Abstract

We present a theory of Gifford-style type-and-effect annotations, where effect annotations are sets of effects, such as memory accesses or exceptions. Our theory accounts for effect-dependent program transformations for functional-imperative languages, as used in optimising compilers. Generality is achieved by recourse to the theory of algebraic effects, a development of Moggi’s monadic theory of computational effects that emphasises the operations causing the effects at hand. The key observation is that annotation effects denote algebraic operations.

After presenting our general type-and-effect system and its semantics, we validate and generalise existing optimisations and add new ones. Our theory also suggests a classification of these optimisations into three classes, structural, local, and global: structural optimisations always hold; local ones depend on the effect theory at hand; and global ones depend on the global nature of that theory, such as idempotency or absorption laws. We also give modularly-checkable necessary and sufficient conditions for validating the optimisations.

Joint work with Gordon Plotkin.