The use of proof plans to sum series [chapter]

Toby Walsh, Alex Nunes, Alan Bundy
1992 Lecture Notes in Computer Science  
We describe a program for nding closed form solutions to nite 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
more » ... 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 di erence 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 di erence matching, will nd wide application in controlling mathematical proofs.
doi:10.1007/3-540-55602-8_175 fatcat:mnpvwypss5hptdwi2yqxztwkde