Abstract

In this talk I will show one way to generalise algebraic effects and handlers to accommodate higher-order operations, including operations delimiting scopes and binding new variables. The basic idea is to shift the perspective from considering algebraic theories of effectful operations on objects to algebraic theories of monads equipped with operations. This idea can be more generally carried out at the level of monoids in monoidal categories, accommodating non-monadic effects such as applicative functors and graded monad, and also resulting in interesting results including a correspondence between monoids and theories of algebraic operations. To make models/handlers of higher-order effects composable, we introduce a concept of modular models of a theory, which transforms monoids equipped with some existing operations to monoids equipped with more operations.