ガチ勢になるための圏論勉強会第百六十七回

10月

6
ガチ勢になるための圏論勉強会第百六十七回

主催 : jun0inoue

募集内容	参加枠1 無料参加者数 0人
開催日時	2019/10/06(日) 17:00 ～ 19:00 Googleカレンダー icsファイル
募集期間	2019/09/23(月) 18:49 〜 2019/10/06(日) 19:00まで
会場	Google Hangouts

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前回は

Thorsten Altenkirch and Jonathan Grattag, "A functional quantum programming language" (https://arxiv.org/pdf/quant-ph/0409065.pdf)

を4.1節まで読みましたが、背景情報が無さすぎて量子情報詳しくない勢には辛かったので、今回は元になったと思しき博士論文

Grattag, "A functional quantum programming language" (http://eprints.nottingham.ac.uk/10250/1/thesis.pdf)

の6章と7章を気持ちを理解する程度に読みました。次はこの博士論文の2章と3章を読みます(発表者I)。

これまでに読んだもの:

Homotopy Type Theoryの教科書のめぼしい部分(http://homotopytypetheory.org/book/)
Andrew Pitts, Relational Properties of Domains (http://www.cl.cam.ac.uk/~amp12/papers/relpod/relpod.ps.gz)
Gordon Plotkin and Matija Pretnar, A Logic for Algebraic Effects (http://homepages.inf.ed.ac.uk/gdp/publications/Logic_Algebraic_Effects.pdf)
Thorsten Altenkirch and Bernhard Reus, Monadic Presentations of Lambda Terms Using Generalized Inductive Types (http://www.cs.nott.ac.uk/~txa/publ/csl99.pdf)
Gordon Plotkin and John Power, "Algebraic Operations and Generic Effects" (http://homepages.inf.ed.ac.uk/gdp/publications/alg_ops_gen_effects.pdf) [眺める程度]
Samson Abramsky and Guy McCusker, Game Semantics (http://www.cs.cmu.edu/~jcr/gamenotes.ps.gz)
Andrew Ker, Hanno Nickau, and Luke Ong, Innocent game models of untyped λ calculus (http://www.cs.ox.ac.uk/andrew.ker/docs/ADK01D.pdf)
[補足資料] Luke Ong, Game Semantics and Its Applications (http://www.cs.ox.ac.uk/luke.ong/personal/talks/shell-2x2.pdf)
Paul-André Melliès, "Functorial boxes in string diagrams" [5節まで]
André Joyal and Ross Street, "Geometry of Tensor Calculus II" [気持ち程度]
Jorge Sousa Pinto, "Parallel Implementation Models for the λ-Calculus Using the Geometry of Interaction"
Samson Abramsky, Esfandiar Haghverdi, and Philip Scott, "Geometry of Interaction and Linear Combinatory Algebras"
Abramsky and Jung, "Domain Theory" (http://www.cs.bham.ac.uk/~axj/pub/papers/handy1.pdf) [第2.2節のみ]
Borceaux and Stubbe, "Short Introduction to Enriched Categories" (https://web.archive.org/web/20150907184148/http://www-lmpa.univ-littoral.fr/~stubbe/PDF/EnrichedCatsKLUWER.pdf)
Hyland and Ong, "On Full Abstraction for PCF: I, II, and III" (https://ora.ox.ac.uk/objects/uuid:63c54392-39f3-46f1-8a68-e6ff0ec90218/datastreams/ATTACHMENT01)
Power and Robinson, "Premonoidal Categories and Notions of Computation" (http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=F2F5668CABD327B6716EF3A3E3826E04?doi=10.1.1.23.1140&rep=rep1&type=pdf) [一部]
Selinger, "Control Categories and Duality" (www.mathstat.dal.ca/~selinger/papers/control.pdf)
Samson Abramsky, "Information, Processes, and Games" (https://arxiv.org/abs/1604.02603)
Rasmus Ejlers Møgelberg and Sam Staton, "Linearly-used state in models of call-by-value" [第4節の翻訳の定義まで]
Jeff Egger, Rasmus Ejlers Mogelberg, and Alex Simpson, "The Enriched Effect Calculus: Syntax and Semantics" (http://homepages.inf.ed.ac.uk/als/Research/Sources/eec.pdf)
Andrea Schalk, "What is a Categorical Model for Linear Logic?" (http://www.cs.man.ac.uk/~schalk/notes/llmodel.pdf)
G. M. Kelly, "Basic Concepts of Enriched Category Theory" (http://www.tac.mta.ca/tac/reprints/articles/10/tr10.pdf) [1.8節まで]
Yuichi Nishiwaki, Yoshihiko Kakutani, and Yuito Murase, "Modality via Iterated Enrichment" (https://arxiv.org/abs/1804.02809)
Stefan Forcey, "Enrichment Over Iterated Monoidal Categories" (https://arxiv.org/abs/math/0403152)
G. A. Kavvos, "Dual-Context Calculi for Modal Logic" (https://arxiv.org/pdf/1602.04860.pdf)
Djordje Cubric, Peter Dybjer, and Philip J. Scott, "Normalization and the Yoneda Embedding" (https://pdfs.semanticscholar.org/dc4f/878e3ac58b60da0b0ab7f63443322bbc6518.pdf)