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‎biblio.bib

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@inbook{synsem,
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place={Cambridge},
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series={Publications of the Newton Institute},
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title={{Syntax and Semantics of Dependent Types}},
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DOI={10.1017/CBO9780511526619.004},
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booktitle={Semantics and Logics of Computation},
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publisher={Cambridge University Press},
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author={Hofmann, Martin},
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year={1997},
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pages={79-–130},
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collection={Publications of the Newton Institute}
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}
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@inproceedings{exteq,
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author={Altenkirch, Thorsten},
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booktitle={Proceedings of the 14th Symposium on Logic in Computer Science},
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title={{Extensional equality in intensional type theory}},
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year={1999},
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pages={412--420},
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doi={10.1109/LICS.1999.782636}
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}
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@inproceedings{relparam,
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author = {Atkey, Robert and Ghani, Neil and Johann, Patricia},
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title = {{A Relationally Parametric Model of Dependent Type Theory}},
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year = {2014},
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isbn = {9781450325448},
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publisher = {Association for Computing Machinery},
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address = {New York, NY, USA},
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doi = {10.1145/2535838.2535852},
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booktitle = {Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages},
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pages = {503-515},
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numpages = {13},
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location = {San Diego, California, USA},
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series = {POPL '14}
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}
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@article{mdtt,
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title={{Modal dependent type theory and dependent right adjoints}},
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volume={30},
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DOI={10.1017/S0960129519000197},
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number={2},
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journal={Mathematical Structures in Computer Science},
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publisher={Cambridge University Press},
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author={Birkedal, Lars and Clouston, Ranald and Mannaa, Bassel and Ejlers Møgelberg, Rasmus and Pitts, Andrew M. and Spitters, Bas},
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year={2020},
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pages={118–138}
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}
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@article{abstractable,
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title = {{A Dependent Type Theory with Abstractable Names}},
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journal = {Electronic Notes in Theoretical Computer Science},
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volume = {312},
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pages = {19--50},
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year = {2015},
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note = {Ninth Workshop on Logical and Semantic Frameworks, with Applications (LSFA 2014)},
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issn = {1571-0661},
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doi = {10.1016/j.entcs.2015.04.003},
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url = {https://www.sciencedirect.com/science/article/pii/S1571066115000079},
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author = {Andrew M. Pitts and Justus Matthiesen and Jasper Derikx}
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}
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@inproceedings{contextual,
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author = {Pientka, Brigitte and Sch\"{o}pp, Ulrich},
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title = {{Semantical Analysis of Contextual Types}},
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year = {2020},
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isbn = {978-3-030-45230-8},
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publisher = {Springer-Verlag},
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address = {Berlin, Heidelberg},
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doi = {10.1007/978-3-030-45231-5\_26},
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booktitle = {Foundations of Software Science and Computation Structures: 23rd International Conference},
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pages = {502–-521},
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numpages = {20},
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location = {Dublin, Ireland}
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}
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@article{undeceq,
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TITLE = {{Undecidability of Equality in the Free Locally Cartesian Closed Category (Extended version)}},
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AUTHOR = {Simon Castellan and Pierre Clairambault and Peter Dybjer},
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DOI = {10.23638/LMCS-13(4:22)2017},
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JOURNAL = {Logical Methods in Computer Science},
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VOLUME = {13},
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NUMBER = {4},
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YEAR = {2017},
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MONTH = Nov
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}
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@article{gatcwf,
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title={{On generalized algebraic theories and categories with families}},
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volume={31},
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DOI={10.1017/S0960129521000268},
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number={9},
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journal={Mathematical Structures in Computer Science},
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publisher={Cambridge University Press},
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author={Bezem, Marc and Coquand, Thierry and Dybjer, Peter and Escard\'o, Mart\'in},
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year={2021},
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pages={1006-–1023}
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}
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@inproceedings{qtt,
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author = {Atkey, Robert},
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title = {{Syntax and Semantics of Quantitative Type Theory}},
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year = {2018},
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isbn = {9781450355834},
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publisher = {Association for Computing Machinery},
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address = {New York, NY, USA},
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doi = {10.1145/3209108.3209189},
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booktitle = {Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science},
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pages = {56–-65},
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numpages = {10},
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location = {Oxford, United Kingdom},
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series = {LICS '18}
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}
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@article{cwf,
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title={{Categories with Families: Unityped, Simply Typed, and Dependently Typed}},
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ISBN={9783030665456},
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ISSN={2211-2766},
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DOI={10.1007/978-3-030-66545-6_5},
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journal={Outstanding Contributions to Logic},
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publisher={Springer International Publishing},
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author={Castellan, Simon and Clairambault, Pierre and Dybjer, Peter},
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year={2021},
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pages={135–-180}
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}
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@InProceedings{itt,
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author={Dybjer, Peter},
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editor={Berardi, Stefano and Coppo, Mario},
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title={Internal type theory},
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booktitle={Types for Proofs and Programs},
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year={1996},
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publisher={Springer Berlin Heidelberg},
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address={Berlin, Heidelberg},
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pages={120--134},
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isbn={978-3-540-70722-6},
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doi={10.1007/3-540-61780-9\_66}
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}
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@phdthesis{actt,
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author = {Uemara, Taichi},
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title = {Abstract and Concrete Type Theories},
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school = {Institute for Logic, Language and Computation},
