Documentation

Newtype n o means that n is a newtype wrapper around o. n must be an instance of Generic. Furthermore, the Coercible n o instance must be visible; this typically means the newtype constructor is visible, but the instance could also have been brought into view by pattern matching on a Coercion.

A single-parameter version of Newtype, similar to the Newtype class in newtype-generics.

Newtype n o is equivalent to (IsNewtype n, o ~ O n).

A version of Newtype with the parameters flipped, for partial application.

Get the underlying type of a newtype.

data N = N Int deriving Generic
-- O N = Int

Two types are Similar if they are built from the same type constructor and the same kind arguments.

Sum Int and Sum Bool are Similar.

Sum Int and Product Int are not Similar because they are built from different type constructors.

Const Int Char and Const Int Maybe are not Similar because they have different kind arguments.

Wrap a value with a newtype constructor.

Unwrap a newtype constructor from a value.

Reverse the type of a "packer".

>>> op All (All True)
True
>>> op (Identity . Sum) (Identity (Sum 3))
3

The workhorse of the package. Given a "packer" and a "higher order function" (hof), it handles the packing and unpacking, and just sends you back a regular old function, with the type varying based on the hof you passed.

The reason for the signature of the hof is due to ala not caring about structure. To illustrate why this is important, consider this alternative implementation of under2:

under2 :: (Newtype n o, Newtype n' o')
       => (o -> n) -> (n -> n -> n') -> (o -> o -> o')
under2' pa f o0 o1 = ala pa (\p -> uncurry f . bimap p p) (o0, o1)

Being handed the "packer", the hof may apply it in any structure of its choosing – in this case a tuple.

>>> ala Sum foldMap [1,2,3,4]
10

This is the original function seen in Conor McBride's work. The way it differs from the ala function in this package, is that it provides an extra hook into the "packer" passed to the hof. However, this normally ends up being id, so ala wraps this function and passes id as the final parameter by default. If you want the convenience of being able to hook right into the hof, you may use this function.

>>> ala' Sum foldMap length ["hello", "world"]
10

>>> ala' First foldMap (readMaybe @Int) ["x", "42", "1"]
Just 42

A very simple operation involving running the function 'under' the newtype.

>>> under Product (stimes 3) 3
27

The opposite of under. I.e., take a function which works on the underlying types, and switch it to a function that works on the newtypes.

>>> over All not (All False)
All {getAll = True}

Lower a binary function to operate on the underlying values.

>>> under2 Any (<>) True False
True

The opposite of under2.

under lifted into a functor.

over lifted into a functor.