In order to build machine-checked proven-secure software, we need formal se curity policies that express what it means to be “secure.” We must then show that the semantics of our software matches the semantics of those policies. This requires formal semantics for both programs and policies. In this dissertation, we explore the semantics of effectful programs and the semantics of authorization policies. The most well-known class of effects are those that can be given semantics via a monad, though current research also focuses on those that can be given a semantics via a comonad. We compare three methods for combining these two popular options: one method requires extra semantic structure, whereas the other methods can be applied to any monadic and comonadic effects. If the extra semantic structure needed for the first method exists then the three semantics are equivalent. Otherwise, we show that the two remaining semantics correspond to strict and lazy interpretations of the effects. On the other side, we use authorization logics to express authorization policies. Authorization logics can be given semantics using either models or a proof system. We build a model theory for an authorization logic that more-closely expresses how authorization logics are used by systems than traditional models. We also build a proof system for an authorization logic that ensures that proofs of authorization respect information-security policies.