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# The data type `Type`

and its friends

GHC's compiles a typed programming lanuage, and GHC's intermediate language is explicitly typed. So the data type that GHC uses to represent types is of central importance.

The first thing to realise is that GHC uses a *single* data type for types, even though there are two different "views".

- The "typechecker view" (or "source view") regards the type as a Haskell type, complete with implicit parameters, class constraints, and the like. For example:
forall a. (Eq a, %x::Int) => a -> Int

- The "core view" regards the type as a Core-language type, where class and implicit parameter constraints are treated as function arguments:
forall a. Eq a -> Int -> a -> Int

These two "views" are supported by a family of functions operating over that view:

- compiler/types/TypeRep.lhs: here is where
`Type`

is defined. - compiler/types/Type.lhs: core-view utility functions over
`Type`

. - compiler/typecheck/TcType.lhs: source-view utility functions over
`Type`

.

The module `TypeRep`

exposes the representation becauese a few other modules (`Type`

, `TcType`

, `Unify`

, etc) work directly on its representation. However, you should not lightly pattern-match on `Type`

; it is meant to be an abstract type. Instead, try to use functions defined by `Type`

, `TcType`

etc.

The single data type `Type`

is used to represent

- Types (possibly of higher kind); e.g.
`[Int]`

,`Maybe`

- Coercions; e.g.
`trans (sym g) h`

- Kinds (which classify types and coercions); e.g.
`(* -> *)`

,`T :=: [Int]`

- Sorts (which classify types); e.g.
`TY`

,`CO`

GHC's use of coercions and equality constraints is important enough to deserve its own page.

## The representation of {{Type}}

Here, then is the representation of types (see compiler/types/TypeRep.lhs for more details):

data Type = TyVarTy TyVar -- Type variable | AppTy Type Type -- Application | TyConApp TyCon [Type] -- Type constructor application | FunTy Type Type -- Arrow type | ForAllTy TyVar Type -- Polymorphic type | PredTy PredType -- Type constraint | NoteTy TyNote Type -- Annotation data PredType = ClassP Class [Type] -- Class predicate | IParam (IPName Name) Type -- Implicit parameter | EqPred Type Type -- Equality predicate (ty1 :=: ty2) data TyNote = FTVNote TyVarSet -- The free type variables of the noted expression

## Kinds

Kinds are represented as types:

type Kind = Type

Basic kinds are now
represented using type constructors, e.g. the kind `*`

is represented as

liftedTypeKind :: Kind liftedTypeKind = TyConApp liftedTypeKindTyCon []

where `liftedTypeKindTyCon`

is a built-in `PrimTyCon`

. The arrow type
constructor is used as the arrow kind constructor, e.g. the kind `* ->*`

is represented internally as

FunTy liftedTypeKind liftedTypeKind

It's easy to extract the kind of a type, or the sort of a kind:

typeKind :: Type -> Kind

The "sort" of a kind is always one of the
sorts: `TY`

(for kinds that classify normal types) or `CO`

(for kinds that
classify coercion evidence). The coercion kind, `T1 :=: T2`

, is
represented by `PredTy (EqPred T1 T2)`

.

## Type variables

Type variables are represented by the `TyVar`

constructor of the data type Var.

Type variables range over both *types* (possibly of higher kind) or *coercions*. You could tell the differnece between these two by taking the `typeKind`

of the kind of the type variable, adn seeing if you have sort `TY`

or `CO`

, but for efficiency the `TyVar`

keeps a boolean flag, and offes a function:

isCoercionVar :: TyVar -> Bool