Vec and Option monads

main.rs

/// https://gist.github.com/edmundsmith/855fcf0cb35dd467c29a9350481f0ecf

struct Forall;

trait Unplug {
    type F;
    type A;
}

trait Plug<A> {
    type Result;
}

trait Functor: Unplug+Plug<<Self as Unplug>::A> {
    fn map<B, F>(self, f:F) -> <Self as Plug<B>>::Result
        where
            Self:Plug<B>,
            F:FnMut(<Self as Unplug>::A) -> B
    ;
}

trait Applicative: Functor {
    fn pure(s:<Self as Unplug>::A) -> Self;
    fn app<B, F>(
        self, f:<Self as Plug<F>>::Result,
    ) -> <Self as Plug<B>>::Result
        where
            F:FnMut(<Self as Unplug>::A) -> B + Clone,
            Self:Plug<F> + Plug<B> + Unplug,
            <Self as Plug<F>>::Result:
            Unplug<F=<Self as Unplug>::F,A=F> +
            Plug<F> +
            Clone,
            <Self as Unplug>::F:Plug<F>
    ;
}

trait Monad : Applicative {
    fn bind<F,B>(self, f:F) -> <Self as Plug<B>>::Result
        where
            Self:Plug<F>+Plug<B>,
            F:FnMut(<Self as Unplug>::A) ->
            <Self as Plug<B>>::Result + Clone
    ;
}

// --------------

impl<A,B> Plug<A> for Vec<B> {
    type Result = Vec<A>;
}

impl<A> Unplug for Vec<A> {
    type F=Vec<Forall>;
    type A=A;
}

impl<A> Functor for Vec<A> {
    fn map<B,F>(self, f:F) -> <Self as Plug<B>>::Result
        where
            F:FnMut(<Self as Unplug>::A) -> B
    {
        self.into_iter().map(f).collect()
    }
}

impl<A:Clone> Applicative for Vec<A> {
    fn pure(a:A) -> Self {
        vec![a]
    }
    fn app<B, F>(
        self, fs:<Self as Plug<F>>::Result
    ) -> <Self as Plug<B>>::Result
        where
            F:FnMut(<Self as Unplug>::A) -> B + Clone,
            <Self as Plug<F>>::Result: Clone,
    {
            self.map(|x|
                fs.clone().map(|f| f.clone()(x.clone())))
                .into_iter()
                .map(|x|x)
                .flatten()
                .collect()
    }
}

impl<A:Clone> Monad for Vec<A> {
    fn bind<F,B>(self, mut f:F) ->
    <Self as Plug<B>>::Result
        where
            F:FnMut(<Self as Unplug>::A)
                -> <Self as Plug<B>>::Result
    {
            self
                .into_iter()
                .map(|x| f(x))
                .flatten().collect()
    }
}

fn vec_monad() {
    fn x2(x: i32) -> i32 { x * 2 }
    fn x20(x: i32) -> i32 { x * 20 }
    let v = vec![1, 2, 3].app(vec![x2 as fn(i32) -> i32, x20]).bind(|x| vec![x + 100]);
    println!("{:?}", v);
}

impl<A, B> Plug<B> for Option<A> {
    type Result = Option<B>;
}

impl<A> Unplug for Option<A> {
    type F = Option<Forall>;
    type A = A;
}

impl<A> Functor for Option<A> {
    fn map<B,F>(self, mut f:F) -> <Self as Plug<B>>::Result
        where
            F:FnMut(<Self as Unplug>::A) -> B
    {
        match self {
            Some(a) => Some(f(a)),
            None => None,
        }
    }
}

impl<A> Applicative for Option<A> {
    fn pure(a: Self::A) -> Self {
        Some(a)
    }

    fn app<B, F>(
        self, fs:<Self as Plug<F>>::Result
    ) -> <Self as Plug<B>>::Result
        where
            F:FnMut(<Self as Unplug>::A) -> B,
    {
        match fs {
            Some(f) => self.map(f),
            None => None,
        }
    }
}

impl<A> Monad for Option<A> {
    fn bind<F,B>(self, mut f:F) ->
    <Self as Plug<B>>::Result
        where
            F:FnMut(<Self as Unplug>::A)
                -> <Self as Plug<B>>::Result
    {
        match self {
            Some(a) => f(a),
            None => None,
        }
    }
}

fn option_monad() {
    let v = Some(1).bind(|x| Some(x * 2)).app(Some(|x| x + 1));
    println!("{:?}", v);
}

fn main() {
    vec_monad();
    option_monad();
}

Why can't we define app as

impl<A:Clone> Applicative for Option<A> {
    fn pure(a: Self::A) -> Self {
        Some(a)
    }

    fn app<B, F>(
        self, fs:<Self as Plug<F>>::Result
    ) -> <Self as Plug<B>>::Result
        where
            F:FnMut(<Self as Unplug>::A) -> B + Clone,
            <Self as Plug<F>>::Result: Clone,
    {
         match fs {
             Some(f) => self.fmap(f),
             None => None,
          }
    }
}

Because I, being a lazy ass, instead of thinking hard about it, just applied an ancient technique to the original Edmund's code, known as copy-paste-fix-compile loop. Thanks for the suggestion, now this pile of crap looks a bit nicer 😄

I'm doing this for my Category Class: https://github.com/GrayJack/gat
Where I'm implementing those thinks in Rust.

I had some headache implementing them, googling about it I found the Edmund's code.
If you want to, you can check it out my impl for Option, Result, Vec and LinkedList, but it lacks Monads