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An example of how compose() unfolds
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<?php | |
//////////////////////////////////////////////////////////////// | |
// compose = foldl (.) id | |
//////////////////////////////////////////////////////////////// | |
function curry(callable $fn, ...$args): \Closure { | |
return function (...$partialArgs) use ($fn, $args) { | |
$args = array_merge($args, $partialArgs); | |
$numRequiredArgs = (new \ReflectionFunction($fn)) | |
->getNumberOfRequiredParameters(); | |
return count($args) < $numRequiredArgs | |
? curry($fn, ...$args) | |
: $fn(...$args); | |
}; | |
} | |
// id :: a -> a | |
$id = function ($x) { return $x; }; | |
// o :: (b -> c) -> (a -> b) -> (a -> c) | |
$o = function (callable $g, callable $f): \Closure { | |
return function ($x) use ($g, $f) { | |
return $g($f($x)); | |
}; | |
}; | |
// foldl :: (a -> b -> a) -> a -> [b] -> a | |
$foldl = curry(function (callable $f, $acc, $head, ...$tail) { | |
$list = count($tail) > 0 | |
? array_merge([$head], $tail) | |
: $head; | |
return array_reduce($list, $f, $acc); | |
}); | |
// compose :: [a -> a] -> (a -> a) | |
$compose = $foldl($o, $id); | |
//////////////////////////////////////////////////////////////// | |
// An example of how compose() unfolds | |
//////////////////////////////////////////////////////////////// | |
// 3 simple functions that prepend their name to a string | |
$f = function ($s) { return 'f' . $s; }; | |
$g = function ($s) { return 'g' . $s; }; | |
$h = function ($s) { return 'h' . $s; }; | |
// Data travels through the composed functions from right to left | |
assert( $h($g($f(''))) === $compose($h, $g, $f)('') ); // 'hgf' === 'hgf' | |
// Some simple algebraic substitutions | |
assert( $compose($h, $g, $f)('') === $foldl($o, $id)($h, $g, $f)('') ); | |
assert( $foldl($o, $id)($h, $g, $f)('') === $foldl($o, $id, [$h, $g, $f])('') ); | |
assert( $foldl($o, $id, [$h, $g, $f])('') === $o($o($o($id, $h), $g), $f)('') ); | |
// Expand step 1: $id_h = $o($id, $h) | |
$id_h = function ($x) { | |
$id = function ($x) { return $x; }; | |
$h = function ($s) { return 'h'.$s; }; | |
return $id($h($x)); | |
}; | |
assert( $id_h('') === $o($id, $h)('') ); | |
// Expand step 2: $id_h_g = $o($id_h, $g) = $o($o($id, $h), $g) | |
$id_h_g = function ($x) { | |
$id_h = function ($x) { | |
$id = function ($x) { return $x; }; | |
$h = function ($s) { return 'h'.$s; }; | |
return $id($h($x)); | |
}; | |
$g = function ($s) { return 'g'.$s; }; | |
return $id_h($g($x)); | |
}; | |
assert( $id_h_g('') === $o($id_h, $g)('') ); | |
// Expand step 3: $id_h_g_f = $o($id_h_g, $f) = $o($o($o($id, $h), $g), $f) | |
$id_h_g_f = function ($x) { | |
$id_h_g = function ($x) { | |
$id_h = function ($x) { | |
$id = function ($x) { return $x; }; | |
$h = function ($s) { return 'h'.$s; }; | |
return $id($h($x)); | |
}; | |
$g = function ($s) { return 'g'.$s; }; | |
return $id_h($g($x)); | |
}; | |
$f = function ($s) { return 'f'.$s; }; | |
return $id_h_g($f($x)); | |
}; | |
assert($o($id_h_g, $f)('') === $id_h_g_f('')); | |
// Prove that $id_h_g_f is our original composition | |
assert( $id_h_g_f('') === $compose($h, $g, $f)('') ); |
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