PROG ::= (INSTR (EOI INSTR)*)?
INSTR ::= EXPR
EXPR ::= IMP

IMP ::= OR (imp OR)?
OR ::= AND (or AND)*
AND ::= EQ (and EQ)*

EQ ::= CMP ((eq | ne) CMP)?
CMP ::= TERM ((lt | le | gt | ge) TERM)?

TERM ::= FACTOR ((add | sub) FACTOR)*
FACTOR ::= UNOP ((mul | div | mod) UNOP)*

UNOP ::= (add | sub | not)? POW
POW ::= GROUP (pow GROUP)?
GROUP ::= BASE | opar EXPR cpar
BASE ::= int | bool