Probabilistic Imperative Programming: a Rigorous Approach

Recent work has extended Kozen's probabilistic semantics 8, 9] to include demonic nondeterminism both at the operational 5] and the logical level 12]. That makes it now possible in principle to treat probabilistic program development with the same standards of rigour that apply, when appropriate, to imperative programming 3]. In this report we treat several practical aspects of the new models, not discussed in their more theoretical presentations 5, 12]: a game-like interpretation of probabilistic and demonic choice acting jointly; the intuition behind the probabilistic`healthiness conditions' for predicate transformers, linking them to standard probability theory; and the use of predicate transformers to measure expected eeciency.