Write R code for following Project$$s description without using any libraries. The output must take functions defination and return dataframe with symbol and decription.

This project is about analyzing a function definition. More precisely, it is about taking a function$$s definition and returning a data frame with two columns. The first one contains all symbols used in the function$$s definition, and the second one has either the environment$$s name containing the definition of the symbol or a description of the symbol$$s type, e$.$g$.,$ locally defined, given as argument, etc.

Technically, you must define a function listSymbols$(),$ taking a single argument f and returning a data frame. It is assumed that the function f is a closure $($not a builtin, as those are compiled functions and we cannot see their code from the level of pure R language$).$ The following examples present the particular functionalities of the required function. Let us start with a straightforward example. First, the function is defined, and then we list all symbols used in defining the function.

g $<-$ function$()\{$

print$("$Hello world!"$)$

$\}$

g$()$

$[1]$ "Hello world!"

When we run the function, it prints the string "Hello world!" to the console. There are two symbols used in the function's definition. One is print, and the other is $\{.$ Both symbols are defined in the package base. We can see it using the function listSymbols$()$ as shown in the following snippet.

listSymbols$($f $=$ g$)$

symbol definition

$1\{$ base

$2$ print base

The output of the function is a data frame containing two columns. The first column shows symbols, while the second column shows an environment where the symbol is defined. Here, both symbols are defined in the base packag