Designing and Interpreting a Mathematical Programming Language

The syntax of the programming languages has a significant impact on the definition and validation of mathematical calculations. In particular, the management of code identification and validation processes can be made easier and faster, depending on the parametric behavior of the functions. In this article, a programming language that supports the use of mathematical function structures is designed and an interpreter, which can evaluate the source code written in this language, is developed. The language syntax is represented by an LL (k) grammar defined in the BNF notation. The interpreter consists of several basic components such as parser, semantic controller and code evaluator, each of which makes a different kind of code interpretation. The LL (k) parser component used for the syntactic analysis of the language is generated via an automatic code generation tool called JavaCC. The other components work on the abstract syntactic tree that this parser generates. To illustrate the use of the language with code samples, several mathematical algorithms that include calculations on different sequences of numbers, are programmed and interpreted. The paper also performs a comparative analysis of the language with some related ones. The paper also performs a comparative analysis of the language with some related ones based on some design principles and mathematical aspects.

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