Editing Monad (functional programming) (section)

===Continuation monad===
A [[continuation]] monad{{efn|name= mccan|1= The reader may wish to follow McCann's thread<ref name=so3322540 /> and compare it with the Types below.}} with return type {{mvar|R}} maps type {{mvar|T}} into functions of type <math>\left(T \rarr R \right) \rarr R</math>. It is used to model [[continuation-passing style]]. The return and bind functions are as follows:

:<math>\begin{array}{ll}
\text{return} \colon &T \rarr \left(T \rarr R \right) \rarr R = t \mapsto f \mapsto f \, t\\
\text{bind} \colon &\left(\left(T \rarr R \right) \rarr R \right) \rarr \left(T \rarr \left(T' \rarr R \right) \rarr R \right) \rarr \left(T' \rarr R \right) \rarr R = c \mapsto f \mapsto k \mapsto c \, \left(t \mapsto f \, t \, k \right)
\end{array}</math>

The [[call-with-current-continuation]] function is defined as follows:

:<math>\text{call/cc} \colon \ \left(\left(T \rarr \left(T' \rarr R \right) \rarr R \right) \rarr \left(T \rarr R \right) \rarr R \right) \rarr \left(T \rarr R \right) \rarr R = f \mapsto k \mapsto \left(f \left(t \mapsto x \mapsto k \, t \right) \, k \right)</math>