Latest revision as of 19:05, 28 September 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, also called monotypes or nullary type constructors, have kind *. Higher order type constructors have kinds of the form P -> Q, where P and Q are kinds. For instance:

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

A type with a more complicated kind is the StateT monad transformer

 newtype StateT s m 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.

@@ Line 1: / Line 1: @@
-'''Kinds''' classify [[type]]s. Kinds are to types and type-constructors what types are to values.
+[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, also called ''monotypes'' or ''nullary'' type constructors, have kind <TT>*</TT>. Higher order type constructors have kinds of the form <TT>P -> Q</TT>, where <TT>P</TT> and <TT>Q</TT> are kinds. For instance:
   Int :: *
@@ Line 10: / Line 10: @@
   (->) :: * -> * -> *
-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 [[unboxed type]]s.
+A type with a more complicated kind is the [https://hackage.haskell.org/package/mtl-2.2.1/docs/Control-Monad-State-Lazy.html#t:StateT StateT monad transformer]
+ <haskell>
+ newtype StateT s m a :: * -> (* -> *) -> * -> *
+ </haskell>
+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 =
+* [[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 (#)]
+* [[Books#Foundations|Pierce, Benjamin. ''Types and Programming Languages'']].
+[[Category:Language]]