The full version of this information is available.
In this note I show how to give a continuation semantics to an extension of Parigot's mu-calculus from which there follows a simple equational presentation and rewrite semantics. Though I have had the semantics since quite a time the idea to use it for extending mu-calculus and deriving a nice rewrite semantics for it from this semantics came to me during a talk of Philippe Audebaud during his talk at the Scott conference in Darmstadt this spring/summer. I don't precisely remember his presentation, so I cannot compare what's below with his work; but it looks simpler to me than what I remember to have seen in the talk. Maybe Philippe has some further equations to guarantee confluence or things like that. I personally haven't checked confluence myself. But it is clear that the machine computations of an extended Krivine's machine are reflected one-to-one by rewrite derivations in the calculus below. Anyway the semantic justification of the rewrite rules may be of interest and facilitate understanding of the calculus.