Definition
An operator or function op is associative if the following holds:
<MATH> (a \text{ op } b) \text{ op } c == a \text{ op } (b \text{ op } c) </MATH>
Parallel
The importance of this to parallel evaluation can be seen if we expand this to four terms:
<MATH> a \text{ op } b \text{ op } c \text{ op } d == (a \text{ op } b) \text{ op } (c \text{ op } d) </MATH>
So we can evaluate (a op b) in parallel with (c op d), and then invoke op on the results.
Linear Algebra
Associativity of function composition: <math>h \circ (g \circ f) = (h \circ g) \circ f</math>
| <math>(h \circ (g \circ f))(x)</math> = | <math>h(g \circ f)(x)</math>
<math>h(g(f(x)))</math> <math>(h \circ g)(f(x))</math> <math>((h \circ g) \circ f)(x)</math> |
Example
Examples of associative operations include:
<MATH> (x + y) + z = x + (y + z) </MATH>