Conjecture Synthesis for Inductive Theories

Johansson, Moa; Dixon, Lucas; Bundy, Alan

doi:10.1007/s10817-010-9193-y

Cited by 64 publications

(68 citation statements)

References 17 publications

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“…Therefore, we want to develop intelligent methods of finding such necessary lemmas, through techniques like IsaCoSy's [11] random perturbation of property terms.…”

Section: Discussionmentioning

confidence: 99%

Zeno: An Automated Prover for Properties of Recursive Data Structures

Sonnex

Drossopoulou

Eisenbach

2012

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. Zeno is a new tool for the automatic generation of proofs of simple properties of functions over recursively defined data structures. It takes a Haskell program and an assertion as its goal and tries to contruct a proof for that goal. If successful, it converts the proof into Isabelle code. Zeno searches for a proof tree by iteratively reducing the goal into a conjunction of sub-goals, terminating when all leaves are proven true.This process requires the exploration of many alternatives. We have adapted known, and developed new, heuristics for the reduction of the search space. Our new heuristics aim to promote the application of function definitions, and avoid the repetition of similar proof steps.We compare with the rippling based tool IsaPlanner and the industrial strength tool ACL2s on the basis of a test suite from the IsaPlanner website. We found that Zeno compared favourably with these tools both in terms of theorem proving power and speed.

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“…Therefore, we want to develop intelligent methods of finding such necessary lemmas, through techniques like IsaCoSy's [11] random perturbation of property terms.…”

Section: Discussionmentioning

confidence: 99%

Zeno: An Automated Prover for Properties of Recursive Data Structures

Sonnex

Drossopoulou

Eisenbach

2012

Tools and Algorithms for the Construction and Analysis of Systems

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“…In standard inductive theorem provers, this lemma would be supplied as a "hint" to the prover, or would be found by an appropriate conjecture mechanism (cf. [16]). …”

Section: Limitationsmentioning

confidence: 99%

“…For example, conjecturing appropriate lemmas (cf. [16]) seems extremely useful in forming back-links during proof search.…”

Section: Related Workmentioning

confidence: 99%

A Generic Cyclic Theorem Prover

Brotherston

Gorogiannis

Petersen

2012

Lecture Notes in Computer Science

133

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Abstract. We describe the design and implementation of an automated theorem prover realising a fully general notion of cyclic proof. Our tool, called Cyclist, is able to construct proofs obeying a very general cycle scheme in which leaves may be linked to any other matching node in the proof, and to verify the general, global infinitary condition on such proof objects ensuring their soundness. Cyclist is based on a new, generic theory of cyclic proofs that can be instantiated to a wide variety of logics. We have developed three such concrete instantiations, based on: (a) first-order logic with inductive definitions; (b) entailments of pure separation logic; and (c) Hoare-style termination proofs for pointer programs. Experiments run on these instantiations indicate that Cyclist offers significant potential as a future platform for inductive theorem proving.

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“…The key ingredient for automatically detecting equivalent instantiations is a term rewrite system (TRS) R. This rewrite system is used to normalise terms such that only irreducible terms are considered [15].…”

Section: Identification Of Equivalent Instantiationsmentioning

confidence: 99%

Scheme-based theorem discovery and concept invention

Montaño-Rivas

McCasland

Dixon

et al. 2012

Expert Systems with Applications

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We describe an approach to automatically invent/explore new mathematical theories, with the goal of producing results comparable to those produced by humans, as represented, for example, in the libraries of the Isabelle proof assistant. Our approach is based on 'schemes', which are terms in higher-order logic. We show that it is possible to automate the instantiation process of schemes to generate conjectures and definitions. We also show how the new definitions and the lemmata discovered during the exploration of a theory can be used, not only to help with the proof obligations during the exploration, but also to reduce redundancies inherent in most theory formation systems.We implemented our ideas in an automated tool, called IsaScheme, which employs Knuth-Bendix completion and recent automatic inductive proof tools.We have evaluated our system in a theory of natural numbers and a theory of lists.

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Conjecture Synthesis for Inductive Theories

Cited by 64 publications

References 17 publications

Zeno: An Automated Prover for Properties of Recursive Data Structures

Zeno: An Automated Prover for Properties of Recursive Data Structures

A Generic Cyclic Theorem Prover

Scheme-based theorem discovery and concept invention

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