FORMAL TESTING OF REALVALUED FUNCTIONS

Abstract

The article discusses the algebraic approach to software design and testing. The aim of the study is to apply methods of formal software design to the development of functions for calculating the length of a meridian arc. Although formal software development methods have not yet been widely adopted in practical activities, their application in mathematical research seems reasonable due to the formal nature of programming languages. Research methods: the research utilizes the basic principles of the RAISE formal development method, which allows the use of formal logic. Specifically, the study explores the use of software development tools provided by the RAISE Method Group to specify functions for calculating the length of a meridian arc and to define conditions for creating a test driver for these functions at an early programming stage. The testing conditions are specified in the form of axioms using the abstract applicative approach. Scientific novelty the novelty of the study lies in demonstrating that the RAISE Specification Language (RSL) and specialized utilities are sufficiently convenient tools for small research teams that lack specialized skills in formal software development. The focus is on mathematical research, particularly on developing complex real-valued functions. In addition to the primary goal, seven coefficients (C0, C2, C4, C6, D2, D4, D6) of the Maclaurin series expansion for the considered functions were clarified. Formulas and calculations for the next two coefficients (C8, D8) were also performed. A practical method for developing generalized test drivers based on inheriting a class from a mock class was proposed, utilizing. NET features such as partial classes. Overall, the article aims to reduce the gap between the theoretical advantages of formal development methods and their insufficient practical application. Conclusions: algebraic design and testing are based on mathematical principles, enabling the following: avoiding ambiguity in functionality descriptions; ensuring precision and clarity in software requirements formulation; automating the generation of test cases and verification processes, thereby enhancing reliability; identifying and fixing errors at the development stage; and accelerating software development.