Functors provide a way to apply a function to value(s) a datatype (lists, trees, maybes, etc).

All elements of the data being mapped over need to be consumable by the lifted function. The simplest way to handle this is to have only one type in the data/collection.

The term lift is used rather than the more common map. First, this makes clear that the use is to lift functions into containers. Second, if you want mapping behaviour on collections, check out Enum.map. In fact, the default implimentation is Enum.map, so you can use this with the build-in datatypes. Third, the naming becomes more consistent with Applicative’s lift2, lift3, and so on.

Properties

Identity

Mapping the identity function over the object returns the same object ex. lift([1,2,3], id) == [1,2,3]

Distributive

lift(data, (f |> g)) == data |> lift(f) |> lift(g)

Associates all objects

Mapping a function onto an object returns a value. ie: does not throw an error, returns a value of the target type (not of the wrong type, or the type none)

Notes:

• The argument order convention is reversed from most other lanaguges
• Most (if not all) implimentations of lift should be expressable in terms of Enum.reduce/3
• Falls back to Enum.map/2

Examples

iex> [1,2,3] |> lift(&(&1 + 1))
[2,3,4]

iex> defimpl Witchcraft.Functor, for: Witchcraft.Id do
iex>   def lift(%Witchcraft.Id{id: inner}, func), do: %Witchcraft.Id{id: func.(inner)}
iex> end
iex> lift(%Witchcraft.Id{id: 1}, &(&1 + 1))
%Witchcraft.Id{id: 2}