Smart Choices and the Selection Monad

Describing systems in terms of choices and their resulting costs rewards offers the promise freeing algorithm designers programmers from specifying how those should be made; implementations, can realized by optimization techniques and, increasingly, machine-learning methods. We study this approach a programming-language perspective. define two small languages that support decision-making abstractions: one with rewards, other additionally probabilities. give both operational denotational semantics. In case second language we consider three semantics, varying degrees correlation between possible program values expected rewards. The semantics combine usual standard constructs over spaces execution strategies. which are compositional, rely on selection monad, to handle choice, augmented an auxiliary monad effects, such as or probability. establish adequacy theorems coincide all cases. also prove full abstraction at base types, notions observation probabilistic corresponding various correlation. present axioms for choice combined probability, establishing completeness types without