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year = {2021},
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month = {Jul},
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doi = {11245.1/41ff0b60-64d4-4003-8182-c244a9afab3b},
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url = {https://hdl.handle.net/11245.1/41ff0b60-64d4-4003-8182-c244a9afab3b}
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}
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@phdthesis{gat,
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author = {Cartmell, John W.},
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title = {Generalised algebraic theories and contextual categories},
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school = {University of Oxford},
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year = {1978}
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}
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@article{nat,
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title={{Natural models of homotopy type theory}},
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volume={28},
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ISSN={1469-8072},
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DOI={10.1017/s0960129516000268},
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number={2},
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journal={Mathematical Structures in Computer Science},
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publisher={Cambridge University Press (CUP)},
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author={Awodey, Steve},
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year={2016},
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month={Nov},
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pages={241–-286}
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}
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@phdthesis{algnat,
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author = {Newstead, Clive},
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title = {Algebraic Models of Dependent Type Theory},
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school = {Carnegie Mellon University},
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year = 2018,
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month = Aug,
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doi = {10.1184/R1/7195124.v1},
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url = {https://kilthub.cmu.edu/articles/thesis/Algebraic\_Models\_of\_Dependent\_Type\_Theory/7195124/1}
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}
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@InProceedings{shallow,
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author={Kaposi, Ambrus and Kov{\'a}cs, Andr{\'a}s and Kraus, Nicolai},
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editor={Hutton, Graham},
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title={{Shallow Embedding of Type Theory is Morally Correct"}},
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booktitle={Mathematics of Program Construction},
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year=2019,
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publisher={Springer International Publishing},
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address={Cham},
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pages={329--365},
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isbn={978-3-030-33636-3},
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doi={10.1007/978-3-030-33636-3\_12}
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}
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@InProceedings{hierarchy,
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author = {Kov\'{a}cs, Andr\'{a}s},
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title = {{Generalized Universe Hierarchies and First-Class Universe Levels}},
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booktitle = {30th EACSL Annual Conference on Computer Science Logic (CSL 2022)},
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pages = {28:1--28:17},
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series = {Leibniz International Proceedings in Informatics (LIPIcs)},
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ISBN = {978-3-95977-218-1},
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ISSN = {1868-8969},
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year = {2022},
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volume = {216},
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editor = {Manea, Florin and Simpson, Alex},
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publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
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address = {Dagstuhl, Germany},
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URN = {urn:nbn:de:0030-drops-157485},
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doi = {10.4230/LIPIcs.CSL.2022.28}
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}
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@inproceedings{kipling,
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author = {McBride, Conor},
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title = {{Outrageous but Meaningful Coincidences: Dependent Type-Safe Syntax and Evaluation}},
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year = {2010},
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isbn = {9781450302517},
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publisher = {Association for Computing Machinery},
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address = {New York, NY, USA},
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doi = {10.1145/1863495.1863497},
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booktitle = {Proceedings of the 6th ACM SIGPLAN Workshop on Generic Programming},
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pages = {1–12},
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numpages = {12},
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location = {Baltimore, Maryland, USA},
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series = {WGP '10}
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}
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@phdthesis{ext,
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author = {Hofmann, Martin},
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school = {University of Edinburgh},
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title = {{Extensional concepts in intensional type theory}},
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year = 1995,
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month = Jul,
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address = {Edinburgh, Scotland},
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url = {http://www.lfcs.inf.ed.ac.uk/reports/95/ECS-LFCS-95-327/}
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}
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@article{obseq,
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author = {Pujet, Lo\"{\i}c and Tabareau, Nicolas},
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title = {{Observational Equality: Now for Good}},
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year = {2022},
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publisher = {Association for Computing Machinery},
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address = {New York, NY, USA},
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volume = {6},
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number = {POPL},
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doi = {10.1145/3498693},
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journal = {Proceedings of the ACM on Programming Languages},
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month = {jan},
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articleno = {32},
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numpages = {27},
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}
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@incollection{groupoid,
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author = {Hofmann, Martin and Streicher, Thomas},
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isbn = {9780198501275},
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title = {{The groupoid interpretation of type theory}},
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booktitle = {Twenty Five Years of Constructive Type Theory},
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publisher = {Oxford University Press},
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year = {1998},
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month = {10},
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doi = {10.1093/oso/9780198501275.003.0008},
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}
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@book{D-sets,
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location = {Boston, {MA}},
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title = {{Semantics of Type Theory}},
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isbn = {978-1-4612-6757-7 978-1-4612-0433-6},
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publisher = {Birkh\"auser Boston},
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author = {Streicher, Thomas},
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year = {1991},
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doi = {10.1007/978-1-4612-0433-6},
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}
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@InProceedings{Lambda-sets,
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author="Altenkirch, Thorsten",
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editor="Barendregt, Henk and Nipkow, Tobias",
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title={Proving strong normalization of CC by modifying realizability semantics},
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booktitle="Types for Proofs and Programs",
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year="1994",
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publisher="Springer Berlin Heidelberg",
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address="Berlin, Heidelberg",
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pages="3--18",
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isbn="978-3-540-48440-0",
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doi="10.1007/3-540-58085-9\_70"
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}
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@unpublished{presheaf,
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author = {Laouar, Alexis},
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title = {{A presheaf model of dependent type theory}},
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year = 2017,
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url = {https://perso.crans.org/alaouar/rapportm1.pdf}
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}

‎iosevka.ttc

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‎kai.ttf

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‎main.tex

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