Bede Island Building, The Gateway,

The transformational programming method of algorithm derivation starts with a formal specification of the result to be achieved, plus some informal ideas as to what techniques will be used in the implementation. The formal specification is then transformed into an implementation, by means of correctness-preserving refinement and transformation steps, guided by the informal ideas. The transformation process will typically include the following stages: (1) Formal specification (2) Elaboration of the specification, (3) Divide and conquer to handle the general case (4) Recursion introduction, (5) Recursion removal, if an iterative solution is desired, (6) Optimisation, if required. At any stage in the process, sub-specifications can be extracted and transformed separately. The main difference between this approach and the invariant based programming approach (and similar stepwise refinement methods) is that loops can be introduced and manipulated while maintaining program correctness and with no need to derive loop invariants. Another difference is that at every stage in the process we are working with a correct program: there is never any need for a separate “verification ” step. These factors help to ensure that the method is capable of scaling up to the development of large and comple