CFG_Calculator

An implementation of a Context Free Grammar for a command-line-based calculator with variable storage, created in C++. Implementing a Lexer for tokenization, a Parser to construct an Abstract Syntax Tree and finally the calculator/interpreter which parses the tree and outputs the result of the equation.

Usage

After running the program there should be some output to the terminal matching:

Welcome to the CFG Calculator!
Enter an expression to calculate
Type 'exit' at any time to quit
>

Note

">" Here represents the user input

The user is then able to enter a mathematical expression, the parsed expression and the result will be displayed

> 2 + 2 * 2
Parsed expression: (2+(2*2))
Result: 6

Setting Variables

To set a variable the input should start with a string followed by a "=" then the expression to set your variable to

> myVariable = 3 + 4 + 6 * (7 - 3)
Parsed expression: (myVariable=((3+4)+(6*(7-3))))
result: 31

Warning

Constants can be overwritten. If the user sets a variable, like pi this will overwrite the constant value of pi.

Now if we want to access the value of myVariable we can just put it into our expressions, like it's a number.

> 3 / myVariable
Parsed expression: (3/myVariable)
Result: 0.0967742

Clearing Variables

To clear the variables, and the terminal the user can simply type clear

> 3 / myVariable
Parsed expression: (3/myVariable)
Result: 0.0967742
> clear

This will clear the terminal and prompt the user to clear their variables

Would you like to clear the variables? (y/n)
> 

Keywords

clear - Clears the terminal and will prompt user to also clear variables

exit - Exits the program

vars - Lists all set variables in the calculator

Grammar

$$\begin{align*} \text{Expression <E>}& \begin{cases} <T> <AO> <T>\\\ <I> = <E>\\\ <T> \end{cases}\\\ \\\ \text{Term <T>}& \begin{cases} <F> <MO> <F>\\\ <F> \end{cases}\\\ \\\ \text{Factor <F>}& \begin{cases} <P> <EO> <F> <P> \end{cases}\\\ \\\ \text{Primary <P>}& \begin{cases} <L>\\\ (<E>)\\\ <I>\\\ <UO> <P> \end{cases}\\\ \\\ \text{Literal <L>}& \begin{cases} \mathbb{R} \end{cases}\\\ \\\ \text{Addition Operations <AO>}& \begin{cases} +\\\ - \end{cases}\\\ \\\ \text{Multiplication Operations <MO>}& \begin{cases} *\\\ / \end{cases}\\\ \\\ \text{Exponential Operations <EO>}& \begin{cases} \widehat{} \end{cases}\\\ \\\ \text{Unary Operations <UO>}& \begin{cases} sqrt \end{cases}\\\ \\\ \text{Indetifier <I>}& \begin{cases} \text{String literal} \end{cases} \end{align*}$$