ambiguous grammar examples

In the last post, We saw 2 possible parse trees for a+a+a. How many are there for a+a+a+a?

There are 5 possible parses:

(a)+((a+a)+a),

(a)+(a+(a+a)),

(a+a)+(a+a),

((a+a)+a)+(a),

(a+(a+a))+(a)


While in general it may be difficult to prove a grammar is ambiguous, the demonstration of two distinct parse trees for the same terminal string is sufficient proof that a grammar is ambiguous.