6.10.1. Equality constraints and Coercible constraint¶
6.10.1.1. Equality constraints¶
A type context can include equality constraints of the form t1 ~ t2
,
which denote that the types t1
and t2
need to be the same. In
the presence of type families, whether two types are equal cannot
generally be decided locally. Hence, the contexts of function signatures
may include equality constraints, as in the following example:
sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 -> c2 -> c2
where we require that the element type of c1
and c2
are the
same. In general, the types t1
and t2
of an equality constraint
may be arbitrary monotypes; i.e., they may not contain any quantifiers,
independent of whether higher-rank types are otherwise enabled.
Equality constraints can also appear in class and instance contexts. The former enable a simple translation of programs using functional dependencies into programs using family synonyms instead. The general idea is to rewrite a class declaration of the form
class C a b | a -> b
to
class (F a ~ b) => C a b where
type F a
That is, we represent every functional dependency (FD) a1 .. an -> b
by an FD type family F a1 .. an
and a superclass context equality
F a1 .. an ~ b
, essentially giving a name to the functional
dependency. In class instances, we define the type instances of FD
families in accordance with the class head. Method signatures are not
affected by that process.
6.10.1.2. Heterogeneous equality¶
GHC also supports kind-heterogeneous equality, which relates two types of
potentially different kinds. Heterogeneous equality is spelled ~~
. Here
are the kinds of ~
and ~~
to better understand their difference:
(~) :: forall k. k -> k -> Constraint
(~~) :: forall k1 k2. k1 -> k2 -> Constraint
Users will most likely want ~
, but ~~
is available if GHC cannot know,
a priori, that the two types of interest have the same kind. Evidence that
(a :: k1) ~~ (b :: k2)
tells GHC both that k1
and k2
are the same
and that a
and b
are the same.
Because ~
is the more common equality relation, GHC prints out ~~
like
~
unless -fprint-equality-relations
is set.
6.10.1.3. Unlifted heterogeneous equality¶
Internal to GHC is yet a third equality relation (~#)
. It is heterogeneous
(like ~~
) and is used only internally. It may appear in error messages
and other output only when -fprint-equality-relations
is enabled.
6.10.1.4. The Coercible
constraint¶
The constraint Coercible t1 t2
is similar to t1 ~ t2
, but
denotes representational equality between t1
and t2
in the sense
of Roles (Roles). It is exported by Data.Coerce, which also
contains the documentation. More details and discussion can be found in the
paper
“Safe Coercions”.