Precursor.Coerce

Documentation

class (~R#) k k a b => Coercible k a b

Coercible is a two-parameter class that has instances for types a and b if the compiler can infer that they have the same representation. This class does not have regular instances; instead they are created on-the-fly during type-checking. Trying to manually declare an instance of Coercible is an error.

Nevertheless one can pretend that the following three kinds of instances exist. First, as a trivial base-case:

instance a a

Furthermore, for every type constructor there is an instance that allows to coerce under the type constructor. For example, let D be a prototypical type constructor (data or newtype) with three type arguments, which have roles nominal, representational resp. phantom. Then there is an instance of the form

instance Coercible b b' => Coercible (D a b c) (D a b' c')

Note that the nominal type arguments are equal, the representational type arguments can differ, but need to have a Coercible instance themself, and the phantom type arguments can be changed arbitrarily.

The third kind of instance exists for every newtype NT = MkNT T and comes in two variants, namely

instance Coercible a T => Coercible a NT

instance Coercible T b => Coercible NT b

This instance is only usable if the constructor MkNT is in scope.

If, as a library author of a type constructor like Set a, you want to prevent a user of your module to write coerce :: Set T -> Set NT, you need to set the role of Set's type parameter to nominal, by writing

type role Set nominal

For more details about this feature, please refer to Safe Coercions by Joachim Breitner, Richard A. Eisenberg, Simon Peyton Jones and Stephanie Weirich.

Since: 4.7.0.0

coerce :: Coercible * a b => a -> b

The function coerce allows you to safely convert between values of types that have the same representation with no run-time overhead. In the simplest case you can use it instead of a newtype constructor, to go from the newtype's concrete type to the abstract type. But it also works in more complicated settings, e.g. converting a list of newtypes to a list of concrete types.

(#.) :: Coercible b c => (b -> c) -> (a -> b) -> a -> c infixr 9

It may be better to use (#.) instead of (.) to avoid potential efficiency problems relating to #7542. The problem, in a nutshell:

If N is a newtype constructor, then N x will always have the same representation as x (something similar applies for a newtype deconstructor). However, if f is a function,

N . f = x -> N (f x)

This looks almost the same as f, but the eta expansion lifts it--the lhs could be _|_, but the rhs never is. This can lead to very inefficient code. Thus we steal a technique from Shachaf and Edward Kmett and adapt it to the current (rather clean) setting. Instead of using N . f, we use N .# f, which is just

coerce f `asTypeOf' (N . f)

That is, we just *pretend* that f has the right type, and thanks to the safety of coerce, the type checker guarantees that nothing really goes wrong. We still have to be a bit careful, though: remember that #. completely ignores the *value* of its left operand.