On continuation-passing transformations and expected cost analysis

We define a continuation-passing style (CPS) translation for typed ?-calculus with probabilistic choice, unbounded recursion, and tick operator — modeling cost. The target language is (non-probabilistic) ?-calculus, enriched type of extended positive reals fixpoint operator. then show that applying the CPS transform an expression M to continuation ? v . 0 yields expected cost also introduce formal system higher-order logic, called EHOL, prove it sound, can derive tight upper bounds on classic examples, including Coupon Collector Random Walk. Moreover, we relate our Kaminski et al.’s ert-calculus, showing latter be recovered by (a generalization of) embedding imperative programs into ?-calculus. Finally, used compute pre-expectations reason about almost sure termination.