Research Paper #563
|The Use of Proof Plans to Sum Series
|Walsh,T; Nunes,A; Bundy,A
|Submitted to CADE-11
|We describe a program for finding closed form solutions to finite sums. The program was built to test the applicability of the proof planning search control technique in a domain of mathematics outwith induction. This experiment was successful. The series summing program extends previous work in this area and was built in a short time just by providing new series summing methods to our existing inductive theorem proving system CLAM. One surprising discovery was the usefulness of the ripple tactic in summing series. Rippling is the key tactic for controlling inductive proofs, and was previously thought to be specialised to such proofs. However, it turns out to be the key sub-tactic used by all the main tactics for summing series. The only change required was that it had to be supplemented by a difference matching algorithm to set up some initial meta-level annotations to guide the rippling process. In inductive proofs these annotations are provided by the application of mathematical induction. This evidence suggests that rippling, supplemented by difference matching, will find application in controlling mathematical proofs.