Reduction Graphs

A reduction graph illustrates all the possible ways an expression might be evaluated.

The expression $square (3+4)$ for example, can be reduced multiple different ways, one might first substitute $(3+4)$ into $square$, and then calculate $3+4$ twice, substituting again, arriving at $7\times 7$. One might also calculate $3+4$, and substitute to $square(7)$, then leading to $7\times 7$.