import TypeClass
defclass Witchcraft.Traversable do
@moduledoc """
Walk through a data structure from left to right,
running some action on each element in turn.
Similar to applicatives, it can be used to do things like collecting some effect
while performing other actions.
## Type Class
An instance of `Witchcraft.Traversable` must also implement `Witchcraft.Foldable`
and `Witchcraft.Functor`, and define `Witchcraft.Foldable.right_fold/3`.
[right_fold/3] Foldable Functor [map/2]
↓ ↓
Traversable
[right_fold/3]
"""
alias __MODULE__
alias Witchcraft.Foldable
extend Witchcraft.Foldable
extend Witchcraft.Functor
use Witchcraft.Internal, deps: [Witchcraft.Foldable, Witchcraft.Functor]
use Witchcraft.Applicative
use Witchcraft.Foldable, except: [equal?: 2]
use Quark
@type t :: any()
@type link :: (any() -> Traversable.t())
where do
@doc """
Convert elements to actions, and then evaluate the actions from left-to-right,
and accumulate the results.
For a version without accumulation, see `then_traverse/2`.
## Examples
iex> traverse([1, 2, 3], fn x -> {x, x * 2, x * 10} end)
{6, 12, [10, 20, 30]}
iex> traverse({1, 2, 3}, fn x -> [x] end)
[{1, 2, 3}]
iex> traverse({1, 2, 3}, fn x -> [x, x * 5, x * 10] end)
[
{1, 2, 3},
{1, 2, 15},
{1, 2, 30}
]
iex> traverse([1, 2, 3], fn x -> [x, x * 5, x * 10] end)
[
#
[1, 2, 3], [1, 2, 15], [1, 2, 30],
[1, 10, 3], [1, 10, 15], [1, 10, 30],
[1, 20, 3], [1, 20, 15], [1, 20, 30],
#
[5, 2, 3], [5, 2, 15], [5, 2, 30],
[5, 10, 3], [5, 10, 15], [5, 10, 30],
[5, 20, 3], [5, 20, 15], [5, 20, 30],
#
[10, 2, 3], [10, 2, 15], [10, 2, 30],
[10, 10, 3], [10, 10, 15], [10, 10, 30],
[10, 20, 3], [10, 20, 15], [10, 20, 30]
]
traverse([1, 2, 3], fn x -> %Algae.Maybe.Just{just: x} end)
#=> %Algae.Maybe.Just{just: [1, 2, 3]}
traverse(%Algae.Maybe.Just{just: 4}, fn x -> [x, x * 10] end)
#=> [
# %Algae.Maybe.Just{just: 4},
# %Algae.Maybe.Just{just: 40}
# ]
traverse([1, 2, 3], fn x ->
if is_even(x) do
%Algae.Maybe.Just{just: x}
else
%Algae.Maybe.Nothing{}
end
end)
#=> %Algae.Maybe.Nothing{}
"""
@spec traverse(Traversable.t(), Traversable.link()) :: Traversable.t()
def traverse(data, link)
end
properties do
def naturality(data) do
a = generate(data)
f = fn x -> [x] end
g = &Quark.id/1
a
|> Traversable.traverse(f)
|> g.()
|> equal?(Traversable.traverse(a, fn x -> x |> f.() |> g.() end))
end
def identity(data) do
a = generate(data)
a
|> Traversable.traverse(fn x -> {x} end)
|> equal?({a})
end
def composition(_data) do
# traverse (Compose . fmap g . f) = Compose . fmap (traverse g) . traverse f
# MAINTAINER COMMENT
# ==================
#
# I cannot get this working. After throwing 1.5 days at this *one* prop,
# I'm walking away for now. If someone has an implementation that works,
# it would be greatly appreciated.
#
# I've implemented %Endo{} and %Compose{}, but Compose's Foldable refused
# to work because there is no Foldable instance for functions (AFAIK).
#
# I believe that the Hakell version works because of the lazy
# recursive call to foldMap in `Foldable f, Foldable g => Compose (f g)`,
# which in Elixir is trying to get dispatched on the partial function.
#
# It's very possible that there's a simple solution that I'm just not seeing
# after staring at the problem for too long
#
# PRs gladly accepted here: https://github.com/expede/witchcraft/compare
#
# ~ Brooklyn Zelenka, @expede
true
end
end
@doc """
`traverse/2` with arguments reversed.
## Examples
iex> fn x -> {x, x * 2, x * 10} end |> through([1, 2, 3])
{6, 12, [10, 20, 30]}
iex> fn x -> [x] end |> through({1, 2, 3})
[{1, 2, 3}]
iex> fn x -> [x, x * 5, x * 10] end |> through({1, 2, 3})
[
{1, 2, 3},
{1, 2, 15},
{1, 2, 30}
]
iex> fn x -> [x, x * 5, x * 10] end |> through([1, 2, 3])
[
#
[1, 2, 3], [1, 2, 15], [1, 2, 30],
[1, 10, 3], [1, 10, 15], [1, 10, 30],
[1, 20, 3], [1, 20, 15], [1, 20, 30],
#
[5, 2, 3], [5, 2, 15], [5, 2, 30],
[5, 10, 3], [5, 10, 15], [5, 10, 30],
[5, 20, 3], [5, 20, 15], [5, 20, 30],
#
[10, 2, 3], [10, 2, 15], [10, 2, 30],
[10, 10, 3], [10, 10, 15], [10, 10, 30],
[10, 20, 3], [10, 20, 15], [10, 20, 30]
]
"""
@spec through(Traversable.link(), Traversable.t()) :: Traversable.t()
def through(link, traversable), do: traverse(traversable, link)
@doc """
Run each action/effect in sequence (from left to right),
and accumulate values along the way.
## Examples
iex> sequence([{1, 2, 3}, {4, 5, 6}])
{5, 7, [3, 6]}
iex> [
...> [1, 2, 3],
...> [4, 5, 6]
...> ]
...> |> sequence()
[
[1, 4],
[1, 5],
[1, 6],
[2, 4],
[2, 5],
[2, 6],
[3, 4],
[3, 5],
[3, 6]
]
"""
@spec sequence(Traversable.t()) :: Foldable.t()
def sequence(traversable), do: traverse(traversable, &Quark.id/1)
end
definst Witchcraft.Traversable, for: Tuple do
use Witchcraft.Functor
def traverse(tuple, link) do
last_index = tuple_size(tuple) - 1
tuple
|> elem(last_index)
|> link.()
~> fn last -> put_elem(tuple, last_index, last) end
end
end
definst Witchcraft.Traversable, for: List do
use Witchcraft.Applicative
use Witchcraft.Foldable
def traverse([], link), do: of(link.([]), [])
def traverse(list = [head | _], link) do
right_fold(list, of(link.(head), []), fn x, acc ->
# credo:disable-for-lines:2 Credo.Check.Refactor.PipeChainStart
fn link_head, link_tail -> [link_head | link_tail] end
|> over(link.(x), acc)
end)
end
end
