3 are evident from the kicking tree description and are straightforward from the

recursive definition.

is a discrete recursive definition, and so we could analyze it exactly as stated by the Discrete MT.

Notice that there can only be one shape function [Omega](z) related to a given continuous recursive definition, except for bizarre shape functions obtained from [Omega](z) by changing its value at a finite number of points, or by similar minor perturbations.

n] be a function defined by a continuous recursive definition, and let B [n.

We begin introducing the concept of divide-and-conquer recursive definition formally.

n]) (k/n) Then we say that F is a DAC recursive definition of [F.

By contrast, (6) is not a DAC recursive definition.

Let F be a DAC recursive definition of a function [F.

a] in [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to denote the fixed points of the

recursive definitions of the overloaded functions a.

We are confronted with two problems here: (a) how an almost homomorphism can be derived from a recursive definition and (b) how a new almost homomorphism can be calculated out of a composition of a function and an old one.

First, we derive an almost homomorphism from the recursive definition of segs2.

Takeichi showed how to define a higher-order function common to all functions mutually defined so that multiple traversals of the same data structures in the mutually recursive definition can be eliminated.

Although some functions cannot be described directly by list homomorphisms, they may be easily described by (mutual) recursive definitions while some other functions might be used (see segs in Section 3 for an example) [Fokkinga 1992].

Practically, not all recursive definitions are in the form of (2).

In this article, we propose a formal and systematic approach to the derivation of efficient parallel programs from specifications of problems via manipulation of almost homomorphisms, namely the construction of almost list homomorphisms from recursive definitions (Theorem 4.