6.4.12. Levity polymorphism¶
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 levity
polymorphism.
Here are the key definitions, all available from GHC.Exts
:
TYPE :: RuntimeRep > Type  highly magical, built into GHC
data RuntimeRep = LiftedRep  for things like `Int`
 UnliftedRep  for things like `Array#`
 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 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. No levitypolymorphic 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
levity polymorphic. We thus forbid such constructions, via the
following straightforward rule:
No variable may have a levitypolymorphic type.
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 levity polymorphic. There are no variables
with a levitypolymorphic 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 levitypolymorphic.
6.4.12.2. Levitypolymorphic bottoms¶
We can use levity 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 levitypolymorphic variable, and so are accepted. Their polymorphism allows users to use these to conveniently stub out functions that return unboxed types.
6.4.12.3. Printing levitypolymorphic types¶

fprintexplicitruntimereps
¶ Print
RuntimeRep
parameters as they appear; otherwise, they are defaulted to'LiftedRep
.
Most GHC users will not need to worry about levity polymorphism
or unboxed types. For these users, seeing the levity 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 levity 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