Inversion Framework: Reasoning about Inversion by Conditional Term Rewriting Systems

An Inversion Tool for Conditional Term Rewriting Systems - A Case Study of Ackermann Inversion

“…The result of the pure partial inversion [6,Fig.6] is shown in Figure 4b. consists of two defined function symbols, namely, the desired partial inverse ack{1}{1}, which depends on another partial inverse ack{1,2}{1}.…”

“…This means that with our tool, we produced all four possible partial inversions (including the special case of full inversion) of the Ackermann function in the course of the three experiments. Using our tool, we also reproduced all of the examples in [6,7].…”

“…Although function inversion is an important concept in mathematics, program inversion has received little attention in computer science. In this paper, we report on a tool implementation of an inversion framework [6] and on some computer experiments within the framework. The implementation includes four well-behaved rule inverters ranging from trivial to full, partial and semi-inverters, several of which have been studied in the literature [7,12,13].…”

“…The implementation includes four well-behaved rule inverters ranging from trivial to full, partial and semi-inverters, several of which have been studied in the literature [7,12,13]. The generic inversion algorithm used by the tool was proven to produce the correct result for all well-behaved rule inverters [6]. The tool reads the standard notation of the established confluence competition (COCO), making it compatible with other term rewriting tools.…”

“…They are intended to be used together. For more details on the generic inversion algorithm and the rule inverters, interested readers are therefore referred to [6].…”