# Kind

From HaskellWiki

Revision as of 19:05, 28 September 2017 by Dschrempf (talk | contribs) (Add a more complicated example (StateT))

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.

# See also

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