Guiding induction proofs

Hutter, Dieter

doi:10.1007/3-540-52885-7_85

Cited by 36 publications

(20 citation statements)

References 4 publications

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“…This approach has been adopted by Hutter,9], and by Clarke and Zhao,7]. Hutter has used the INKA inductive theorem prover system to verify sums and to prove properties of them, e.g.…”

Section: Veri Cationmentioning

confidence: 99%

“…In this example, for a 6 = There has been limited research into this domain. Some researchers have tackled the topic as a veri cation problem, 9,7]; both these teams use mathematical induction to prove that a series is equal to a user supplied closed form. In the work reported below, the closed form solution to a series is simultaneously synthesised and veri ed.…”

Section: Introductionmentioning

confidence: 99%

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The use of proof plans to sum series

Walsh

Nunes

Bundy

1992

Automated Deduction—CADE-11

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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 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 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.

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“…This approach has been adopted by Hutter,9], and by Clarke and Zhao,7]. Hutter has used the INKA inductive theorem prover system to verify sums and to prove properties of them, e.g.…”

Section: Veri Cationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The use of proof plans to sum series

Walsh

Nunes

Bundy

1992

Automated Deduction—CADE-11

View full text Add to dashboard Cite

show abstract

“…The first five rules are further examples of wave-rules not formed from recursive definitions. Note that rules (15) and (16) The advantages of multi-wave-rules of format (12) compared to simple wave-rules of format (3) are as follows.…”

Section: Max_ht( Tree(u V__)]) ~ [S(max(max_ht(v)max_ht(v) ) )mentioning

confidence: 99%

“…If the maximally merged normal form is used, then the matcher must be modified to dynamically split wavefronts as required. The INKA system records wave-fronts by annotating each symbol as either in the wave-front or in the skeleton [15]. This solution has some similarity to the maximally split normal form.…”

Section: • Even(x + Y)mentioning

confidence: 99%

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Rippling: A heuristic for guiding inductive proofs

Bundy

Stevens

Harmelen

et al. 1993

Artificial Intelligence

170

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We describe rippling: a tactic for the heuristic control of the key part of proofs by mathematical induction. This tactic significantly reduces the search for a proof of a wide variety of inductive theorems. We first present a basic version of rippling, followed by various extensions which are necessary to capture larger classes of inductive proofs. Finally, we present a generalised form of rippling which embodies these extensions as special cases. We prove that generalised rippling always terminates, and we discuss the implementation of the tactic and its relation with other inductive proof search heuristics.

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Reasoning Inductively about Z Specifications via Unification

Duffy

Toyn

2000

ZB 2000: Formal Specification and Development in Z and B

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Guiding induction proofs

Cited by 36 publications

References 4 publications

The use of proof plans to sum series

The use of proof plans to sum series

Rippling: A heuristic for guiding inductive proofs

Reasoning Inductively about Z Specifications via Unification

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