Semantics, Logics, and Calculi pp 1-32
Effect Systems Revisited—Control-Flow Algebra and Semantics
Effect systems were originally conceived as an inference-based program analysis to capture program behaviour—as a set of (representations of) effects. Two orthogonal developments have since happened. First, motivated by static analysis, effects were generalised to values in an algebra, to better model control flow (e.g. for may/must analyses and concurrency). Second, motivated by semantic questions, the syntactic notion of set- (or semilattice-) based effect system was linked to the semantic notion of monads and more recently to graded monads which give a more precise semantic account of effects.
We give a lightweight tutorial explanation of the concepts involved in these two threads and then unify them via the notion of an effect-directed semantics for a control-flow algebra of effects. For the case of effectful programming with sequencing, alternation and parallelism—illustrated with music—we identify a form of graded joinads as the appropriate structure for unifying effect analysis and semantics.