Theories of computation related to the semantics of programming languages, like those of McCarthy and Scott, rely on non‐constructive mathematical “ideas.” Turing's theory does not assume any mathematical “ideas.” In the approaches of Floyd, McCarthy and Scott the attempt is to develop a general theory of “meaning of programs” and then to consider the problem of correctness and equivalence. From a constructive point of view, suggested in this paper, correctness is considered only from that of meaning of a particular program. A general theory of meaning is rejected because of its ontological assumptions. It is shown why for a constructive semantics of programming languages the distinction in ontology between a “mathematical algorithm” and the corresponding program is so fundamental.