It’s not official confirmation from Microsoft but Nvidia’s CEO, Jen-Hsun Huang, is claiming so:
he believes that apps written for Windows Phone 7 will run on Windows 8, which is an operating system designed for both PCs and tablets.
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Commentary: Windows 8, which is the next major operating system of Microsoft for desktop and notebook computers, will feature some interesting things like support for for touch tablets and ability to run also on ARM processors (that many manufacturers, including Nvidia, is licensing), not only on x86 processors (that are made mainly by Intel and AMD). However since Windows Phone 7 apps (XNA, Silverlight) are based on .NET then inherently they are processor independent so would be able to run even on computers with x86 processors.
… and since Windows 8 uses similar tiles like Windows Phone 7, one could even say: buy Windows Phone 7 now and get a glimpse into the future of desktop Windows OS from Microsoft!