Xcode 4.1 can’t reinstall. App store says “installed”

Edited on 2016-02-02

Starting from iOS 6 SKStoreProductViewController class was introduced. You can link an app without leaving your app. Code snippet in Swift 3.x/2.x and Objective-C is here.

A SKStoreProductViewController object presents a store that allows the user to purchase other media from the App Store. For example, your app might display the store to allow the user to purchase another app.

From News and Announcement For Apple Developers.

Drive Customers Directly to Your App on the App Store with iTunes Links With iTunes links you can provide your customers with an easy way to access your apps on the App Store directly from your website or marketing campaigns. Creating an iTunes link is simple and can be made to direct customers to either a single app, all your apps, or to a specific app with your company name specified.

To send customers to a specific application: http://itunes.com/apps/appname

To send customers to a list of apps you have on the App Store: http://itunes.com/apps/developername

To send customers to a specific app with your company name included in the URL: http://itunes.com/apps/developername/appname

Additional notes:

You can replace http:// with itms:// or itms-apps:// to avoid redirects.

Please note that itms:// will send the user to the iTunes store and itms-apps:// with send them to the App Store!

For info on naming, see Apple QA1633:

https://developer.apple.com/library/content/qa/qa1633/_index.html.

Edit (as of January 2015):

itunes.com/apps links should be updated to appstore.com/apps. See QA1633 above, which has been updated. A new QA1629 suggests these steps and code for launching the store from an app:

1. Launch iTunes on your computer.
2. Search for the item you want to link to.
3. Right-click or control-click on the item's name in iTunes, then choose "Copy iTunes Store URL" from the pop-up menu.
4. In your application, create an NSURL object with the copied iTunes URL, then pass this object to UIApplication' s openURL: method to open your item in the App Store.

Sample code:

NSString *iTunesLink = @"itms://itunes.apple.com/app/apple-store/id375380948?mt=8";
[[UIApplication sharedApplication] openURL:[NSURL URLWithString:iTunesLink]];

iOS10+:

 [[UIApplication sharedApplication] openURL:[NSURL URLWithString:iTunesLink] options:@{} completionHandler:nil];

Swift 4.2

   let urlStr = "itms-apps://itunes.apple.com/app/apple-store/id375380948?mt=8"
    if #available(iOS 10.0, *) {
        UIApplication.shared.open(URL(string: urlStr)!, options: [:], completionHandler: nil)
        
    } else {
        UIApplication.shared.openURL(URL(string: urlStr)!)
    }

Just to explain further...

The App Store download had actually worked

What you saw when you looked at Xcode was your old install, because you had not yet run the installer at that point.

Just find the "XCode installer" in your applications folder and run that to complete the install.

It caught me out too.