composition Glue types Higher inductive types Indexed inductive types Cubical identity types and computational HoTT/UF Cubical Agda with erased Glue References Appendix: Cubical Agda primitives Cubical compatible variety of features from Cubical Type Theory. In particular, computational univalence and higher inductive types which hence gives computational meaning to Homotopy Type Theory and Univalent Foundations warning is enabled (it is by default), Agda will print a warning for every definition whose computational behaviour could not be extended to cover transports. Internally, transports are represented by

elements Homogeneous composition Glue types Higher inductive types Cubical identity types and computational HoTT/UF References Appendix: Cubical Agda primitives Cumulativity Basics Example usage: N-ary variety of features from Cubical Type Theory. In particular, computational univalence and higher inductive types which hence gives computational meaning to Homotopy Type Theory and Univalent Foundations types see: https://github.com/agda/cubical/tree/master/Cubical/HITs. Cubical identity types and computational HoTT/UF As mentioned above the computation rule for J does not hold definitionally for path types

elements Homogeneous composition Glue types Higher inductive types Cubical identity types and computational HoTT/UF References Appendix: Cubical Agda primitives Cumulativity Basics Example usage: N-ary variety of features from Cubical Type Theory. In particular, computational univalence and higher inductive types which hence gives computational meaning to Homotopy Type Theory and Univalent Foundations types see: https://github.com/agda/cubical/tree/master/Cubical/HITs. Cubical identity types and computational HoTT/UF As mentioned above the computation rule for J does not hold definitionally for path types

elements Homogeneous composition Glue types Higher inductive types Cubical identity types and computational HoTT/UF References Appendix: Cubical Agda primitives Cumulativity Basics Example usage: N-ary variety of features from Cubical Type Theory. In particular, computational univalence and higher inductive types which hence gives computational meaning to Homotopy Type Theory and Univalent Foundations types see: https://github.com/agda/cubical/tree/master/Cubical/HITs. Cubical identity types and computational HoTT/UF As mentioned above the computation rule for J does not hold definitionally for path types

elements Homogeneous composition Glue types Higher inductive types Cubical identity types and computational HoTT/UF References Appendix: Cubical Agda primitives Cumulativity Basics Example usage: N-ary variety of features from Cubical Type Theory. In particular, computational univalence and higher inductive types which hence gives computational meaning to Homotopy Type Theory and Univalent Foundations types see: https://github.com/agda/cubical/tree/master/Cubical/HITs. Cubical identity types and computational HoTT/UF As mentioned above the computation rule for J does not hold definitionally for path types

elements Homogeneous composition Glue types Higher inductive types Cubical identity types and computational HoTT/UF References Appendix: Cubical Agda primitives Data Types Simple datatypes Parametrized variety of features from Cubical Type Theory. In particular, computational univalence and higher inductive types which hence gives computational meaning to Homotopy Type Theory and Univalent Foundations types see: https://github.com/agda/cubical/tree/master/Cubical/HITs. Cubical identity types and computational HoTT/UF As mentioned above the computation rule for J does not hold definitionally for path types

elements Homogeneous composition Glue types Higher inductive types Cubical identity types and computational HoTT/UF References Appendix: Cubical Agda primitives Data Types Simple datatypes Parametrized variety of features from Cubical Type Theory. In particular, computational univalence and higher inductive types which hence gives computational meaning to Homotopy Type Theory and Univalent Foundations types see: https://github.com/agda/cubical/tree/master/Cubical/HITs. Cubical identity types and computational HoTT/UF As mentioned above the computation rule for J does not hold definitionally for path types

elements Homogeneous composition Glue types Higher inductive types Cubical identity types and computational HoTT/UF References Appendix: Cubical Agda primitives Cumulativity Basics Example usage: N-ary variety of features from Cubical Type Theory. In particular, computational univalence and higher inductive types which hence gives computational meaning to Homotopy Type Theory and Univalent Foundations types see: https://github.com/agda/cubical/tree/master/Cubical/HITs. Cubical identity types and computational HoTT/UF As mentioned above the computation rule for J does not hold definitionally for path types

elements Homogeneous composition Glue types Higher inductive types Cubical identity types and computational HoTT/UF Cubical Agda with erased glue References Appendix: Cubical Agda primitives Cumulativity variety of features from Cubical Type Theory. In particular, computational univalence and higher inductive types which hence gives computational meaning to Homotopy Type Theory and Univalent Foundations types see: https://github.com/agda/cubical/tree/master/Cubical/HITs. Cubical identity types and computational HoTT/UF As mentioned above the computation rule for J does not hold definitionally for path types

elements Homogeneous composition Glue types Higher inductive types Cubical identity types and computational HoTT/UF References Appendix: Cubical Agda primitives Cumulativity Basics Example usage: N-ary variety of features from Cubical Type Theory. In particular, computational univalence and higher inductive types which hence gives computational meaning to Homotopy Type Theory and Univalent Foundations types see: https://github.com/agda/cubical/tree/master/Cubical/HITs. Cubical identity types and computational HoTT/UF As mentioned above the computation rule for J does not hold definitionally for path types