# Difference between revisions of "Kind"

From HaskellWiki

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(Include Wikipedia introduction, which is clearer (to me) and link to TaPL) |
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− | '''Kinds''' classify [[type]]s. Kinds are to types and type-constructors what types are to values. |
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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." |
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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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* [[GHC/Kinds]] |
* [[GHC/Kinds]] |
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* [http://hackage.haskell.org/trac/ghc/wiki/IntermediateTypes#KindsareTypes Kinds ?, ??, # and (#)] |
* [http://hackage.haskell.org/trac/ghc/wiki/IntermediateTypes#KindsareTypes Kinds ?, ??, # and (#)] |
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+ | * [[Books#Foundations|Pierce, Benjamin. ''Types and Programming Languages'']]. |
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[[Category:Language]] |
[[Category:Language]] |

## Revision as of 19:44, 26 August 2012

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 unboxed types.