lifted 0.1.0

Higher-kinded types in Rust.
Documentation 
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//! The higher-kinded trait of a `Monad`.

use super::applicative::Applicative;
use super::*;
use super::types::*;

pub trait Monad: Applicative {
    fn bind<A, B, F: Fn(A) -> K1<Self, B>>(a: K1<Self, A>, f: F) -> K1<Self, B>;
}

impl Monad for OptionC {
    fn bind<A, B, G: Fn(A) -> K1<Self, B>>(a: K1<Self, A>, g: G) -> K1<Self, B> {
        match a.into_inner() {
            Some(x) => g(x),
            None => OptionC::new(None),
        }
    }
}

impl Monad for VecC {
    fn bind<A, B, G: Fn(A) -> K1<Self, B>>(a: K1<Self, A>, g: G) -> K1<Self, B> {
        Self::new(
            a.into_inner()
                .into_iter()
                .flat_map(move |x| g(x).into_inner())
                .collect()
        )
    }
}

#[cfg(test)]
mod test {
    use super::*;

    fn check_law_left_identity<M: Monad, A, B, F>(a: A, f: F)
    where
        M: Kind1<B>,
        A: Clone,
        F: Fn(A) -> K1<M, B> + Clone,
        K1<M, B>: PartialEq + Clone + core::fmt::Debug,
    {
        let return_bind = M::bind(M::pure(a.clone()), f.clone());
        let just_call = f(a);
        assert_eq!(return_bind, just_call);
    }

    fn check_law_right_identity<T: Clone, M: Monad>(m: K1<M, T>)
    where
        M: Kind1<T>,
        K1<M, T>: PartialEq + Clone + core::fmt::Debug,
    {
        let m_return = M::bind(m.clone(), M::pure);
        assert_eq!(m_return, m);
    }

    fn check_law_associativity<A, B, C, M: Monad, F, G>(m: K1<M, A>, f: F, g: G)
    where
        M: Kind1<A> + Kind1<C>,
        K1<M, A>: Clone,
        K1<M, C>: PartialEq + Clone + core::fmt::Debug,
        F: Fn(A) -> K1<M, B> + Clone,
        G: Fn(B) -> K1<M, C> + Clone,
    {
        let left_first = M::bind(M::bind(m.clone(), f.clone()), g.clone());
        let right_first = M::bind(m, move |x| M::bind(f(x), g.clone()));
        assert_eq!(left_first, right_first);
    }

    #[test]
    fn option_monad_law_left_identity() {
        check_law_left_identity(42, |x| OptionC::new(Some(x + 1)));
    }

    #[test]
    fn option_monad_law_right_identity() {
        check_law_right_identity::<i32, _>(OptionC::new(None));
        check_law_right_identity(OptionC::new(Some(42)));
    }

    #[test]
    fn option_monad_law_associativity() {
        check_law_associativity(
            OptionC::new(Some(42)),
            |x| OptionC::new(Some(x + 1)),
            |x| OptionC::new(Some(x * 2)),
        );
        check_law_associativity::<i32, _, _, _, _, _>(
            OptionC::new(None),
            |x| OptionC::new(Some(x + 1)),
            |x| OptionC::new(Some(x * 2)),
        );
        check_law_associativity::<_, i32, _, _, _, _>(
            OptionC::new(Some(42)),
            |_| OptionC::new(None),
            |x| OptionC::new(Some(x * 2)),
        );
        check_law_associativity::<_, _, i32, _, _, _>(
            OptionC::new(Some(42)),
            |x| OptionC::new(Some(x + 1)),
            |_| OptionC::new(None),
        );
    }

    #[test]
    fn vec_monad_law_left_identity() {
        check_law_left_identity(42, |x| VecC::new(vec![x + 1]));
    }

    #[test]
    fn vec_monad_law_right_identity() {
        check_law_right_identity::<i32, _>(VecC::new(vec![]));
        check_law_right_identity(VecC::new(vec![42]));
    }

    #[test]
    fn vec_monad_law_associativity() {
        check_law_associativity(
            VecC::new(vec![42, 0]),
            |x| VecC::new(vec![x + 1, x - 1]),
            |x| VecC::new(vec![x * 2, x]),
        );
        check_law_associativity::<i32, _, _, _, _, _>(
            VecC::new(vec![]),
            |x| VecC::new(vec![x + 1, x - 1]),
            |x| VecC::new(vec![x * 2, x]),
        );
        check_law_associativity::<_, i32, _, _, _, _>(
            VecC::new(vec![42, 0]),
            |_| VecC::new(vec![]),
            |x| VecC::new(vec![x * 2, x]),
        );
        check_law_associativity::<_, _, i32, _, _, _>(
            VecC::new(vec![42, 0]),
            |x| VecC::new(vec![x + 1, x - 1]),
            |_| VecC::new(vec![]),
        );
    }
}