Algebraic Effects and Handlers

Andrej Bauer

Basics

Take the operation symbol for $plus$:

$plus: 1 \times \Z^2 \rightarrow \Z$

3 + (4 + 5)

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

$Op \colon A^n \rightarrow A$

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

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$Op \colon B \times A^n \rightarrow A$

where $B$ is the parameter type, a monad

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$Op \colon B \times A^C \rightarrow A$

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