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// Declaration
BOOL APCheckIfAppInstalled(NSString *bundleIdentifier); // Bundle identifier (eg. com.apple.mobilesafari) used to track apps

// Implementation

BOOL APCheckIfAppInstalled(NSString *bundleIdentifier)
{
	static NSString *const cacheFileName = @"com.apple.mobile.installation.plist";
	NSString *relativeCachePath = [[@"Library" stringByAppendingPathComponent: @"Caches"] stringByAppendingPathComponent: cacheFileName];
	NSDictionary *cacheDict = nil;
	NSString *path = nil;
	// Loop through all possible paths the cache could be in
	for (short i = 0; 1; i++)
	{
	
		switch (i) {
	case 0: // Jailbroken apps will find the cache here; their home directory is /var/mobile
		path = [NSHomeDirectory() stringByAppendingPathComponent: relativeCachePath];
		break;
	case 1: // App Store apps and Simulator will find the cache here; home (/var/mobile/) is 2 directories above sandbox folder
		path = [[NSHomeDirectory() stringByAppendingPathComponent: @"../.."] stringByAppendingPathComponent: relativeCachePath];
		break;
	case 2: // If the app is anywhere else, default to hardcoded /var/mobile/
		path = [@"/var/mobile" stringByAppendingPathComponent: relativeCachePath];
		break;
	default: // Cache not found (loop not broken)
		return NO;
		break; }
		
		BOOL isDir = NO;
		if ([[NSFileManager defaultManager] fileExistsAtPath: path isDirectory: &isDir] && !isDir) // Ensure that file exists
			cacheDict = [NSDictionary dictionaryWithContentsOfFile: path];
		
		if (cacheDict) // If cache is loaded, then break the loop. If the loop is not "broken," it will return NO later (default: case)
			break;
	}
	
	NSDictionary *system = [cacheDict objectForKey: @"System"]; // First check all system (jailbroken) apps
	if ([system objectForKey: bundleIdentifier]) return YES;
	NSDictionary *user = [cacheDict objectForKey: @"User"]; // Then all the user (App Store /var/mobile/Applications) apps
	if ([user objectForKey: bundleIdentifier]) return YES;
	
	// If nothing returned YES already, we'll return NO now
	return NO;
}
Here is an example of this, assuming that your app is named "yourselfmadeapp" and is an app in the app store. 
Code:
NSArray *bundles2Check = [NSArray arrayWithObjects: @"com.apple.mobilesafari", @"com.yourcompany.yourselfmadeapp", @"com.blahblah.nonexistent", nil];
for (NSString *identifier in bundles2Check)
	if (APCheckIfAppInstalled(identifier))
		NSLog(@"App installed: %@", identifier);
	else
		NSLog(@"App not installed: %@", identifier);