59 research outputs found
Automating Inductive Proofs using Theory Exploration
HipSpec is a system for automatically deriving and proving properties about functional programs. It uses a novel approach, combining theory exploration, counterexample testing and inductive theorem proving. HipSpec automatically generates a set of equational theorems about the available recursive functions of a program. These equational properties make up an algebraic specification for the program and can in addition be used as a background theory for proving additional user-stated properties. Experimental results are encouraging: HipSpec compares favourably to other inductive theorem provers and theory exploration systems
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
Dynamic Rippling, Middle-Out Reasoning and Lemma Discovery
We present a succinct account of dynamic rippling, a technique
used to guide the automation of inductive proofs. This simplifies
termination proofs for rippling and hence facilitates extending the technique
in ways that preserve termination. We illustrate this by extending
rippling with a terminating version of middle-out reasoning for lemma
speculation. This supports automatic speculation of schematic lemmas
which are incrementally instantiated by unification as the rippling proof
progresses. Middle-out reasoning and lemma speculation have been implemented
in higher-order logic and evaluated on typical libraries of formalised
mathematics. This reveals that, when applied, the technique
often finds the needed lemmas to complete the proof, but it is not as
frequently applicable as initially expected. In comparison, we show that
theory formation methods, combined with simpler proof methods, offer
an effective alternative
Parameterized abstractions used for proof-planning
In order to cope with large case studies arising from the application of formal methods in an industrial setting, this paper presents new techniques to support hierarchical proof planning. Following the paradigm of difference reduction, proofs are obtained by removing syntactical differences between parts of the formula to be proven step by step. To guide this manipulation we introduce dynamic abstractions of terms. These abstractions are parameterized by the individual goals of the manipulation and are especially designed to ease the proof search based on heuristics. The hierarchical approach and thus the decomposition of the original goal into several subgoals enables the use of different abstractions or different parameters of an abstraction within the proof search. In this paper we will present one of these dynamic abstractions together with heuristics to guide the proof search in the abstract space
- …