<?php
declare(strict_types=1);

// ((a, ...) -> z) -> a -> ... -> z
function curry(callable $f, ...$args) {
    return function (...$partialArgs) use ($f, $args) {
        return (function ($args) use ($f) {
            return \count($args) < (new \ReflectionFunction($f))->getNumberOfRequiredParameters()
                ? curry($f, ...$args)
                : $f(...$args);
        })(\array_merge($args, $partialArgs));
    };
}

interface Functor {
    // Functor F => (a -> b) -> F b
    public function map(callable $f)/*: Functor*/;
}

// Functor F => (a -> b) -> F a -> F b
function fmap(...$args) {
    return curry(function(callable $f, Functor $F) {
        return $F->map($f);
    })(...$args);
}

interface Applicative extends Functor {
    // Applicative F => a -> F a
    public static function pure($x)/*: Applicative*/;
    // Applicative F => F a -> F b
    public function ap(Applicative $F)/*: Applicative*/;
}

// Applicative A => A (a -> b) -> A a -> A b
function ap(...$args) {
    return curry(function(Applicative $F1, Applicative $F2) {
        return $F1->ap($F2);
    })(...$args);
}

// Applicative A => (a -> b -> c) -> A a -> A b -> A c
function liftA2(...$args) {
    return curry(function (callable $f, Applicative $F1, Applicative $F2) {
        return $F1->map($f)->ap($F2);
    })(...$args);
}

interface Monad extends Applicative {
    // Monad M => M (M a) -> M a
    public function join()/*: Monad*/;
    // Monad M => (a -> M b) -> M b
    public function bind(callable $f)/*: Monad*/;
}

// Monad M => (a -> M b) -> M a -> M b
function bind(...$args) {
    return curry(function (callable $f, Monad $M) {
        return $M->map($f)->join();
    })(...$args);
}

// ====

class Maybe implements Functor, Applicative, Monad
{
    /** @var bool */
    private $isJust;

    /** @var mixed|null */
    private $value;

    public static function just($value): Maybe
    {
        return new self(true, $value);
    }

    public static function nothing(): Maybe
    {
        return new self(false);
    }

    public function match(callable $just, callable $nothing)
    {
        return $this->isJust
            ? $just($this->value)
            : $nothing();
    }

    public function map(callable $f): Maybe
    {
        return $this->isJust
            ? self::just($f($this->value))
            : self::nothing();
    }

    public static function pure($value): Maybe
    {
        return self::just($value);
    }

    public function ap(Applicative $F): Maybe
    {
        return $F->map($this->value);
    }

    public function join(): Maybe
    {
        return $this->isJust
            ? $this->value
            : self::nothing();
    }

    public function bind(callable $f): Maybe
    {
        return $this->map($f)->join();
    }

    private function __construct(bool $isJust, $value = null)
    {
        $this->isJust = $isJust;
        $this->value = $value;
    }
}

// a -> Maybe a -> a
function fromMaybe(...$args) {
    return curry(function ($default, Maybe $a) {
        return $a->match(
            function ($value) { return $value; },
            function () use ($default) { return $default; }
        );
    })(...$args);
}

// b -> (a -> b) -> Maybe a -> b
function maybe(...$args) {
    return curry(function($default, callable $f, Maybe $a) {
        return $a->match(
            function ($value) use ($f) { return $f($value); },
            function () use ($default) { return $default; }
        );
    })(...$args);
}

// ====

// example 1
function odd(int $x): bool { return $x % 2 === 1; }
assert(true === maybe('nope', 'odd', Maybe::just(1)));
assert(false === maybe('nope', 'odd', Maybe::just(2)));
assert('nope' === maybe('nope', 'odd', Maybe::nothing()));

// example 2
function add(...$args) {
    return curry(function (int $x, int $y): int {
        return $x + $y;
    })(...$args);
}
assert(3 === fromMaybe('nope', liftA2('add', Maybe::just(1), Maybe::just(2))));
assert('nope' === fromMaybe('nope', liftA2('add', Maybe::just(1), Maybe::nothing())));

// example 3
function divByX(int $x): Maybe/*int*/ {
    return $x !== 0
        ? Maybe::just(10 / $x)
        : Maybe::nothing();
}
assert(5 === fromMaybe('nope', bind('divByX', Maybe::just(2))));
assert('nope' === fromMaybe('nope', bind('divByX', Maybe::just(0))));
assert('nope' === fromMaybe('nope', bind('divByX', Maybe::nothing())));

// example 4
class X {
    private $a;

    public function __construct(Maybe/*int*/ $a)
    {
        $this->a = $a;
    }

    public function getA(): Maybe/*int*/
    {
        return $this->a;
    }
}
assert(1 === fromMaybe('nope', (new X(Maybe::just(1)))->getA()));
assert('nope' === fromMaybe('nope', (new X(Maybe::nothing()))->getA()));