Consider the following grammars:
| Grammar 1: | E | → T | | E ^ T | |
| T | → I | | ( E ) | ||
| Grammar 2: | E | → T | | T ^ E | |
| T | → I | | ( E ) | ||
| Grammar 3: | E | → I | | E ^ E | | ( E) |
If ^ represents exponentiation, how many of these grammars force 2^3^2 to evaluate to 512?
Which operator associativity (left or right) does ^ need to have for 2^3^2 to evaluate to 512?
How does left- and right-recursion patterns in a production correspond to the associativity of the operator defined by the production?
How does the double-recursion pattern (i.e., simultaneous left- and right-recursion) in a production impact the associativity of the operator defined by the production?