Calculating Accumulations 1 Calculating Accumulations

The accumulation strategy consists of generalizing a function over an algebraic data structure by inclusion of an extra parameter, an accumulating parameter, for reusing and propagating intermediate results. It is one of the standard optimization techniques taught to functional programmers 13). However , there remain two major diculties in this accumulation strategy. One is to determine where and when to generalize the original function. By \where," we mean what part in the denition of the function should be generalized; we may generalize a constant to a variable or an expression to a new function 24). By \when," we mean how many steps of unfolding are needed to nd a suitable place for generalization. One general way, known as forcing generalization , is to do generalization in case folding cannot be done during unfold/fold transformations 2, 6, 24, 25) , although related studies remain in an ad-hoc level. The other diculty, surprisingly not yet receiving its worthy consideration, is how to manipulate accumulations. We believe this is very important, particularly in functional programming where bigger functions are often dened as a composition of smaller and simpler functions. So, for a rather complicated function