How do I determine the extension(s) associated with a MIME type in PHP?

Not built-in, but it's not terribly hard to roll your own:

function system_extension_mime_types() {
    # Returns the system MIME type mapping of extensions to MIME types, as defined in /etc/mime.types.
    $out = array();
    $file = fopen('/etc/mime.types', 'r');
    while(($line = fgets($file)) !== false) {
        $line = trim(preg_replace('/#.*/', '', $line));
        if(!$line)
            continue;
        $parts = preg_split('/s+/', $line);
        if(count($parts) == 1)
            continue;
        $type = array_shift($parts);
        foreach($parts as $part)
            $out[$part] = $type;
    }
    fclose($file);
    return $out;
}

function system_extension_mime_type($file) {
    # Returns the system MIME type (as defined in /etc/mime.types) for the filename specified.
    #
    # $file - the filename to examine
    static $types;
    if(!isset($types))
        $types = system_extension_mime_types();
    $ext = pathinfo($file, PATHINFO_EXTENSION);
    if(!$ext)
        $ext = $file;
    $ext = strtolower($ext);
    return isset($types[$ext]) ? $types[$ext] : null;
}

function system_mime_type_extensions() {
    # Returns the system MIME type mapping of MIME types to extensions, as defined in /etc/mime.types (considering the first
    # extension listed to be canonical).
    $out = array();
    $file = fopen('/etc/mime.types', 'r');
    while(($line = fgets($file)) !== false) {
        $line = trim(preg_replace('/#.*/', '', $line));
        if(!$line)
            continue;
        $parts = preg_split('/s+/', $line);
        if(count($parts) == 1)
            continue;
        $type = array_shift($parts);
        if(!isset($out[$type]))
            $out[$type] = array_shift($parts);
    }
    fclose($file);
    return $out;
}

function system_mime_type_extension($type) {
    # Returns the canonical file extension for the MIME type specified, as defined in /etc/mime.types (considering the first
    # extension listed to be canonical).
    #
    # $type - the MIME type
    static $exts;
    if(!isset($exts))
        $exts = system_mime_type_extensions();
    return isset($exts[$type]) ? $exts[$type] : null;
}

I know this works for zip files, but I'm not too sure about xlsx files. It's worth a try:

To list the files in a zip archive:

$zip = new ZipArchive;
$res = $zip->open('test.zip');
if ($res === TRUE) {
    for ($i=0; $i<$zip->numFiles; $i++) {
        print_r($zip->statIndex($i));
    }
    $zip->close();
} else {
    echo 'failed, code:' . $res;
}

This will print all the files like this:

Array
(
    [name] => file.png
    [index] => 2
    [crc] => -485783131
    [size] => 1486337
    [mtime] => 1311209860
    [comp_size] => 1484832
    [comp_method] => 8
)

As you can see here, it gives the size and the comp_size for each archive. If it is an archive bomb, the ratio between these two numbers will be astronomical. You could simply put a limit of however many megabytes you want the maximum decompressed file size and if it exceeds that amount, skip that file and give an error message back to the user, else proceed with your extraction. See the manual for more information.

This technique works well for me:

if (-not ([System.Management.Automation.PSTypeName]'MyClass').Type)
{
    Add-Type -TypeDefinition 'public class MyClass { }'
}

• The type name can be enclosed in quotes 'MyClass', square brackets [MyClass], or both '[MyClass]' (v3+ only).
• The type name lookup is not case-sensitive.
• You must use the full name of the type, unless it is part of the System namespace (e.g. [System.DateTime] can be looked up via 'DateTime', but [System.Reflection.Assembly] cannot be looked up via 'Assembly').
• I've only tested this in Win8.1; PowerShell v2, v3, v4.

Internally, the PSTypeName class calls the LanguagePrimitives.ConvertStringToType() method which handles the heavy lifting. It caches the lookup string when successful, so additional lookups are faster.

I have not confirmed whether or not any exceptions are thrown internally as mentioned by x0n and Justin D.