# The data type `Type` and its friends

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

The single data type `Type` is used to represent

- Types (possibly of higher kind); e.g.
`[Int]`,`Maybe` - Kinds (which classify types and coercions); e.g.
`(* -> *)`,`T :=: [Int]`. See Commentary/Compiler/Kinds - 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 module `TypeRep` exposes the representation because 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.

## Views of types

Even when considering only types (not kinds, sorts, coercions) you need to know that GHC uses a *single* data type for types. You can look at the same type in different ways:

- The "typechecker 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

Functions in`TcType`take this view of types; e.g.`tcSplitSigmaTy`splits up a type into its forall'd type variables, its constraints, and the rest.

- 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

Functions in`Type`take this view.

The data type `Type` represents type synonym applications in un-expanded form. E.g.

type T a = a -> a f :: T Int

Here `f`'s type doesn't look like a function type, but it really is. The function `Type.coreView :: Type -> Maybe Type` takes a type and, if it's a type synonym application, it expands the synonym and returns `Just <expanded-type>`. Otherwise it returns `Nothing`.

Now, other functions use `coreView` to expand where necessary, thus:

splitFunTy_maybe :: Type -> Maybe (Type,Type) splitFunTy_maybe ty | Just ty' <- coreView ty = splitFunTy_maybe ty' splitFunTy_maybe (FunTy t1 t2) = Just (t1,t2) splitFunTy_maybe other = Nothing

Notice the first line, which uses the view, and recurses when the view 'fires'. Since `coreView` is non-recursive, GHC will inline it, and the optimiser will ultimately produce something like:

splitFunTy_maybe :: Type -> Maybe (Type,Type) splitFunTy_maybe (PredTy p) = splitFunTy_maybe (predTypeRep p) splitFunTy_maybe (NoteTy _ ty) = splitFunTy_maybe ty splitFunTy_maybe (FunTy t1 t2) = Just (t1,t2) splitFunTy_maybe other = Nothing

## The representation of `Type`

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

type TyVar = Var data Type = TyVarTy TyVar -- Type variable | AppTy Type Type -- Application | TyConApp TyCon [Type] -- Type constructor application | FunTy Type Type -- Arrow type | ForAllTy Var Type -- Polymorphic type | LitTy TyLit -- Type literals data TyLit = NumTyLit Integer -- A number | StrTyLit FastString -- A string

Invariant: if the head of a type application is a `TyCon`, GHC *always* uses the `TyConApp` constructor, not `AppTy`.
This invariant is maintained internally by 'smart constructors'.
A similar invariant applies to `FunTy`; `TyConApp` is never used with an arrow type.

Type variables are represented by the `TyVar` constructor of the data type Var.

## Overloaded types

In Haskell we write

f :: forall a. Num a => a -> a

but in Core the `=>` is represented by an ordinary `FunTy`. So f's type looks like this:

ForAllTy a (TyConApp num [TyVarTy a] `FunTy` TyVarTy a `FunTy` TyVarTy a) where a :: TyVar num :: TyCon

Nevertheless, we can tell when a function argument is actually a predicate (and hence should be displayed with `=>`, etc), using

isPredTy :: Type -> Bool

The various forms of predicate can be extracted thus:

classifyPredType :: Type -> PredTree data PredTree = ClassPred Class [Type] -- Class predicates e.g. (Num a) | EqPred Type Type -- Equality predicates e.g. (a ~ b) | TuplePred [PredType] -- Tuples of predicates e.g. (Num a, a~b) | IrredPred PredType -- Higher order predicates e.g. (c a)

These functions are defined in module `Type`.

## Classifying types

GHC uses the following nomenclature for types:

**Unboxed**- A type is unboxed iff its representation is other than a pointer. Unboxed types are also unlifted.

**Lifted**- A type is lifted iff it has bottom as an element. Closures always have lifted types: i.e. any let-bound identifier in Core must have a lifted type. Operationally, a lifted object is one that can be entered. Only lifted types may be unified with a type variable.

**Data**- A type declared with
. Also boxed tuples.`data`

**Algebraic**- An algebraic data type is a data type with one or more constructors, whether declared with
`data`or`newtype`. An algebraic type is one that can be deconstructed with a case expression. "Algebraic" is**NOT**the same as "lifted", because unboxed (and thus unlifted) tuples count as "algebraic".

**Primitive**- a type is primitive iff it is a built-in type that can't be expressed in Haskell. Currently, all primitive types are unlifted, but that's not necessarily the case. (E.g. Int could be primitive.)

Some primitive types are unboxed, such as Int#, whereas some are boxed but unlifted (such as

ByteArray#). The only primitive types that we classify as algebraic are the unboxed tuples.

Examples of type classifications:

Primitive | Boxed | Lifted | Algebraic
| |

Int# | Yes | No | No | No |

ByteArray# | Yes | Yes | No | No |

(# a, b #) | Yes | No | No | Yes |

( a, b ) | No | Yes | Yes | Yes |

[a] | No | Yes | Yes | Yes |