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前回は

• Anders Mörteberg, "Cubical Methods in Homotopy Type Theory and Univalent Foundations" (https://staff.math.su.se/anders.mortberg/papers/cubicalmethods.pdf)

の companion material である証明支援系プロトタイプ (https://github.com/mortberg/cubicaltt) に付属の lecture3.ctt までやりました。今回は lecture4.ctt をやっていきます。(講師F) なお、1/20 にもう一度 S さんの発表練習をはさみます。

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)
• Thorsten Altenkirch and Jonathan Grattag, "A functional quantum programming language" (https://arxiv.org/pdf/quant-ph/0409065.pdf)
• Grattag, "A functional quantum programming language" (http://eprints.nottingham.ac.uk/10250/1/thesis.pdf)
• Milner, Parrow, and Walker, "A Calculus for Mobile Processes" (https://reader.elsevier.com/reader/sd/pii/0890540192900084?token=314F25758D6B289FAA989571D84CA0A9C1625DDD238A3525F774BCC1D7ABD7EABBC2EF316050E2360004E292902D459B)
• Cattani, Stark, and Winskel, "Presheaf models for the π-calculus" (http://homepages.inf.ed.ac.uk/stark/prempc.pdf)
• Cyril Cohen, Thierry Coquand, Simon Huber, and Anders Mörtberg, "Cubical Type Theory: a constructive interpretation of the univalence axiom"

第四十三回までのバックナンバーは partake にあったんですが、ドメインごと消えました(´ﾟдﾟ｀)

第七十七〜七十九回はページを作り忘れましたが、PintoのD論をやりました。

※Pintoの論文はどうもオンラインでは手に入らないようなので、欲しい人は言って下さい。Mackieの論文も、ACMのpaywallに阻まれているようです。