Maitar

Maitar is a rust library providing some functional programming constructions like:

• Semigroup,
• Monoid,
• Functor,
• Applicative;
• Bind and
• Monad

Some incarnations are available like:

• Identity,
• Option,
• Result,
• Either
• Vector,
• Reader and
• Writer.

Note: The curried version is not optimal since it relies on Boxed polymorphic functions and then dynamic dispatch.

Philosophy

In Rust, we can specify abstract types in a trait, i.e. Higher-Kinded Polymorphism (HKP for short). Therefore, such types are inhabited by trait implementations.

HKP

We propose a simple basic trait HKP where an abstract type T is defined. An essential remark about this type is its capability to accept a parametric type. This is important if we want to propose constructions coming from the category theory.

pub trait HKP {
    type T<A>;
}

Functor specification

The functional approach has been chosen to prohibit the use of self. There is no specific relationship between the structure that will implement the trait and the implementation of the trait.

use crate::core::hkp::HKP;

pub trait Functor: HKP {
    fn map<A, B, MAP>(f: MAP, ma: Self::T<A>) -> Self::T<B>
        where
            MAP: Fn(A) -> B;
}

Infix trait

The Infix trait provides the capability to use data with the Rust idiomatic approach thanks to the self first method parameter.

pub mod infix {
    use crate::specs::functor::Functor as Api;

    pub trait Functor<A> {
        type This: Api;
        type T<B>: Functor<B>;

        fn hkp_to_self<B>(a: <Self::This as HKP>::T<B>) -> Self::T<B>;

        fn self_to_hkp(self) -> <Self::This as HKP>::T<A>;

        fn map<B, MAP>(self, f: MAP) -> Self::T<B>
            where
                MAP: Fn(A) -> B,
                Self: Sized,
        {
            Self::hkp_to_self(Self::This::map(f, self.to_hkp()))
        }
    }
}

Functor usage

fn generalized_increment<F: Functor>(ma: F::T<i32>) -> F::T<i32> {
    F::map(|a| a + 1, ma)
}

Functor implementation

Implementation requires an initial definition of the basic structure. This can be seen as the ability to use or open one type of module, and nothing else. For Option we introduce OptionK and this one should implement HKP.

pub struct OptionK;

impl HKP for OptionK {
    type T<A> = Option<A>;
}

Then we can implement Option functor using the underlying map implementation.

impl Functor for OptionK {
    fn map<A, B, MAP>(f: MAP, ma: Self::T<A>) -> Self::T<B>
        where
            MAP: Fn(A) -> B,
    {
        ma.map(f)
    }
}

Infix implementation

impl<A> Functor<A> for Option<A> {
    type This = OptionK;
    type T<B> = Option<B>;

    fn from_hkp<B>(a: <Self::This as HKP>::T<B>) -> Self::T<B> {
        a
    }

    fn to_hkp(self) -> <Self::This as HKP>::T<A> {
        self
    }
}

Note: In reality, such material is done once per implementation thanks to the Transform trait.

Why Maitar?

See Maitar definition for more information. Composition is the main idea behind this word.

Other approaches and propositions

• Idiomatic monads in Rust
• Algar project

License

MIT License

Copyright (c) 2023 Didier Plaindoux

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