erlang-monads.markdown

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Monads in Erlang

monads are simple

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a monad is a monoid in the category of endofunctors

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problem?

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monads get a bad wrap from monad tutorials

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a monad is a Burrito

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a computation container

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category theory

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i'll give a concrete definition, in Erlang

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@@@ erlang
-type monad() :: term().

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@@@ erlang
-type list(Something).

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@@@ erlang
-spec return(term()) -> monad().

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@@@ erlang
-spec bind(monad(), fun((term()) -> monad())) -> monad().

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@@@ erlang
-type either() :: {ok, term()} | {error, term()}.

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@@@ erlang
-spec return(term()) -> either().
return(Value) ->
    {ok, Value}.

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@@@ erlang
-spec bind(monad(), fun((term()) -> either())) -> either().
bind({ok, Val}, MonadicFun) ->
    MonadicFun(Val);
bind({error, _Reason}=Error, _MonadicFun) ->
    Error.

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motivation

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@@@ erlang
doThatThing() ->
    case partOne() of
        {ok, Result1} ->
            case partTwo(Result1) of
                {ok, Result2} ->
                    {ok, 'wow_you_followed_this_far?'};
                {error, _Reason2}=Reason2 ->
                    Reason2
            end;
        {error, _Reason1}=Reason1 ->
            Reason1
    end.

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what we really want to say

@@@ erlang
[fun partOne/0, fun partTwo/1].

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@@@ erlang
bind(partOne(), fun partTwo/1).

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we can chain this together

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@@@ erlang
pipe(Monad, Funs) ->
    lists:foldl(flip(fun bind/2), Monad, Funs).

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@@@ erlang
mAddOne(Val) ->
    Val + 1.

mAlwaysError(Val) ->
    {error, Val}.

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@@@ erlang
pipe({ok, 0}, [fun mAddOne/1, fun mAddOne/1, mAddOne/1, fun mAlwaysError/1]).

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polymorphism

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fucking erlang

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modules

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@@@ erlang
ModuleVar:bind(...)
ModuleVar:return(...)

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other monads

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writer monad

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@@@ erlang
return(Val) ->
    {Val, []}.

writer_bind({Val, SideVal}, MonadFun) ->
    {NewVal, NewSideVal} = MonadFun(Val),
    {NewVal, SideVal ++ NewSideVal}.

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questions?

---

A brief digression, function composition

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Result = g(f(X)).

NOTE: we can reason about this

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Composition is associative

(g ∘ f)(x) = g(f(x)) 

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Let's write comp in Erlang

comp(A, B) ->
    fun(Input) ->
        A(B(Input))
    end.

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Now let's use it,

(comp(fun addOne/1, fun multiplyTwo/1))(5) %% -> 11

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Functions aren't just abstractions, we've generalized them.

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Sometimes we have a domain-specific idea of how to compose data or computation. This is a monad.

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Return the first 'failure', otherwise keep going

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[fun thingOne/1,
 fun thingTwo/1,
 fun thingThree/1].

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But here's what we do

doThatThing() ->
    case partOne() of
        {ok, Result1} ->
            case partTwo(Result1) of
                {ok, Result2} ->
                    {ok, 'wow_you_followed_this_far?'};
                {error, _Reason2}=Reason2 ->
                    Reason2
            end;
        {error, _Reason1}=Reason1 ->
            Reason1
    end.

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In programming, a concrete monad implements the monad 'interface'

bind
return

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bind defines how your data or compuation composes.

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return takes a non-monadic value and places it inside the monad

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For our failure monad, we might define bind like this:

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bind({ok, X}, NextFun) ->
    NextFun(X);
bind({error, _Reason}=Reason, _NextFun) ->
    Reason.

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return(Val) ->
    {ok, Val}.

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There are actually two other monad functions, but they're not as important:

>>
fail

[Note: writer monad for timings?]

Is there a video of the talk anywhere?