1
+ @inbook {synsem ,
2
+ place ={ Cambridge} ,
3
+ series ={ Publications of the Newton Institute} ,
4
+ title ={ {Syntax and Semantics of Dependent Types}} ,
5
+ DOI ={ 10.1017/CBO9780511526619.004} ,
6
+ booktitle ={ Semantics and Logics of Computation} ,
7
+ publisher ={ Cambridge University Press} ,
8
+ author ={ Hofmann, Martin} ,
9
+ year ={ 1997} ,
10
+ pages ={ 79-–130} ,
11
+ collection ={ Publications of the Newton Institute}
12
+ }
13
+
14
+ @inproceedings {exteq ,
15
+ author ={ Altenkirch, Thorsten} ,
16
+ booktitle ={ Proceedings of the 14th Symposium on Logic in Computer Science} ,
17
+ title ={ {Extensional equality in intensional type theory}} ,
18
+ year ={ 1999} ,
19
+ pages ={ 412--420} ,
20
+ doi ={ 10.1109/LICS.1999.782636}
21
+ }
22
+
23
+ @inproceedings {relparam ,
24
+ author = { Atkey, Robert and Ghani, Neil and Johann, Patricia} ,
25
+ title = { {A Relationally Parametric Model of Dependent Type Theory}} ,
26
+ year = { 2014} ,
27
+ isbn = { 9781450325448} ,
28
+ publisher = { Association for Computing Machinery} ,
29
+ address = { New York, NY, USA} ,
30
+ doi = { 10.1145/2535838.2535852} ,
31
+ booktitle = { Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages} ,
32
+ pages = { 503-515} ,
33
+ numpages = { 13} ,
34
+ location = { San Diego, California, USA} ,
35
+ series = { POPL '14}
36
+ }
37
+
38
+ @article {mdtt ,
39
+ title ={ {Modal dependent type theory and dependent right adjoints}} ,
40
+ volume ={ 30} ,
41
+ DOI ={ 10.1017/S0960129519000197} ,
42
+ number ={ 2} ,
43
+ journal ={ Mathematical Structures in Computer Science} ,
44
+ publisher ={ Cambridge University Press} ,
45
+ author ={ Birkedal, Lars and Clouston, Ranald and Mannaa, Bassel and Ejlers Møgelberg, Rasmus and Pitts, Andrew M. and Spitters, Bas} ,
46
+ year ={ 2020} ,
47
+ pages ={ 118–138}
48
+ }
49
+
50
+ @article {abstractable ,
51
+ title = { {A Dependent Type Theory with Abstractable Names}} ,
52
+ journal = { Electronic Notes in Theoretical Computer Science} ,
53
+ volume = { 312} ,
54
+ pages = { 19--50} ,
55
+ year = { 2015} ,
56
+ note = { Ninth Workshop on Logical and Semantic Frameworks, with Applications (LSFA 2014)} ,
57
+ issn = { 1571-0661} ,
58
+ doi = { 10.1016/j.entcs.2015.04.003} ,
59
+ url = { https://www.sciencedirect.com/science/article/pii/S1571066115000079} ,
60
+ author = { Andrew M. Pitts and Justus Matthiesen and Jasper Derikx}
61
+ }
62
+
63
+ @inproceedings {contextual ,
64
+ author = { Pientka, Brigitte and Sch\"{o}pp, Ulrich} ,
65
+ title = { {Semantical Analysis of Contextual Types}} ,
66
+ year = { 2020} ,
67
+ isbn = { 978-3-030-45230-8} ,
68
+ publisher = { Springer-Verlag} ,
69
+ address = { Berlin, Heidelberg} ,
70
+ doi = { 10.1007/978-3-030-45231-5\_26} ,
71
+ booktitle = { Foundations of Software Science and Computation Structures: 23rd International Conference} ,
72
+ pages = { 502–-521} ,
73
+ numpages = { 20} ,
74
+ location = { Dublin, Ireland}
75
+ }
76
+
77
+ @article {undeceq ,
78
+ 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} ,
80
+ DOI = { 10.23638/LMCS-13(4:22)2017} ,
81
+ JOURNAL = { Logical Methods in Computer Science} ,
82
+ VOLUME = { 13} ,
83
+ NUMBER = { 4} ,
84
+ YEAR = { 2017} ,
85
+ MONTH = Nov
86
+ }
87
+
88
+ @article {gatcwf ,
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+ title ={ {On generalized algebraic theories and categories with families}} ,
90
+ volume ={ 31} ,
91
+ DOI ={ 10.1017/S0960129521000268} ,
92
+ number ={ 9} ,
93
+ journal ={ Mathematical Structures in Computer Science} ,
94
+ publisher ={ Cambridge University Press} ,
95
+ author ={ Bezem, Marc and Coquand, Thierry and Dybjer, Peter and Escard\'o, Mart\'in} ,
96
+ year ={ 2021} ,
97
+ pages ={ 1006-–1023}
98
+ }
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+
100
+ @inproceedings {qtt ,
101
+ author = { Atkey, Robert} ,
102
