Given the following answer $3.$

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

I Add

I Sub

$|$ Mul

I Div

type expr larr

I Num of number

$|$ Var of string

$|$ FuncExpr of string $$ expr

I CallExpr of expr $$ expr

$1$ BopExor of exor $$ bod $$ exor

Using your language from Question $1$:

$($a$)$ Write an expression containing at least one function definition, one function application, and one arithmetic

operation. Then, use the basic constraint$-$generation$/$solving approach discussed in class to infer the type

of your expression.

$($b$)$ What are the preliminary types?

$($c$)$ What are the constraints?

$($d$)$ What is the solution to the constraints obtained from unification?