Goal-Oriented Conjecturing for Isabelle/HOL

  title={Goal-Oriented Conjecturing for Isabelle/HOL},
  author={Yutaka Nagashima and Julian Parsert},
We present PGT, a Proof Goal Transformer for Isabelle/HOL. Given a proof goal and its background context, PGT attempts to generate conjectures from the original goal by transforming the original proof goal. These conjectures should be weak enough to be provable by automation but sufficiently strong to identify and prove the original goal. By incorporating PGT into the pre-existing PSL framework, we exploit Isabelle’s strong automation to identify and prove such conjectures. 
Smart Induction for Isabelle/HOL (System Description)
This work presents smart_induct, a system that lists promising arguments for the induct tactic without relying on a search to solve an inductive problem in any problem domain.
Smart Induction for Isabelle/HOL (Tool Paper)
  • Yutaka Nagashima
  • Computer Science
    2020 Formal Methods in Computer Aided Design (FMCAD)
  • 2020
This work presents smart_induct, an interactive tool that lists promising arguments for the induct tactic without relying on a search that can be used to narrow the search space of automatic inductive provers.
Towards evolutionary theorem proving for isabelle/HOL
This paper proposes a novel approach to improve heuristics of automatic proof search in Isabelle/HOL using evolutionary computation and identifies challenges in discovering heuristic for automaticProof search.
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Evaluation of sem ind, a recommendation tool for proof by induction in Isabelle/HOL, shows that it improves the accuracy of recommendation and increases the median value of execution time for the most promising candidates within 5.0 seconds of timeout.
Faster Smarter Induction in Isabelle/HOL
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LiFtEr: Language to Encode Induction Heuristics for Isabelle/HOL
Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however they did not have a systematic way to
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Intelligent Computer Mathematics
A general overview of the PIDE project and its underlying document model, with built-in parallel evaluation and asynchronous interaction and ideas for the future are provided.
SeLFiE: Modular Semantic Reasoning for Induction in Isabelle/HOL
SeLFiE, a domain-specific language to encode experienced users' expertise on how to apply the induct tactic in Isabelle/HOL, facilitates the intricate interaction between syntactic and semantic analyses using semantic constructs while maintaining the modularity of each analysis.
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SeLFiE, a domain-specific language to encode experienced users' expertise on how to apply the induct tactic in Isabelle/HOL is presented, and semantic_induct, an automatic tool to recommend how to applied the induction tactic is presented.


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This work introduces a language, PSL, designed to capture high level proof strategies in Isabelle/HOL, and presents PSL's monadic interpreter to show that the underlying idea of PSL is transferable to other ITPs.
Conjecture Synthesis for Inductive Theories
A program for inductive theory formation, called IsaCoSy, which synthesises conjectures ‘bottom-up’ from the available constants and free variables, and is evaluated as a tool for automatically generating the background theories one would expect in a mature proof assistant, such as the Isabelle system.
Nitpick: A Counterexample Generator for Isabelle/HOL Based on the Relational Model Finder Kodkod
Experimental results on Isabelle theories and the TPTP library indicate that Nitpick generates more counterexamples than other model finders for higher-order logic, without restrictions on the form of the formulas to falsify.
The New Quickcheck for Isabelle - Random, Exhaustive and Symbolic Testing under One Roof
The new Quickcheck is a counterexample generator for Isabelle/HOL that uncovers faulty specifications and invalid conjectures using various testing strategies and integrates two novel testing strategies: exhaustive testing with concrete values; and symbolic testing, evaluating conjectures with a narrowing strategy.
Hipster: Integrating Theory Exploration in a Proof Assistant
Hipster’s proof mode complements and boosts existing proof automation techniques that rely on automatically selecting existing lemmas, by inventing new lemma that need induction to be proved.
Nitpick: A Counterexample Generator for Higher-Order Logic Based on a Relational Model Finder
Nitpick is a counterexample generator for Isabelle/HOL that builds on Kodkod, a SAT-based first-order relational model finder. Nitpick supports unbounded quantification, (co)inductive predicates and
Sharing HOL4 and HOL Light Proof Knowledge
A number of methods are proposed and evaluated, which strengthen proof automation by learning from proof libraries of different provers, which can be proved directly from the dependencies induced by similar proofs in the other library.
Initial Experiments with Statistical Conjecturing over Large Formal Corpora
This work proposes and implements methods for generating conjectures by using statistical analogies extracted from large formal libraries, and provides their initial evaluation.
Theory exploration with theorema
  • 2000
Isabelle/HOL - a proof assistant for higherorder logic, Lecture Notes in Computer Science, vol
  • 2283. Springer
  • 2002