+ title = { {Syntax and Semantics of Quantitative Type Theory}} ,
103
+ year = { 2018} ,
104
+ isbn = { 9781450355834} ,
105
+ publisher = { Association for Computing Machinery} ,
106
+ address = { New York, NY, USA} ,
107
+ doi = { 10.1145/3209108.3209189} ,
108
+ booktitle = { Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science} ,
109
+ pages = { 56–-65} ,
110
+ numpages = { 10} ,
111
+ location = { Oxford, United Kingdom} ,
112
+ series = { LICS '18}
113
+ }
114
+
115
+ @article {cwf ,
116
+ title ={ {Categories with Families: Unityped, Simply Typed, and Dependently Typed}} ,
117
+ ISBN ={ 9783030665456} ,
118
+ ISSN ={ 2211-2766} ,
119
+ DOI ={ 10.1007/978-3-030-66545-6_5} ,
120
+ journal ={ Outstanding Contributions to Logic} ,
121
+ publisher ={ Springer International Publishing} ,
122
+ author ={ Castellan, Simon and Clairambault, Pierre and Dybjer, Peter} ,
123
+ year ={ 2021} ,
124
+ pages ={ 135–-180}
125
+ }
126
+
127
+ @InProceedings {itt ,
128
+ author ={ Dybjer, Peter} ,
129
+ editor ={ Berardi, Stefano and Coppo, Mario} ,
130
+ title ={ Internal type theory} ,
131
+ booktitle ={ Types for Proofs and Programs} ,
132
+ year ={ 1996} ,
133
+ publisher ={ Springer Berlin Heidelberg} ,
134
+ address ={ Berlin, Heidelberg} ,
135
+ pages ={ 120--134} ,
136
+ isbn ={ 978-3-540-70722-6} ,
137
+ doi ={ 10.1007/3-540-61780-9\_66}
138
+ }
139
+
140
+ @phdthesis {actt ,
141
+ author = { Uemara, Taichi} ,
142
+ title = { Abstract and Concrete Type Theories} ,
143
+ school = { Institute for Logic, Language and Computation} ,
144
+ year = { 2021} ,
145
+ month = { Jul} ,
146
+ doi = { 11245.1/41ff0b60-64d4-4003-8182-c244a9afab3b} ,
147
+ url = { https://hdl.handle.net/11245.1/41ff0b60-64d4-4003-8182-c244a9afab3b}
148
+ }
149
+
150
+ @phdthesis {gat ,
151
+ author = { Cartmell, John W.} ,
152
+ title = { Generalised algebraic theories and contextual categories} ,
153
+ school = { University of Oxford} ,
154
+ year = { 1978}
155
+ }
156
+
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+ @article {nat ,
158
+ title ={ {Natural models of homotopy type theory}} ,
159
+ volume ={ 28} ,
160
+ ISSN ={ 1469-8072} ,
161
+ DOI ={ 10.1017/s0960129516000268} ,
162
+ number ={ 2} ,
163
+ journal ={ Mathematical Structures in Computer Science} ,
164
+ publisher ={ Cambridge University Press (CUP)} ,
165
+ author ={ Awodey, Steve} ,
166
+ year ={ 2016} ,
167
+ month ={ Nov} ,
168
+ pages ={ 241–-286}
169
+ }
170
+
171
+ @phdthesis {algnat ,
172
+ author = { Newstead, Clive} ,
173
+ title = { Algebraic Models of Dependent Type Theory} ,
174
+ school = { Carnegie Mellon University} ,
175
+ year = 2018 ,
176
+ month = Aug,
177
+ doi = { 10.1184/R1/7195124.v1} ,
178
+ url = { https://kilthub.cmu.edu/articles/thesis/Algebraic\_Models\_of\_Dependent\_Type\_Theory/7195124/1}
179
+ }
180
+
181
+ @InProceedings {shallow ,
182
+ author ={ Kaposi, Ambrus and Kov{\'a}cs, Andr{\'a}s and Kraus, Nicolai} ,
183
+ editor ={ Hutton, Graham} ,
184
+ title ={ {Shallow Embedding of Type Theory is Morally Correct"}} ,
185
+ booktitle ={ Mathematics of Program Construction} ,
186
+ year =2019 ,
187
+ publisher ={ Springer International Publishing} ,
188
+ address ={ Cham} ,
189
+ pages ={ 329--365} ,
190
+ isbn ={ 978-3-030-33636-3} ,
191
+ doi ={ 10.1007/978-3-030-33636-3\_12}
192
+ }
193
+
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+ @InProceedings {hierarchy ,
195
+ author = { Kov\'{a}cs, Andr\'{a}s} ,
196
+ title = { {Generalized Universe Hierarchies and First-Class Universe Levels}} ,
197
+ booktitle = { 30th EACSL Annual Conference on Computer Science Logic (CSL 2022)} ,
198
+ pages = { 28:1--28:17} ,
199
+ series = { Leibniz International Proceedings in Informatics (LIPIcs)} ,
200
+ ISBN = { 978-3-95977-218-1} ,
201
+ ISSN = { 1868-8969} ,
202
+ year = { 2022} ,
203
+ volume = { 216} ,
204
+ editor = { Manea, Florin and Simpson, Alex} ,
