Goal-Oriented Conjecturing for Isabelle/HOL

@inproceedings{Nagashima2018GoalOrientedCF,
  title={Goal-Oriented Conjecturing for Isabelle/HOL},
  author={Yutaka Nagashima and Julian Parsert},
  booktitle={CICM},
  year={2018}
}
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. 
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References

SHOWING 1-10 OF 10 REFERENCES
A Proof Strategy Language and Proof Script Generation for Isabelle/HOL
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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
TLDR
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