EWD249 - 54

                   "arg:=.....; fun:= FUN(arg)"

thereby maintaining the relation

                   fun = FUN(arg)     .

As a result of the validity of this relation, wherever version A calls for the evaluation of FUN(arg), version B will call for the current value of the variable fun.

There are two possible reasons to prefer version B to version A. When the value of FUN(arg) is more frequently requested than assignments to arg take place, version B could require less computation time. If necessary the technique can be refined by the introduction of a further (boolean) variable "fun up to date", indicating whether the relation "fun = FUN(arg)" is assumed to hold. Assignment to arg is then associated with

                   "fun up to date:= false" ;

whenever the value of FUN(arg) is needed, inspection of this boolean variable will tell, whether FUN(arg) has to be computed afresh; if so, the computed value will be assigned to fun and in accordance with its meaning "fun up to date" will be set to true. Let us call the last program version C. It is clear that these three programs, only differing where version A assigns to arg or uses the value of FUN(arg) are equivalent as far as their output is concerned; it is certainly not inconceivable that version B or C is derived from version A by mechanical means.

But quite often the situation is not as simple as that and now we come to the second reason for introducing such a variable "fun". Often it is very unattractive to compute FUN(arg) from scratch for arbitrary values of arg, while it is much easier to compute how the value of FUN(arg) changes when the value of arg is changed. In that case, the adjustment of the value of "fun" is more intimately linked with the nature of the functional dependence than is suggested by "arg:=.......; fun:= FUN(arg)".

Often this possibility is not only intimately linked to the nature of the functional dependence, but also to the "history of the variable arg" as the computation proceeds! We have seen a very striking example in the program for the