These higher-level app development stacks are support F#:
Xamarin Mobile - Use F# to develop for iOS, Android, Mac and Windows development
WebSharper - Can be used for cross-tier client/server HTML5 development and more
Windows Store - You can use F# Portable libraries as components in Windows 8 and Windows 8 Phone applications
MonoGame is an open implementation of a cross-platform gaming framework originally based on the XNA 4 framework design. The goal of the project is to allow XNA developers on Xbox 360, Windows & Windows Phone to port their games to the iOS, Android, Mac OS X, Linux, Windows 8 Metro, and PlayStation Mobile.
Xamarin provide game and app development tools for Android, iOS and other platforms. They support F# as part of their stack.
Some resources for game development with F# and Xamarin tools:
Resources specific to iOS:
You will need to familiarize yourself with Xamarin C# iOS programming and will likely need some knowledge of Objective-C as well. The Xamarin Developer Center contains the primary documentation.
Sample iOS games and apps are available from Neil Danson’s repository:
F# is ideal for the sever-side of game and app development. For example, F# is used on the server-side of one of the largest Facebook social games, as described in this interview.
Microsoft XNA is a set of tools with a managed runtime environment that facilitates video game development and management.