Implementation of an Experimental System for Automatic Program Transformation Based on Generalized Partial Computation

data types of auxiliary functions. A simplification process is successful if the result entails the elimination of all recursive calls to the (user defined) source program through folding. Since the folding process comes after this process, the simplification process is nondeterministic. That is, if the folding process is unsuccessful, we backtrack our SDFU process to the simplification process that caused the folding process and undo the simplification and try another simplification if possible. Examples of simplification are shown below: 1. Let the current environment be i and a source program be a conditional expression such as if p(u) then e1 else e2. Then if p(u) is provable from i then the residual program is the result of GPC of e1 with repect to i∧ p(u). If ¬p(u) is provable from i then the residual program is the result of GPC of e2 with repect to i ∧ ¬p(u). If neither of the above cases holds within a predetermined time, then the residual program is if p(u) then (residual progam of GPC of e1 with repect to i∧p(u)) else (residual program of GPC of e2 with repect to i ∧ ¬p(u)). 2. Let mod(x, d) be a function computing the remainder of x÷d. Then mod(x∗ y, d) is replaced by mod(mod(x, d) ∗ mod(y, d), d). The purpose of this replacement is to move the mod function into the multiplication. This makes the folding of composite function with mod easier. 3. If we know the termination of function f , f(x) ≡ if p(x) then a else f(d(x)) is replaced by a, where a is a constant. 4. If f(a) = a, then f(a) is replaced by a for m > 0. Distribution Suppose that a source program e contains a conditional expression such as if p(u) then e1 else e2. Let e be Cont [if p(u) then e1 else e2]. Then the operation to produce a program if p(u) then Cont [e1] else Cont [e2] from e is called distribution. Since WSDFU deals with only strict programs, the distribution operation preserves semantics of programs. GPC of e wrt i produces a GPC tree shown in Fig. 1. In the figure, N1, N2 and N3 are new names attached to nodes. They also stand for function names defined by GPC subtrees. For example, N1(u) ≡ if p(u) then Cont [e1] else Cont [e2]. Environments of nodes N2 and N3 are i ∧ p(u) and i ∧ ¬p(u), respectively. i Cont [if p(u) then e1 else e2] N1(u) p(u) ¬p(u) N2(u) Cont [e1] Cont [e2] N3(u) Fig. 1. GPC tree for distribution of a context over a conditional expression Suppose that a source program e does not contain a conditional expression. Let e be Cont [e1] and e ′ 1 be the result of GPC of e1 wrt i. Then GPC of e wrt i 4 Yoshihiko Futamura, Zenjiro Konishi, and Robert Glück produces a GPC tree shown in Fig. 2. In the figure, the environment of node N2 is i. This process can be considered as a part of the distribution.