A New Algorithm to Parse a Mathematical Expression and its Application to Create a Customizable Programming Language

摘要

This paper presents an algorithm to parse a string containing a mathematical expression. This algorithm represents an alternative to other parsing algorithms, e.g., the Dijkstra "shunting-yard" algorithm. The algorithm presented here, has the same time complexity, but in our point of view it is easier to implement and to extend. As an example of extending this algorithm, we also present how it can be used to implement a fully customizable scripting programming language. The reference implementation language will be C++.