Yesterday when I was preparing slides for the recitation, I found a very interesting usecase for knowing context-free grammar, c.f. Theory of Computation , Sipser 2013.

$STMT\rightarrow ASSIGN|IF-THEN|IF-THEN-ELSE$

$IF-THEN\rightarrow\mbox{ if condition then }STMT$

$IF-THEN-ELSE\rightarrow\mbox{ if condition then }STMT\mbox{ else }STMT$

$ASSIGN\rightarrow\mbox{ a:=1 }$

$\Sigma=\{\mbox{ if, condition, then, else, a:=1 }\}$

$V=\{STMT, IF-THEN, IF-THEN-ELSE, ASSIGN\}$

It turns out that this grammar is ambiguous. A very quick fix is to eliminate the ambiguity is to add brackets, by introducing the order of evaluation. However, we all know that C syntax allows the pair of brackets ommitted. What if there is ambiguouty when brackets not showing up? This is known as the dangling-else problem and most of C compilers solve it by associating the "else" with the nearest "if".