Testing data types implementations from algebraic specifications

TL;DR

This paper explores testing data type implementations using algebraic specifications, focusing on formal conformance, test set selection, and addressing the gap between abstract specifications and concrete implementations.

Contribution

It introduces a formal testing framework based on algebraic specifications, including criteria for finite test set selection and solutions for the oracle problem.

Findings

Proposes a formal conformance relation based on axioms

Introduces criteria for selecting finite test sets

Addresses the gap between abstract specifications and concrete implementations

Abstract

Algebraic specifications of data types provide a natural basis for testing data types implementations. In this framework, the conformance relation is based on the satisfaction of axioms. This makes it possible to formally state the fundamental concepts of testing: exhaustive test set, testability hypotheses, oracle. Various criteria for selecting finite test sets have been proposed. They depend on the form of the axioms, and on the possibilities of observation of the implementation under test. This last point is related to the well-known oracle problem. As the main interest of algebraic specifications is data type abstraction, testing a concrete implementation raises the issue of the gap between the abstract description and the concrete representation. The observational semantics of algebraic specifications bring solutions on the basis of the so-called observable contexts. After a description of testing methods based on algebraic specifications, the chapter gives a brief presentation of some tools and case studies, and presents some applications to other formal methods involving datatypes.