In order to allow full flexibility in how kinds are used, it is necessary to use the kind system to differentiate between boxed, lifted types (normal, everyday types like Int
and [Bool]
) and unboxed, primitive types (Unboxed types and primitive operations) like Int#
. We thus have socalled representation polymorphism.
Here are the key definitions, all available from GHC.Exts
:
TYPE :: RuntimeRep > Type  highly magical, built into GHC
data Levity = Lifted  for things like `Int`
 Unlifted  for things like `Array#`
data RuntimeRep = BoxedRep Levity  for anything represented by a GCmanaged pointer
 IntRep  for `Int#`
 TupleRep [RuntimeRep]  unboxed tuples, indexed by the representations of the elements
 SumRep [RuntimeRep]  unboxed sums, indexed by the representations of the disjuncts
 ...
type LiftedRep = BoxedRep Lifted
type Type = TYPE LiftedRep  Type is just an ordinary type synonym
The idea is that we have a new fundamental type constant TYPE
, which is parameterised by a RuntimeRep
. We thus get Int# :: TYPE IntRep
and Bool :: TYPE LiftedRep
. Anything with a type of the form TYPE x
can appear to either side of a function arrow >
. We can thus say that >
has type TYPE r1 > TYPE r2 > TYPE LiftedRep
. The result is always lifted because all functions are lifted in GHC.
6.4.12.1. Levity polymorphism
A special case of representation polymorphism is levity polymorphism, where we abstract over a variable of kind Levity
, such as:
example :: forall (l :: Levity) (a :: TYPE (BoxedRep l)). (Int > a) > a
example f = f 42
With UnliftedDatatypes
, we can even declare levitypolymorphic data types:
type PEither :: Type > Type > TYPE (BoxedRep l)
data PEither l r = PLeft l  PRight r
6.4.12.2. No representationpolymorphic variables or arguments
If GHC didn’t have to compile programs that run in the real world, that would be the end of the story. But representation polymorphism can cause quite a bit of trouble for GHC’s code generator. Consider
bad :: forall (r1 :: RuntimeRep) (r2 :: RuntimeRep)
(a :: TYPE r1) (b :: TYPE r2).
(a > b) > a > b
bad f x = f x
This seems like a generalisation of the standard $
operator. If we think about compiling this to runnable code, though, problems appear. In particular, when we call bad
, we must somehow pass x
into bad
. How wide (that is, how many bits) is x
? Is it a pointer? What kind of register (floatingpoint or integral) should x
go in? It’s all impossible to say, because x
’s type, a :: TYPE r1
is representationpolymorphic. We thus forbid such constructions, via the following straightforward rule:
This eliminates bad
because the variable x
would have a representationpolymorphic type.
However, not all is lost. We can still do this:
($) :: forall r (a :: Type) (b :: TYPE r).
(a > b) > a > b
f $ x = f x
Here, only b
is representationpolymorphic. There are no variables with a representationpolymorphic type. And the code generator has no trouble with this. Indeed, this is the true type of GHC’s $
operator, slightly more general than the Haskell 98 version.
Because the code generator must store and move arguments as well as variables, the logic above applies equally well to function arguments, which may not be representationpolymorphic.
6.4.12.3. Representationpolymorphic bottoms
We can use representation polymorphism to good effect with error
and undefined
, whose types are given here:
undefined :: forall (r :: RuntimeRep) (a :: TYPE r).
HasCallStack => a
error :: forall (r :: RuntimeRep) (a :: TYPE r).
HasCallStack => String > a
These functions do not bind a representationpolymorphic variable, and so are accepted. Their polymorphism allows users to use these to conveniently stub out functions that return unboxed types.
6.4.12.4. Printing representationpolymorphic types
fprintexplicitruntimereps

Print
RuntimeRep
andLevity
parameters as they appear; otherwise, they are defaulted toLiftedRep
andLifted
, respectively.
Most GHC users will not need to worry about representation polymorphism or unboxed types. For these users, seeing the representation polymorphism in the type of $
is unhelpful. And thus, by default, it is suppressed, by supposing all type variables of type RuntimeRep
to be LiftedRep
when printing, and printing TYPE LiftedRep
as Type
(or *
when StarIsType
is on).
Should you wish to see representation polymorphism in your types, enable the flag fprintexplicitruntimereps
. For example,
ghci> :t ($)
($) :: (a > b) > a > b
ghci> :set fprintexplicitruntimereps
ghci> :t ($)
($)
:: forall (r :: GHC.Types.RuntimeRep) a (b :: TYPE r).
(a > b) > a > b