$5.(2$ points$)$ Operation Semantics Rules $($a$)(1$ point$)$ Consider the operation semantics rules for function calls $($or function applications$)$ presented in Lecture $11$ or Assignment $4$: EAGEREval A ; e$\_1($ fun x $->$ e$)$ A ; e$\_2$ v$\_1$ A$,$ x: v$\_1$ ; e $$ v$\_2/$A ; e$\_1$ e$\_2$ v $2$ We call this rule EAGEREval because it evaluates the function application argument e$\_2$ to a value before evaluating the function body e from e$\_1.$ Using this evaluation rule, the interpreter can reduce the OCaml program $($fun x $->$ fun y $->$ x y $1)($fun c $->$ c$)(($ fun a $->$ a$)($ fun b $->$ b$))$ in the following few steps $($we omit the environment A for simplicity$)$: $[($ fun x $->$ fun y $->$ x y $1)($ fun c $->$ c$)(($ fun a $->$ a$)($ fun b $->$ b$))$; $($ fun y $->($ fun c $->$ c$)$ y $1)(($ fun a $->$ a$)($ fun b $->$ b$))$; $($ fun y $->($ fun c $->$ c$)$ y $1)($ fun b $->$ b$)$; $($ fun c $->$ c$)($ fun b $->$ b$)1$; $($ fun b $->$ b$)1$; $1]$ It is important to note that function application is left$-$associative e$.$g$.$ x y z$=([$ x y $])$ z$.$ We now define a new function application evaluation rule called LAZYEvAL as follows: LAZYEvaL A ; e$\_1($ fun x $->$ e$)$ A ; e$\{$e$\_2/$ x$\}$ v$\_2/$A ; e$\_1$ e$\_2$ v $2$ Here, e$\{$e$\_2/$ x$\}$ means "the expression after substituting occurrences of x in e with e$\_2".$ The key point is that we defer the evaluation of the functional application argument e$\_2$ until it has to be evaluated. This is often referred as "lazy evaluation". Reduce the same OCaml program $($fun x $->$ fun y $->$ x y $)($fun c $->$ c$)(($ fun a $->$ a$)($fun b $->$ b $))$ using this new evaluation rule to witness the key difference between EAGEREval and LAzyEval.