• Coinduction • Copatterns • Core language • Coverage Checking • Cubical • Cubical compatible • Cumulativity • Data Types • Flat Modality • Foreign Function Function Definitions • Function Types • Generalization of Declared Variables • Guarded Cubical • Implicit Arguments • Instance Arguments • Irrelevance • Lambda Abstraction Theory. [https://favonia.org/courses/hdtt2020/](CSCI 8980), courses on homotopy type theory and cubical type theory, Favonia, the University of Minnesota, Spring 2020 - Correct-by-construction Programming

definitions - Built-ins - Coinduction - Copatterns - Core language - Coverage Checking - Cubical - Cumulativity - Data Types - Flat Modality - Foreign Function Interface - Function Function Definitions - Function Types - Generalization of Declared Variables - Guarded Cubical - Implicit Arguments - Instance Arguments - Irrelevance - Lambda Abstraction - Local Definitions: Theory. [https://favonia.org/courses/hdtt2020/](CSCI 8980), courses on homotopy type theory and cubical type theory, Favonia, the University of Minnesota, Spring 2020 - Correct-by-construction Programming

definitions 13 3.2 Built-ins 16 3.3 Coinduction 26 3.4 Copatterns 28 3.5 Core language 31 3.6 Cubical 32 3.7 Data Types 44 3.8 Foreign Function Interface 47 3.9 Function Definitions 52 3.10 Function relevant position, but created -- in an irrelevant context. ### 3.6 Cubical The Cubical mode extends Agda with a variety of features from Cubical Type Theory. In particular, computational univalence and higher Homotopy Type Theory and Univalent Foundations. The version of Cubical Type Theory that Agda implements is a variation of the CCHM Cubical Type Theory where the Kan composition operations are decomposed

Coinduction 43 3.4 Copatterns 46 3.5 Core language 50 3.6 Coverage Checking 53 3.7 Cubical 56 3.8 Cubical compatible 73 3.9 Cumulativity 74 3.10 Data Types 75 3.11 Flat Modality 78 3.12 Definitions 85 3.14 Function Types 89 3.15 Generalization of Declared Variables 90 3.16 Guarded Cubical 95 3.17 Implicit Arguments 96 3.18 Instance Arguments 98 3.19 Irrelevance 105 3.20 Lambda Hötzel Escardó • Higher-Dimensional Type Theory (CSCI 8980), courses on homotopy type theory and cubical type theory, Favonia, the University of Minnesota, Spring 2020 • Correct-by-construction Programming

Coinduction 43 3.4 Copatterns 47 3.5 Core language 50 3.6 Coverage Checking 53 3.7 Cubical 57 3.8 Cubical compatible 74 3.9 Cumulativity 74 3.10 Data Types 76 3.11 Flat Modality 79 3.12 Hötzel Escardó • Higher-Dimensional Type Theory (CSCI 8980), courses on homotopy type theory and cubical type theory, Favonia, the University of Minnesota, Spring 2020 • Correct-by-construction Programming dependent (co)pattern matching: No pattern left behind. ### 3.7 Cubical The Cubical mode extends Agda with a variety of features from Cubical Type Theory. In particular, computational univalence and higher

Coinduction 43 3.4 Copatterns 47 3.5 Core language 50 3.6 Coverage Checking 53 3.7 Cubical 57 3.8 Cubical compatible 72 3.9 Cumulativity 73 3.10 Data Types 74 3.11 Flat Modality 77 3.12 Hötzel Escardó • Higher-Dimensional Type Theory (CSCI 8980), courses on homotopy type theory and cubical type theory, Favonia, the University of Minnesota, Spring 2020 • Correct-by-construction Programming dependent (co)pattern matching: No pattern left behind. ### 3.7 Cubical The Cubical mode extends Agda with a variety of features from Cubical Type Theory. In particular, it adds computational univalence

Coinduction 43 3.4 Copatterns 47 3.5 Core language 51 3.6 Coverage Checking 54 3.7 Cubical 57 3.8 Cubical compatible 73 3.9 Cumulativity 73 3.10 Data Types 75 3.11 Flat Modality 78 3.12 Hötzel Escardó • Higher-Dimensional Type Theory (CSCI 8980), courses on homotopy type theory and cubical type theory, Favonia, the University of Minnesota, Spring 2020 • Correct-by-construction Programming dependent (co)pattern matching: No pattern left behind. ### 3.7 Cubical The Cubical mode extends Agda with a variety of features from Cubical Type Theory. In particular, it adds computational univalence

Coinduction 43 3.4 Copatterns 47 3.5 Core language 51 3.6 Coverage Checking 54 3.7 Cubical 57 3.8 Cubical compatible 73 3.9 Cumulativity 73 3.10 Data Types 75 3.11 Flat Modality 78 3.12 Hötzel Escardó • Higher-Dimensional Type Theory (CSCI 8980), courses on homotopy type theory and cubical type theory, Favonia, the University of Minnesota, Spring 2020 • Correct-by-construction Programming dependent (co)pattern matching: No pattern left behind. ### 3.7 Cubical The Cubical mode extends Agda with a variety of features from Cubical Type Theory. In particular, it adds computational univalence

Built-ins • Coinduction • Copatterns • Core language • Coverage Checking • Cubical • Cumulativity • Data Types • Flat Modality • Foreign Function Interface Function Definitions • Function Types • Generalization of Declared Variables • Guarded Cubical • Implicit Arguments • Instance Arguments • Irrelevance • Lambda Abstraction Theory. [https://favonia.org/courses/hdtt2020/](CSCI 8980), courses on homotopy type theory and cubical type theory, Favonia, the University of Minnesota, Spring 2020 - Correct-by-construction Programming

- Built-ins - Coinduction - Copatterns - Core language - Cubical - Data Types - Foreign Function Interface - Function Definitions Core language - Cubical - The interval and path types - Transport - Partial elements - Homogeneous composition - Glue types - Higher inductive types • Cubical identity types and and computational HoTT/UF • References • Appendix: Cubical Agda primitives • Data Types • Simple datatypes • Parametrized datatypes • Indexed datatypes • Strict positivity