ALGEBRAIC SOFTWARE DESIGN

Abstract

Abstract. The article discusses an algebraic approach to designing and testing software. The purpose of the article is to develop a class that implements Peano arithmetic. Peano arithmetic is one of the fundamental constructs in axiomatic mathematics. The arithmetic class presented in the article represents a semigroup of natural numbers and this class is the first example in the hierarchy of numerical classes (integers, integer rings, rational number fields) that demonstrates the potential unsafety of universal inclusion polymorphism and violations of the Liskov substitution principle. Research methods. During the study, basic principles of the Bertrand Meyer’s design by contract method and the formal development method RAISE are used, which allow applying formal logic. Scientific novelty. The modified interpretation of the functional type of class methods and the consistent use of requirements in the form of algebraic equalities make it possible at the time of design to indicate the unsafety of universal inclusion polymorphism. Additionally, attention is drawn to the categoricality (rigitity) of algebraic model, which makes incorrect implementations impossible, and to direct analogies between the axiomatic presentation of mathematical theory and the development of specifications. Furthermore, this approach significantly simplifies the of smoke test design. Conclusions. Algebraic design and testing are based on mathematical principles, allowing for the avoidance of ambiguity and uncertainty in functionality descriptions, ensuring accuracy and unambiguity in formulating specifications, automating the process of test cases design and verification of software requirements, thereby makes it easier to detect and correct a design and coding errors.