ExpressionSolver

A solver for simple mathematical expressions.

This project demonstrates the use of context free grammars to solve expressions by traversing the syntax tree of the expression.

How it works

The parser uses a context free grammar which respects operator precedence and associativity:

<sum>           ::= <sum> <binop-add-sub> <product> | <product>
<product>       ::= <power> | <product> <binop-mul-div> <power>
<power>         ::= <atom> | <atom> <binop-pow> <power> | <unop> <power>
<atom>          ::= <brackets> | <integer> | <real> | <variable> | <function>
<brackets>      ::= '(' <sum> ')'
<binop-add-sub> ::= '+' | '-'
<binop-mul-div> ::= '*' | '/'
<binop-pow>     ::= '^'
<unop>          ::= '+' | '-'
<integer>       ::= <integer> <digit> | <digit>
<real>          ::= <integer> '.' <integer>
<digit>         ::= '0' | '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9'
<variable>      ::= <string>
<function>      ::= <string> '(' <arguments> ')'
<arguments>     ::= <sum> | <arguments> ',' <sum>
<string>        ::= <string> <letter> | <letter>
<letter>        ::= "A" | "B" | "C" | "D" | "E" | "F" | "G" | "H" | "I" | "J" | "K" | "L" | "M" | "N" | "O" | "P" | "Q" | "R" | "S" | "T" | "U" | "V" | "W" | "X" | "Y" | "Z" | "a" | "b" | "c" | "d" | "e" | "f" | "g" | "h" | "i" | "j" | "k" | "l" | "m" | "n" | "o" | "p" | "q" | "r" | "s" | "t" | "u" | "v" | "w" | "x" | "y" | "z"

Examples:

> -3^2^3
-6561.0
> tanh(pi/5+1/3*-e)
-0.270844926380908
> ((-e^5+log(sin(e+pi)+3))*(4^sin(-2)+4))
-631.652183876061