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.

The constraint `Coercible t1 t2`

is similar to ```
t1 ~
t2
```

, but denotes representational equality between
`t1`

and `t2`

in the sense of Roles
(Section 7.27, “Roles
”). It is exported by
`Data.Coerce`

,
which also contains the documentation. More details and discussion can be found in
the paper
Safe Coercions".