B.RANDELL 3 PROGRAM PROOF AND MANIPULATION 2 Some techniques for proving correctness of programs which alter data structures.

This paper documents an investigation into the role that the late Alan Turing played in the development of electronic computers. Evidence is presented that during the war he was associated with a group that designed and built a series of special purpose electronic computers, which were in at least a limited sense'program controlled', and that the origins of several post-war general purpose computer projects in Britain can be traced back to these wartime computers. INTRODUCTION During my amateur investigations into computer history, I grew intrigued by the lack of information concerning the role played by the late Alan Turing.

The equivalence problem for program schemes, or for programs, is reduced to the proving of a theorem in second-order logic. This work extends Manna's first-order logic reductions. Some examples of the technique are given together with a suggested method for obtaining proofs in special cases by firstorder methods. INTRODUCTION Several workers in recent years have considered using techniques and ideas of various mathematical theories of computation for proving interesting results about computer programs. This paper is concerned with two of these approaches.

R.M.BURSTALL 373 23 Assertions: programs written without specifying unnecessary order.