$.(2$ points$)$ Consider the integer tree type

type t r e e $=$

$|$ L e a f

$|$ Node of t r e e $$ i n t $$ t r e e

The simplest way to calculate the sum of an integer tree is:

l e t r e c sum t $=$ match t with

$|$ L e a f $>0$

$|$ Node $($ l $,$ v $,$ r $)>$ sum l $+$ v $+$ sum r

However, this implementation is not tail$-$recursive. Write a tail recursive function sumtailrec

: tree $>$ int that sums up the integer values in a tree. $($Hint: Use an auxiliary function of

type: int $>$ tree list $>$ int $).$

Operational Semantics

$4.(1$ point$)$ Derivations

Fill in the blanks in the derivation tree for evaluating let x $=8$ in $3>$ x $4$ using the oper$-$

ational semantics in Fig. $1.$

Blank $1$:

Blank $2$:

Blank $3$: