# Kind

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− | ''' | + | [http://en.wikipedia.org/wiki/Kind_%28type_theory%29 Wikipedia] says, "In type theory, a '''kind''' is the type of a type constructor or, less commonly, the type of a higher-order type operator. A kind system is essentially a simply typed lambda calculus 'one level up,' endowed with a primitive type, denoted * and called 'type', which is the kind of any (monomorphic) data type." |

Ordinary types have kind <TT>*</TT>. Type constructors have kind <TT>P -> Q</TT>, where <TT>P</TT> and <TT>Q</TT> are kinds. For instance: | Ordinary types have kind <TT>*</TT>. Type constructors have kind <TT>P -> Q</TT>, where <TT>P</TT> and <TT>Q</TT> are kinds. For instance: | ||

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(->) :: * -> * -> * | (->) :: * -> * -> * | ||

− | In Haskell 98, <TT>*</TT> is the only '''inhabited kind''', that is, all values have types of kind <TT>*</TT>. GHC introduces another inhabited kind, <TT>#</TT>, for [[ | + | In Haskell 98, <TT>*</TT> is the only '''inhabited kind''', that is, all values have types of kind <TT>*</TT>. GHC introduces another inhabited kind, <TT>#</TT>, for [[unlifted type]]s. |

= See also = | = See also = | ||

* [[GHC/Kinds]] | * [[GHC/Kinds]] | ||

+ | * [https://ghc.haskell.org/trac/ghc/wiki/Commentary/Compiler/Kinds Kinds] on the GHC Commentary | ||

+ | * [https://ghc.haskell.org/trac/ghc/wiki/Commentary/Compiler/TypeType TypeType] on the GHC Commentary | ||

* [http://hackage.haskell.org/trac/ghc/wiki/IntermediateTypes#KindsareTypes Kinds ?, ??, # and (#)] | * [http://hackage.haskell.org/trac/ghc/wiki/IntermediateTypes#KindsareTypes Kinds ?, ??, # and (#)] | ||

+ | * [[Books#Foundations|Pierce, Benjamin. ''Types and Programming Languages'']]. | ||

[[Category:Language]] | [[Category:Language]] |

## Latest revision as of 03:52, 14 January 2017

Wikipedia says, "In type theory, a **kind** is the type of a type constructor or, less commonly, the type of a higher-order type operator. A kind system is essentially a simply typed lambda calculus 'one level up,' endowed with a primitive type, denoted * and called 'type', which is the kind of any (monomorphic) data type."

Ordinary types have kind `*`. Type constructors have kind `P -> Q`, where `P` and `Q` are kinds. For instance:

Int :: * Maybe :: * -> * Maybe Bool :: * a -> a :: * [] :: * -> * (->) :: * -> * -> *

In Haskell 98, `*` is the only **inhabited kind**, that is, all values have types of kind `*`. GHC introduces another inhabited kind, `#`, for unlifted types.

# [edit] See also

- GHC/Kinds
- Kinds on the GHC Commentary
- TypeType on the GHC Commentary
- Kinds ?, ??, # and (#)
- Pierce, Benjamin.
*Types and Programming Languages*.