Not by equations alone: Reasoning with extensible effects

Abstract The challenge of reasoning about programs with (multiple) effects such as mutation, jumps, or IO dates back to the inception of program semantics in the works of Strachey and Landin. Using monads to represent individual effects and the associated equational laws to reason about them proved exceptionally effective. Even then it is not always clear what laws are to be associated with a monad—for a good reason, as we …