function.php

<?php
return (function() {
    $id = function($x) use(&$id) {
        return $x;
    };
    $const = function($x) use(&$const, &$id) {
        return function($_) use(&$const, &$id, &$x) {
            return $x;
        };
    };
    $compose = function($f) use(&$compose, &$const, &$id) {
        return function($g) use(&$compose, &$const, &$f, &$id) {
            return function($x) use(&$compose, &$const, &$f, &$g, &$id) {
                return ($f)(($g)($x));
            };
        };
    };
    $category = (object)[
        'compose' => $compose,
        'compose-id' => $id,
    ];
    $semigroup = (object)[
        'append' => function($f) use(&$category, &$compose, &$const, &$id, &$semigroup) {
            return function($g) use(&$category, &$compose, &$const, &$f, &$id, &$semigroup) {
                return (($compose)($f))($g);
            };
        },
    ];
    $monoid = (object)[
        'append' => ($semigroup)->append,
        'append-id' => $id,
    ];
    return (object)[
        'category' => $category,
        'compose' => $compose,
        'const' => $const,
        'id' => $id,
        'monoid' => $monoid,
        'semigroup' => $semigroup,
    ];
})();