Consider the language of expressions with variables

E in Exp ::$=$ N $$ T $$ F $$ x $$ E$1+$ E$2$ E$1*$ E$2$ E$1$ E$2$ E$1$ E$2$E$1$ E$1=$ E$2$ E$1>$ E$2$

Encode the type$-$checking relation in PROLOG as a predicate hastype$($G$,$E$,$T$).$