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We consider an extension QPDL of Segerberg-Pratt's Propositional Dynamic Logic PDL, with program quantification, and study its expressive power and complexity. A mild form of program quantification is obtained in the calculus @mPDL, extending PDL with recursive procedures (i.e. context free programs), which is known to be @P"1^1-complete. The unrestricted program quantification we consider leads to complexity equivalent to that of second-order logic (and second-order arithmetic), i.e. outside the analytical hierarchy. However, the deterministic variant of QPDL has complexity @P"1^1.