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Does it compile code on the iPad or does it use some online API like the other Haskell programs on the Apple App Store?

It compiles to a virtual machine, then interprets on the iPad. No internet connection is required.

This is allowed by Apple because no code is loaded from the net right?

Yes, interpreters are ok, but they must not execute downloadable code (including email imports and iTunes sync)

I read somewhere that it's ook if it is javascript executed with jscore; know if that is true? That would give slightly more leeway.

I think so. It is hard to disallow that without crippling the OS.