On the concepts of problem and problem-solving method

Abstract The concepts of problem, problem-solving method, and the application of a problem-solving method to a problem are given precise formulations, based on abstract data types. These formulations are argued to agree with the intuitive understanding of these ideas, thereby formalizing them. This formalization is based on few basic concepts: abstract data type and an extension mechanism (here, a general cluster-like module). Moreover, by embodying ideas related to stepwise refinement they are applicable both to problem solving in general and to the process of program development. Examples are provided to illustrate the main ideas and their application.