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

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

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

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

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

Structural recursion With-functions Pragmas and Options References Universe Levels Introduction to universes Universe polymorphism With-Abstraction Usage Technical details Without K Restrictions on pattern [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.3494&rank=1] Universe Levels Introduction to universes Russell’s paradox implies that the collection of all sets is not itself a set. Namely, if there so on. A type whose elements are types is called a universe; Agda provides an infinite number of universes Set, Set₁, Set₂, Set₃, …, each of which is an element of the next one. In fact, Set itself is just

Structural recursion With-functions Pragmas and Options References Universe Levels Introduction to universes Universe polymorphism With-Abstraction Usage Technical details Without K Restrictions on pattern [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.3494&rank=1] Universe Levels Introduction to universes Russell’s paradox implies that the collection of all sets is not itself a set. Namely, if there so on. A type whose elements are types is called a universe; Agda provides an infinite number of universes Set, Set₁, Set₂, Set₃, …, each of which is an element of the next one. In fact, Set itself is just