Editing Operator associativity (section)

=== A detailed example ===

Consider the expression <code>5^4^3^2</code>, in which <code>^</code> is taken to be a right-associative exponentiation operator. A parser reading the tokens from left to right would apply the associativity rule to a branch, because of the right-associativity of <code>^</code>, in the following way:
# Term <code>5</code> is read.
# Nonterminal  <code>^</code> is read. Node: "<code>5^</code>".
# Term <code>4</code> is read. Node: "<code>5^4</code>".
# Nonterminal <code>^</code> is read, triggering the right-associativity rule. Associativity decides node: "<code>5^(4^</code>".
# Term <code>3</code> is read. Node: "<code>5^(4^3</code>".
# Nonterminal <code>^</code> is read, triggering the re-application of the right-associativity rule. Node "<code>5^(4^(3^</code>".
# Term <code>2</code> is read. Node "<code>5^(4^(3^2</code>". 
# No tokens to read.  Apply associativity to produce parse tree "<code>5^(4^(3^2))</code>".
This can then be evaluated depth-first, starting at the top node (the first <code>^</code>):
# The evaluator walks down the tree, from the first, over the second, to the third <code>^</code> expression.
# It evaluates as: 3{{sup|2}} = 9. The result replaces the expression branch as the second operand of the second <code>^</code>.
# Evaluation continues one level up the [[parse tree]] as: 4{{sup|9}} = {{formatnum:262144}}. Again, the result replaces the expression branch as the second operand of the first <code>^</code>. 
# Again, the evaluator steps up the tree to the root expression and evaluates as: 5{{sup|262144}} ≈ {{val|6.2060699|e=183230}}. The last remaining branch collapses and the result becomes the overall result, therefore completing overall evaluation.
A left-associative evaluation would have resulted in the parse tree  <code>((5^4)^3)^2</code> and the completely different result (625{{sup|3}}){{sup|2}} = {{formatnum:244140625}}{{sup|2}} ≈ {{val|5.9604645|e=16}}.