kotlin-monads

An attempt to implement monads in Kotlin, deeply inspired by Haskell monads, but restricted within the Kotlin type system.

The monad type

Monadic types are represented by the Monad<M, T> interface, where M should be the type of the implementation with only its T star-projected. Examples: Maybe<T> : Monad<Maybe<*>, T>, State<S, T> : Monad<State<S, *>, T>.

With Monad defined in this way, we are almost able to say in terms of the Kotlin type system that a function returns the same Monad implementation but with a different type argument R instead of T:

fun <T, R, M : Monad<M, *>> Monad<M, T>.map(f: (T) -> R) = bind { returns(f(it)) }

val m = just(3).map { it * 2 } as Maybe

We still need the downcast as Maybe, but at least it's checked.

Usage

Add as a dependency:

repositories {
    ...
    maven { url 'https://jitpack.io' }
}

dependencies {
    ...
    compile 'com.github.h0tk3y:kotlin-monads:0.5'
}

See the usage examples in tests.

How to implement a monad

Monad<M, T> is defined as follows:

interface Return<M> {
    fun <T> returns(t: T): Monad<M, T>
}

interface Monad<This, out T> {
    infix fun <R> bind(f: Return<This>.(T) -> Monad<This, R>): Monad<This, R>
}

The monad implementation should only provide one function bind (Haskell: >>=), no separate return is there, instead, if you look at the signature of bind, you'll see that the function to bind with is f: Return<This>.(T) -> Monad<This, R>. It means that a Monad<M, T> implementation should provide the Return<M> as well and pass it to f each time, so that inside f its returns could be used:

just(3) bind { returns(it * it) }

There seems to be no direct equivalent to Haskell return, which could be used outside any context like bind blocks. Outside the bind blocks, you should either wrap the values into your monads manually or require a Return<M>, which can wrap T into Monad<M, T> for you.

Mind the monad laws. A correct monad implementation follows these three rules (rephrased in terms of kotlin-monads):

1. Left identity: returns(x) bind { f(it) } should be equivalent to f(x)

2. Right identity: m bind { returns(it) } should be equivalent to m

3. Associativity: m bind { f(it) } bind { g(it) } should be equivalent to m bind { f(it) bind { g(it) } }

Also, it's good to make the return type of bind narrower, e.g. bind of Maybe<T> would rather return Maybe<R> than Monad<Maybe<*>, R>, it allows not to cast the result of a bind called on a known monad type.

val m = monadListOf(1, 2, 3) bind { monadListOf("$it", "$it") } // already `MonadList<String>`, no need to cast

Example implementation:

sealed class Maybe<out T> : Monad<Maybe<*>, T> {
    class Just<T>(val value: T) : Maybe<T>()
    class None : Maybe<Nothing>()

    override fun <R> bind(f: Binder<Maybe<*>, T, R>): Maybe<R> = when (this) {
        is Just -> f(MaybeReturn, value) as Maybe
        is None -> None()
    }
}

object MaybeReturn : Return<Maybe<*>> {
    override fun <T> returns(t: T) = Maybe.Just(t)
}

Monads implementations bundled

• Maybe<T>
• Either<F, T>
• MonadList<T>
• Reader<E, T>
• Writer<T> (no monoid for now, just String)
• State<S, T>

Do notation

With the power of Kotlin coroutines, we can even have an equivalent of the Haskell do notation:

Simple example that performs a monadic list nondeterministic expansion:

val m = doReturning(MonadListReturn) {
    val x = bind(monadListOf(1, 2, 3))
    val y = bind(monadListOf(x, x + 1))
    monadListOf(y, x * y)
}

assertEquals(monadListOf(1, 1, 2, 2, 2, 4, 3, 6, 3, 9, 4, 12), m)

Or applied to an existing monad for convenience:

val m = monadListOf(1, 2, 3).bindDo { x ->
    val y = bind(monadListOf(x, x + 1))
    monadListOf(y, x * y)
}

This is effectively equivalent to the following code written with only simple bind:

val m = monadListOf(1, 2, 3).bind { x ->
    monadListOf(x, x + 1).bind { y -> 
        monadList(y, x * y)
    }
}

Note that, with simple bind, each transformation requires another inner scope if it uses the variables bound outside, which would lead to some kind of callback hell. This problem is effectively solved using the Kotlin coroutines: the compiler performs the CPS transformation of a plain code block under the hood. However, this coroutines use case is somewhat out of conventions: it might resume the same continuation several times and uses quite a dirty hack to do that.

The result type parameter (R in Monad<M, R>) is usually inferred, and the compiler controls the flow inside a do block, but still you need to downcast the Monad<M, R> to your actual monad type (e.g. Monad<Maybe<*>, R> to Maybe), because the type system doesn't seem to allow this to be done automatically (if you know a way, please tell me).

Be careful with mutable state in do blocks, since all continuation calls will share it, sometimes resulting into counter-intuitive results:

 val m = doReturning(MonadListReturn) {
     for (i in 1..10)
         bind(monadListOf(0, 0))
     returns(0)
 } as MonadList

One would expect 1024 items here, but the result only contains 11! That's because i is mutable and is shared between all the calls that bind makes.