From Constructivism to Computer Science

My eld is mathematical logic, with a special interest in constructivism, and I would not dare to call myself a computer scientist. But some computer scientists regard my work as a contribution to their eld; and in this text I shall try to explain how this is possible, by taking a look at the history of ideas. I want to describe how two interrelated ideas, connected with the con-structivistic trend in the foundations of mathematics, developed within mathematical logic and ultimately diiused into computer science. It will be seen that this development has not been a quite straightforward one. In the history of ideas it often looks as if a certain idea has to be discovered several times, by diierent people, before it really enters into the \consciousness" of science. 1 The proof interpretation The rst of these ideas is the so-called proof interpretation of intuitionis-tic logic, also known as the Brouwer{Heyting{Kolmogorov interpretation, since it is implicit in the writings of L.E.J. Brouwer, and made explicit by A.Heyting and, independently, by A. Kolmogorov. The Dutch mathematician L.E.J. Brouwer (1881{1966) achieved international fame by his contributions to topology. However, his earliest interest was in the foundations of mathematics. His philosophy of mathematics, a special form of constructivism, which became known under the somewhat misleading name of intuitionism, generated a lot of interest, gave rise to a