A hoare-like proof system for analysing the computation time of programs

Versions of Hoare logic have been introduced to prove partial and total correctness properties of programs. In this paper it is shown how a Hoare-like proof system for while programs may be extended to prove properties of the computation time as well. It should be stressed that the system does not require the programs to be modified by inserting explicit operations upon a clock variable. We generalize the notions of arithmetically sound and complete and show that the proof system satisfies these. Also we derive formal rules corresponding to the informal rules for determining the computation time of while programs. The applicability of the proof system is illustrated by an example, the bubble sorting algorithm.