The use of proof plans to sum series:
Abstract: "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 prev...
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Edinburgh
1991
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| Series: | University <Edinburgh> / Department of Artificial Intelligence: DAI research paper
563 |
| Subjects: | |
| Summary: | Abstract: "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 CL[superscript A]M. 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 wide application in controlling mathematical proofs. |
| Physical Description: | 17 S. |
Staff View
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| 245 | 1 | 0 | |a The use of proof plans to sum series |c Toby Walsh ; Alex Nunes and Alan Bundy |
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| 490 | 1 | |a University <Edinburgh> / Department of Artificial Intelligence: DAI research paper |v 563 | |
| 520 | 3 | |a Abstract: "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 CL[superscript A]M. 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 | |
| 520 | 3 | |a 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 wide application in controlling mathematical proofs. | |
| 650 | 7 | |a Applied statistics, operational research |2 sigle | |
| 650 | 7 | |a Computer software |2 sigle | |
| 650 | 4 | |a Automatic theorem proving | |
| 700 | 1 | |a Nunes, Alex |e Verfasser |4 aut | |
| 700 | 1 | |a Bundy, Alan |e Verfasser |4 aut | |
| 810 | 2 | |a Department of Artificial Intelligence: DAI research paper |t University <Edinburgh> |v 563 |w (DE-604)BV010450646 |9 563 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-006968127 | |
Record in the Search Index
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| author | Walsh, Toby Nunes, Alex Bundy, Alan |
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| id | DE-604.BV010459032 |
| illustrated | Not Illustrated |
| indexdate | 2024-10-15T10:07:52Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006968127 |
| oclc_num | 1070930004 |
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| owner_facet | DE-91G DE-BY-TUM |
| physical | 17 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| record_format | marc |
| series2 | University <Edinburgh> / Department of Artificial Intelligence: DAI research paper |
| spelling | Walsh, Toby Verfasser aut The use of proof plans to sum series Toby Walsh ; Alex Nunes and Alan Bundy Edinburgh 1991 17 S. txt rdacontent n rdamedia nc rdacarrier University <Edinburgh> / Department of Artificial Intelligence: DAI research paper 563 Abstract: "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 CL[superscript A]M. 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 wide application in controlling mathematical proofs. Applied statistics, operational research sigle Computer software sigle Automatic theorem proving Nunes, Alex Verfasser aut Bundy, Alan Verfasser aut Department of Artificial Intelligence: DAI research paper University <Edinburgh> 563 (DE-604)BV010450646 563 |
| spellingShingle | Walsh, Toby Nunes, Alex Bundy, Alan The use of proof plans to sum series Applied statistics, operational research sigle Computer software sigle Automatic theorem proving |
| title | The use of proof plans to sum series |
| title_auth | The use of proof plans to sum series |
| title_exact_search | The use of proof plans to sum series |
| title_full | The use of proof plans to sum series Toby Walsh ; Alex Nunes and Alan Bundy |
| title_fullStr | The use of proof plans to sum series Toby Walsh ; Alex Nunes and Alan Bundy |
| title_full_unstemmed | The use of proof plans to sum series Toby Walsh ; Alex Nunes and Alan Bundy |
| title_short | The use of proof plans to sum series |
| title_sort | the use of proof plans to sum series |
| topic | Applied statistics, operational research sigle Computer software sigle Automatic theorem proving |
| topic_facet | Applied statistics, operational research Computer software Automatic theorem proving |
| volume_link | (DE-604)BV010450646 |
| work_keys_str_mv | AT walshtoby theuseofproofplanstosumseries AT nunesalex theuseofproofplanstosumseries AT bundyalan theuseofproofplanstosumseries |