Testing data types implementations from algebraic specifications

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

Symbolic Test Case Generation for Primitive Recursive Functions

We present a method for the automatic generation of test cases for HOL formulae containing primitive recursive predicates. These test cases may be used for the animation of specifications as well as for black-box-testing of external programs. Our method is two-staged: first, the original formula is partitioned into test cases by transformation into a Horn-clause normal form (CNF). Second, the test cases are analyzed for ground instances satisfying the premises of the clauses. Particular emphasis is put on the control of test hypothesis’ and test hierarchies to avoid intractability. We applied our method to several examples, including AVL-trees and the red-black implementation in the standard library from SML/NJ

Symbolic Test Case Generation for Primitive Recursive Functions

We present a method for the automatic generation of test cases for HOL formulae containing primitive recursive predicates. These test cases may be used for the animation of specifications as well as for black-box-testing of external programs. Our method is two-staged: first, the original formula is partitioned into test cases by transformation into a Horn-clause normal form (CNF). Second, the test cases are analyzed for ground instances satisfying the premises of the clauses. Particular emphasis is put on the control of test hypothesis ’ and test hierarchies to avoid intractability. We applied our method to several examples, including AVL-trees and the red-black implementation in the standard library from SML/NJ