Algebraic Effects and Handlers

Andrej Bauer

Basics

Take the operation symbol for $plus$:

$plus:1\times {\mathbb{Z}}^2\to \mathbb{Z}$

3 + (4 + 5)

plus(b:2 if b = 0 then 3
         else plus(c:2 if c = 0 then 4
                       else 5))

$Op:A^n\to A$

where $n$ is the arity, or number of distinct effects

$Op:B\times A^n\to A$

where $B$ is the parameter type, a monad

$Op:B\times A^C\to A$

where $C$ is an unbounded type; a delimited continuation