Automatic generation and step by step solution of indeterminate limit expressions

In this paper, the solution of limit problems, which is an important subject of high school and university mathematics is presented by using JavaCC code generation tool and symbolic computation methods. Although JavaCC is generally used for generating programming language interpreters, in a similar way it can also be used in the evaluation of mathematical expressions. In this work, first the general grammar rules of limit expressions is extracted. Then parser code for the limit expressions is generated with JavaCC according to the grammar rules. Using the list of the tokens into which a limit expression is parsed with this code, an Abstract Syntax Tree (AST) is constructed. Finally, the solution is obtained by interpreting the AST with a class of Visitor Design Pattern. In the second part of the study, it has been claimed that existing approaches are not suitable for the production of indeterminate limit expression and a method based on generating random AST is presented. Finally a system for step by step solution and generating indeterminate limit expressions is proposed therefore the study can be regarded as a promising contribution to computer assisted education.