205
+ publisher = { Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik} ,
206
+ address = { Dagstuhl, Germany} ,
207
+ URN = { urn:nbn:de:0030-drops-157485} ,
208
+ doi = { 10.4230/LIPIcs.CSL.2022.28}
209
+ }
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+
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+ @inproceedings {kipling ,
212
+ author = { McBride, Conor} ,
213
+ title = { {Outrageous but Meaningful Coincidences: Dependent Type-Safe Syntax and Evaluation}} ,
214
+ year = { 2010} ,
215
+ isbn = { 9781450302517} ,
216
+ publisher = { Association for Computing Machinery} ,
217
+ address = { New York, NY, USA} ,
218
+ doi = { 10.1145/1863495.1863497} ,
219
+ booktitle = { Proceedings of the 6th ACM SIGPLAN Workshop on Generic Programming} ,
220
+ pages = { 1–12} ,
221
+ numpages = { 12} ,
222
+ location = { Baltimore, Maryland, USA} ,
223
+ series = { WGP '10}
224
+ }
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+
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+ @phdthesis {ext ,
227
+ author = { Hofmann, Martin} ,
228
+ school = { University of Edinburgh} ,
229
+ title = { {Extensional concepts in intensional type theory}} ,
230
+ year = 1995 ,
231
+ month = Jul,
232
+ address = { Edinburgh, Scotland} ,
233
+ url = { http://www.lfcs.inf.ed.ac.uk/reports/95/ECS-LFCS-95-327/}
234
+ }
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+
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+ @article {obseq ,
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+ author = { Pujet, Lo\"{\i}c and Tabareau, Nicolas} ,
238
+ title = { {Observational Equality: Now for Good}} ,
239
+ year = { 2022} ,
240
+ publisher = { Association for Computing Machinery} ,
241
+ address = { New York, NY, USA} ,
242
+ volume = { 6} ,
243
+ number = { POPL} ,
244
+ doi = { 10.1145/3498693} ,
245
+ journal = { Proceedings of the ACM on Programming Languages} ,
246
+ month = { jan} ,
247
+ articleno = { 32} ,
248
+ numpages = { 27} ,
249
+ }
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+
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+ @incollection {groupoid ,
252
+ author = { Hofmann, Martin and Streicher, Thomas} ,
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+ isbn = { 9780198501275} ,
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+ title = { {The groupoid interpretation of type theory}} ,
255
+ booktitle = { Twenty Five Years of Constructive Type Theory} ,
256
+ publisher = { Oxford University Press} ,
257
+ year = { 1998} ,
258
+ month = { 10} ,
259
+ doi = { 10.1093/oso/9780198501275.003.0008} ,
260
+ }
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+
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+ @book {D-sets ,
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+ location = { Boston, {MA}} ,
264
+ title = { {Semantics of Type Theory}} ,
265
+ isbn = { 978-1-4612-6757-7 978-1-4612-0433-6} ,
266
+ publisher = { Birkh\"auser Boston} ,
267
+ author = { Streicher, Thomas} ,
268
+ year = { 1991} ,
269
+ doi = { 10.1007/978-1-4612-0433-6} ,
270
+ }
271
+
272
+ @InProceedings {Lambda-sets ,
273
+ author =" Altenkirch, Thorsten" ,
274
+ editor =" Barendregt, Henk and Nipkow, Tobias" ,
275
+ title ={ Proving strong normalization of CC by modifying realizability semantics} ,
276
+ booktitle =" Types for Proofs and Programs" ,
277
+ year =" 1994" ,
278
+ publisher =" Springer Berlin Heidelberg" ,
279
+ address =" Berlin, Heidelberg" ,
280
+ pages =" 3--18" ,
281
+ isbn =" 978-3-540-48440-0" ,
282
+ doi =" 10.1007/3-540-58085-9\_70"
283
+ }
284
+
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+ @unpublished {presheaf ,
286
+ author = { Laouar, Alexis} ,
287
+ title = { {A presheaf model of dependent type theory}} ,
288
+ year = 2017 ,
289
+ url = { https://perso.crans.org/alaouar/rapportm1.pdf}
290
+ }
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