Witchcraft.Monad (Witchcraft v1.0.4) View Source

Very similar to Chain, Monad provides a way to link actions, and a way to bring plain values into the correct context (Applicative).

This allows us to view actions in a full framework along the lines of functor and applicative:

           data ---------------- function ----------------------------> result
             |                      |                                     |
 of(Container, data)          of/2, or similar                of(Container, result)
             ↓                      ↓                                     ↓
%Container<data> --- (data -> %Container<updated_data>) ---> %Container<updated_data>

As you can see, the linking function may just be of now that we have that.

For a nice, illustrated introduction, see Functors, Applicatives, And Monads In Pictures.

Having of also lets us enhance do-notation with a convenient return function (see monad/2)

Type Class

An instance of Witchcraft.Monad must also implement Witchcraft.Applicative and Wicthcraft.Chainable.

                 Functor     [map/2]
                    ↓
                  Apply      [convey/2]
                  ↓   ↓
[of/2]  Applicative   Chain  [chain/2]
                  ↓   ↓
                  Monad
                   [_]

Link to this section Summary

Functions

async(sample, list)

Variant of monad/2 where each step internally occurs asynchonously, but lines run strictly one after another.

async_bind(chainable, link)

Alias for async_chain/2

async_chain(chainable, link)

Asynchronous variant of Witchcraft.Chain.chain/2.

async_draw(link, chainable)

Asynchronous variant of Witchcraft.Chain.draw/2.

monad(sample, list)

do-notation enhanced with a return operation.

Link to this section Types

t()

Specs

t() :: any()

Link to this section Functions

async(sample, list)

(macro)

Variant of monad/2 where each step internally occurs asynchonously, but lines run strictly one after another.

Examples

iex> async [] do
...>   [1, 2, 3]
...> end
[1, 2, 3]

iex> async [] do
...>   [1, 2, 3]
...>   [4, 5, 6]
...>   [7, 8, 9]
...> end
[
7, 8, 9,
7, 8, 9,
7, 8, 9,
7, 8, 9,
7, 8, 9,
7, 8, 9,
7, 8, 9,
7, 8, 9,
7, 8, 9
]

iex> async [] do
...>   Witchcraft.Applicative.of([], 1)
...> end
[1]

iex> async [] do
...>  a <- [1,2,3]
...>  b <- [4,5,6]
...>  return(a * b)
...> end
[
  4,  5,  6,
  8,  10, 12,
  12, 15, 18
]

iex> async [] do
...>   a <- return 1
...>   b <- return 2
...>   return(a + b)
...> end
[3]

async_bind(chainable, link)

Specs

async_bind(Witchcraft.Chain.t(), Witchcraft.Chain.link()) ::
  Witchcraft.Chain.t()

Alias for async_chain/2

async_chain(chainable, link)

Specs

async_chain(Witchcraft.Chain.t(), Witchcraft.Chain.link()) ::
  Witchcraft.Chain.t()

Asynchronous variant of Witchcraft.Chain.chain/2.

Note that each async_chain call awaits that step's completion. This is a feature not a bug, since chain can introduce dependencies between nested links. However, this means that the async features on only really useful on larger data sets, because otherwise we're just sparking tasks and immediaetly waiting a single application.

Examples

iex> async_chain([1, 2, 3], fn x -> [x, x] end)
[1, 1, 2, 2, 3, 3]

iex> async_chain([1, 2, 3], fn x ->
...>   async_chain([x + 1], fn y ->
...>     [x * y]
...>   end)
...> end)
[2, 6, 12]

0..10_000
|> Enum.to_list()
|> async_chain(fn x ->
  async_chain([x + 1], fn y ->
    Process.sleep(500)
    [x * y]
  end)
end)
#=> [0, 2, 6, 12, 20, 30, 42, ...] in around a second

async_draw(link, chainable)

Specs

async_draw(Witchcraft.Chain.t(), Witchcraft.Chain.link()) ::
  Witchcraft.Chain.t()

Asynchronous variant of Witchcraft.Chain.draw/2.

Note that each async_draw call awaits that step's completion. This is a feature not a bug, since chain can introduce dependencies between nested links. However, this means that the async features on only really useful on larger data sets, because otherwise we're just sparking tasks and immediaetly waiting a single application.

Examples

iex> async_draw(fn x -> [x, x] end, [1, 2, 3])
[1, 1, 2, 2, 3, 3]

iex> (fn y -> [y * 5, y * 10] end)
...> |> async_draw(fn x -> [x, x] end
...> |> async_draw([1, 2, 3])) # note the "extra" closing paren
[5, 10, 5, 10, 10, 20, 10, 20, 15, 30, 15, 30]

iex> fn x ->
...>   fn y ->
...>     [x * y]
...>   end
...>   |> async_draw([x + 1])
...> end
...> |> async_draw([1, 2, 3])
[2, 6, 12]

fn x ->
  fn y ->
    Process.sleep(500)
    [x * y]
  end
  |> async_draw([x + 1])
end
|> async_draw(Enum.to_list(0..10_000))
[0, 2, 6, 12, ...] # in under a second

monad(sample, list)

(macro)

do-notation enhanced with a return operation.

return is the simplest possible linking function, providing the correct of/2 instance for your monad.

Examples

iex> monad [] do
...>   [1, 2, 3]
...> end
[1, 2, 3]

iex> monad [] do
...>   [1, 2, 3]
...>   [4, 5, 6]
...>   [7, 8, 9]
...> end
[
  7, 8, 9,
  7, 8, 9,
  7, 8, 9,
  7, 8, 9,
  7, 8, 9,
  7, 8, 9,
  7, 8, 9,
  7, 8, 9,
  7, 8, 9
]

iex> monad [] do
...>   Witchcraft.Applicative.of([], 1)
...> end
[1]

iex> monad [] do
...>   return 1
...> end
[1]

iex> monad [] do
...>   monad {999} do
...>     return 1
...>   end
...> end
{1}

iex> monad [] do
...>  a <- [1,2,3]
...>  b <- [4,5,6]
...>  return(a * b)
...> end
[
  4,  5,  6,
  8,  10, 12,
  12, 15, 18
]

iex> monad [] do
...>   a <- return 1
...>   b <- return 2
...>   return(a + b)
...> end
[3]