwichtenberg |first2=H. |author2-link=Helmut Schwichtenberg|year=2000|orig-year=1996 |title=Basic Proof Theory |series=Cambridge Tracts in Theoretical Computer Science |volume=43|___location=Cambridge |publisher=Cambridge University Press |isbnpages=0-521-77911-1XII, 417|edition=2nd|isbn=9780521779111|doi=10.1017/CBO9781139168717|oclc=951181823}}

* {{cite web |title=A Taste of Linear Logic |last=Wadler| first=Philip|url=http://homepages.inf.ed.ac.uk/wadler/topics/linear-logic.html }}