946 research outputs found
Hipster: Integrating Theory Exploration in a Proof Assistant
This paper describes Hipster, a system integrating theory exploration with
the proof assistant Isabelle/HOL. Theory exploration is a technique for
automatically discovering new interesting lemmas in a given theory development.
Hipster can be used in two main modes. The first is exploratory mode, used for
automatically generating basic lemmas about a given set of datatypes and
functions in a new theory development. The second is proof mode, used in a
particular proof attempt, trying to discover the missing lemmas which would
allow the current goal to be proved. Hipster's proof mode complements and
boosts existing proof automation techniques that rely on automatically
selecting existing lemmas, by inventing new lemmas that need induction to be
proved. We show example uses of both modes
Anti-unification and Generalization: A Survey
Anti-unification (AU), also known as generalization, is a fundamental
operation used for inductive inference and is the dual operation to
unification, an operation at the foundation of theorem proving. Interest in AU
from the AI and related communities is growing, but without a systematic study
of the concept, nor surveys of existing work, investigations7 often resort to
developing application-specific methods that may be covered by existing
approaches. We provide the first survey of AU research and its applications,
together with a general framework for categorizing existing and future
developments.Comment: Accepted at IJCAI 2023 - Survey Trac
Proof-Pattern Recognition and Lemma Discovery in ACL2
We present a novel technique for combining statistical machine learning for
proof-pattern recognition with symbolic methods for lemma discovery. The
resulting tool, ACL2(ml), gathers proof statistics and uses statistical
pattern-recognition to pre-processes data from libraries, and then suggests
auxiliary lemmas in new proofs by analogy with already seen examples. This
paper presents the implementation of ACL2(ml) alongside theoretical
descriptions of the proof-pattern recognition and lemma discovery methods
involved in it
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