1 3.9 Cumulativity 3.9.1 Basics Since version 2.6.1, Agda supports optional cumulativity of universes under the --cumulativity flag. {-# OPTIONS --cumulativity #-} When the --cumulativity flag is 3 Limitations Currently cumulativity only enables subtyping between universes, but not between any other types containing universes. For example, List Set is not a subtype of List Set1. Agda also does Language Reference Agda User Manual, Release 2.6.4.1 3.40 Sort System Sorts (also known as universes) are types whose members themselves are again types. The fundamental sort in Agda is named Set and

modules. 3.9 Cumulativity 3.9.1 Basics Since version 2.6.1, Agda supports optional cumulativity of universes under the --cumulativity flag. {-# OPTIONS --cumulativity #-} When the --cumulativity flag is 3 Limitations Currently cumulativity only enables subtyping between universes, but not between any other types containing universes. For example, List Set is not a subtype of List Set1. Agda also does Dmitriy Traytel, LMCS Vol. 13(3:28)2017, pp. 1–22 (2017). 3.40 Sort System Sorts (also known as universes) are types whose members themselves are again types. The fundamental sort in Agda is named Set and

modules. 3.9 Cumulativity 3.9.1 Basics Since version 2.6.1, Agda supports optional cumulativity of universes under the --cumulativity flag. {-# OPTIONS --cumulativity #-} When the --cumulativity flag is 3 Limitations Currently cumulativity only enables subtyping between universes, but not between any other types containing universes. For example, List Set is not a subtype of List Set1. Agda also does Dmitriy Traytel, LMCS Vol. 13(3:28)2017, pp. 1–22 (2017). 3.40 Sort System Sorts (also known as universes) are types whose members themselves are again types. The fundamental sort in Agda is named Set and

modules. 3.9 Cumulativity 3.9.1 Basics Since version 2.6.1, Agda supports optional cumulativity of universes under the --cumulativity flag. {-# OPTIONS --cumulativity #-} When the --cumulativity flag is 3 Limitations Currently cumulativity only enables subtyping between universes, but not between any other types containing universes. For example, List Set is not a subtype of List Set1. Agda also does Dmitriy Traytel, LMCS Vol. 13(3:28)2017, pp. 1–22 (2017). 3.40 Sort System Sorts (also known as universes) are types whose members themselves are again types. The fundamental sort in Agda is named Set and

Sized Types Example for coinduction: finite languages References Sort System Introduction to universes Agda’s sort system Sort metavariables and unknown sorts Syntactic Sugar Do-notation Idiom brackets importing modules. Cumulativity Basics Since version 2.6.1, Agda supports optional cumulativity of universes under the -- cumulativity flag. {-# OPTIONS --cumulativity #-} When the --cumulativity flag is Limitations Currently cumulativity only enables subtyping between universes, but not between any other types containing universes. For example, List Set is not a subtype of List Set₁. Agda also does

modules. 3.9 Cumulativity 3.9.1 Basics Since version 2.6.1, Agda supports optional cumulativity of universes under the --cumulativity flag. {-# OPTIONS --cumulativity #-} When the --cumulativity flag is 3 Limitations Currently cumulativity only enables subtyping between universes, but not between any other types containing universes. For example, List Set is not a subtype of List Set1. Agda also does Dmitriy Traytel, LMCS Vol. 13(3:28)2017, pp. 1–22 (2017). 3.39 Sort System Sorts (also known as universes) are types whose members themselves are again types. The fundamental sort in Agda is named Set and

Sized Types Example for coinduction: finite languages References Sort System Introduction to universes Agda’s sort system Sort metavariables and unknown sorts Syntactic Sugar Do-notation Idiom brackets x y) → C y p Cumulativity Basics Since version 2.6.1, Agda supports optional cumulativity of universes under the -- cumulativity flag. {-# OPTIONS --cumulativity #-} When the --cumulativity flag is Limitations Currently cumulativity only enables subtyping between universes, but not between any other types containing universes. For example, List Set is not a subtype of List Set₁. Agda also does

Sized Types Example for coinduction: finite languages References Sort System Introduction to universes Agda’s sort system Sort metavariables and unknown sorts Syntactic Sugar Do-notation Idiom brackets x y) → C y p Cumulativity Basics Since version 2.6.1, Agda supports optional cumulativity of universes under the -- cumulativity flag. {-# OPTIONS --cumulativity #-} When the --cumulativity flag is Limitations Currently cumulativity only enables subtyping between universes, but not between any other types containing universes. For example, List Set is not a subtype of List Set₁. Agda also does

Sized Types Example for coinduction: finite languages References Sort System Introduction to universes Agda’s sort system Sort metavariables and unknown sorts Syntactic Sugar Do-notation Idiom brackets x y) → C y p Cumulativity Basics Since version 2.6.1, Agda supports optional cumulativity of universes under the -- cumulativity flag. {-# OPTIONS --cumulativity #-} When the --cumulativity flag is Limitations Currently cumulativity only enables subtyping between universes, but not between any other types containing universes. For example, List Set is not a subtype of List Set₁. Agda also does

Structural recursion With-functions Pragmas and Options References Universe Levels Introduction to universes Universe polymorphism Pragmas and options With-Abstraction Usage Technical details Without K x y) → C y p Cumulativity Basics Since version 2.6.1, Agda supports optional cumulativity of universes under the -- cumulativity flag. {-# OPTIONS --cumulativity #-} When the --cumulativity flag is Limitations Currently cumulativity only enables subtyping between universes, but not between any other types containing universes. For example, List Set is not a subtype of List Set₁. Agda also does