Given the following answer $2.$

$1.$ Consider a language based on the lambda calculus that includes function definition, function application,

numbers, and arithmetic operations $($addition$,$ subtraction, multiplication, division$)$:

$($a$)$ Write a context$-$free grammar for this language.

$($b$)$ Write a variant for the abstract syntax of this language.

type bop larr

Add

I Sub

Mul

$|$ Div

type expr larr

I Num of number

$|$ Var of string

$|$ FuncExpr of string $$ expr

$|$ CallExpr of expr $$ expr

i BooExor of exor $$ boo $$ exor

$2.$ Using your langunge syntax from Question $1$:

$($a$)$ Write an expression containing at least two function definitions and two function applications.

$($b$)$ Evaluate this expression using dynamic scope.

$($c$)$ Evaluate this expression using lerical scope.