private function toComparableNames(array $types, array $symbolShortNames)
    {
        $normalized = array_map(
            function ($type) use ($symbolShortNames) {
                $type = strtolower($type);

                if (isset($symbolShortNames[$type])) {
                    return $symbolShortNames[$type];
                }

                return $type;
            },
            $types
        );

        sort($normalized);

        return $normalized;
    }