Programming Languages in String Diagrams
A series of four lectures given at the Oregon Programming Languages Summer School 2011.
References of the course:
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A survey on linear logic and its categorical semantics,
including game semantics and various notions of string diagrams:
P-A. Mellies
Categorical semantics of linear logic
Published in « Interactive models of computation and program behaviour ».
Pierre-Louis Curien, Hugo Herbelin, Jean-Louis Krivine,
Paul-André Melliès.
Panoramas et Synthèses 27,
Société Mathématique de France, 2009.
Pdf (213 pages)
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First lecture -- an introduction to string diagrams and its relationship
to linear logic and the semantics of fixpoints:
P-A. Mellies
Functorial boxes in string diagrams.
Invited paper at the Computer Science Logic 2006
conference.
Lecture Notes in Computer Science 4207, Springer Verlag.
Pdf (44 pages)
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First lecture -- a survey on string diagrams and diagrammatic notation
for various notions of monoidal categories:
P. Selinger
A survey of graphical languages for monoidal categories
New Structures for Physics, Springer Lecture Notes in Physics 813, pp. 289-355, 2011.
Pdf (63 pages).
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Second lecture -- a historical survey of game semantics
and its connections to logic and programming languages:
P-L. Curien
Notes on game semantics
Unpublished manuscript
Pdf (64 pages).
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Second lecture -- a research paper on asynchronous games describing
the reconstruction of the syntax of the lambda-calculus:
P-A. Mellies
Asynchronous games 2: the true concurrency of innocence.
Special Issue
« Selected papers of CONCUR 2004 »
of Theoretical Computer Science
Volume 358, Issues 2-3, pages 200-228, 2006.
Pdf (45 pages)
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Fourth lecture -- Segal condition meets computational effects
P-A. Mellies
Proceedings of the 25th Annual Symposium on Logic in Computer Science, Edinburgh, 2010.
Pdf (20 pages)