PHPでチャーチ数を使ってフィボナッチ数列

fib.php

<?php declare(strict_types=1);

global $succ;
$succ = function ($n) {
    return function ($f) use ($n) {
        return function ($x) use ($n, $f) {
            // ^n. ^f. ^x. f (n f x)
            return $f($n($f)($x));
        };
    };
};

global $plus;
$plus = function ($n) {
    return function ($m) use ($n) {
        return function ($f) use ($n, $m) {
            return function ($x) use ($n, $m, $f) {
                // ^n. ^m. ^f. ^x. n f (m f x)
                return $n($f)($m($f)($x));
            };
        };
    };
};

$fib = function ($n): \Closure {
    // ^n. n (^p. ^f. p (^a. ^b. f (plus a b) a))
    return $n(
        function ($p) {
            return function ($f) use ($p) {
                // p (^a. ^b. f (plus a b) a)
                return $p(function ($a) use ($f) {
                    return function ($b) use ($f, $a) {
                        global $plus;
                        // f (plus a b) a
                        return $f($plus($a)($b))($a);
                    };
                });
            };
        }
    )
    // (^f. f 1 0)
    (function ($f) { return $f(n(1))(n(0)); })
    // (^a. ^b. b)
    (function ($a) {
        return function ($b) use ($a) {
            return $b;
        };
    });
};


assert(0 === toInt(n(0)));
assert(1 === toInt(n(1)));
assert(2 === toInt(n(2)));
assert(0 === toInt($plus(n(0))(n(0))));
assert(1 === toInt($plus(n(0))(n(1))));
assert(2 === toInt($plus(n(1))(n(1))));

assert( 1 === toInt($fib(n(1))));
assert( 1 === toInt($fib(n(2))));
assert( 2 === toInt($fib(n(3))));
assert( 3 === toInt($fib(n(4))));
assert( 5 === toInt($fib(n(5))));
assert( 8 === toInt($fib(n(6))));
assert(13 === toInt($fib(n(7))));
assert(21 === toInt($fib(n(8))));

echo "ok", PHP_EOL;
exit;

function toInt(\Closure $f)
{
    //var_dump($f);
    return $f(function ($n) { return $n + 1; })(0);
}

function n(int $n)
{
    global $succ;
    static $num = [];
    if (empty($num)) {
        $num[0] = function ($s) { return function ($z) use ($s) { return $z; }; };
        $num[1] = function ($s) { return function ($z) use ($s) { return $s($z); }; };
    }

    if (!isset($num[$n])) {
        $num[$n] = $succ(n($n - 1));
    }

    return $num[$n];
}