Improvements in Formula Generalization

Aderhold, Markus

doi:10.1007/978-3-540-73595-3_16

Cited by 6 publications

(8 citation statements)

References 7 publications

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“…The need for a lemma is typically observed when a proof attempt is blocked, or when fertilisation leaves a non-trivial subgoal 5 . There are various heuristics for lemma discovery, the most successful being lemma calculation which applies common subterm generalisation to the goal and attempts to prove the resulting lemma by induction [5,13,9,1].…”

Section: Ripplingmentioning

confidence: 99%

Case-Analysis for Rippling and Inductive Proof

Johansson

Dixon

Bundy

2010

Interactive Theorem Proving

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Abstract. Rippling is a heuristic used to guide rewriting and is typically used for inductive theorem proving. We introduce a method to support case-analysis within rippling. Like earlier work, this allows goals containing if-statements to be proved automatically. The new contribution is that our method also supports case-analysis on datatypes. By locating the case-analysis as a step within rippling we also maintain the termination. The work has been implemented in IsaPlanner and used to extend the existing inductive proof method. We evaluate this extended prover on a large set of examples from Isabelle's theory library and from the inductive theorem proving literature. We find that this leads to a significant improvement in the coverage of inductive theorem proving. The main limitations of the extended prover are identified, highlight the need for advances in the treatment of assumptions during rippling and when conjecturing lemmas.

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Section: Ripplingmentioning

confidence: 99%

Case-Analysis for Rippling and Inductive Proof

Johansson

Dixon

Bundy

2010

Interactive Theorem Proving

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“…The lemma created by calculation is then subjected to an inductive proof attempt. Other generalisation techniques used in lemma calculation have been studied in [1]. The proof-plan for the stepcase of our inductive prover is summarised by the functional pseudo-tactic shown in Fig.…”

Section: Definition 6 (Blocked)mentioning

confidence: 99%

“…We use the symbol @ for the list append function, # for cons, [ ] for nil, as well as the usual notation where [1,2,3] is the list 1#2#3#[ ]. Variables which are allowed to be instantiated by unification are written ?F , following the Isabelle convention.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Rippling, Middle-Out Reasoning and Lemma Discovery

Johansson

Dixon

Bundy

2010

Verification, Induction, Termination Analysis

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Abstract. 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.

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“…The automation of inductive proofs has been a research topic for more than 30 years. Several systems for reasoning about programs in functional programming languages have induction heuristics, most notably ACL2 [8,7], Verifun [29,1], RRL [18], and Rippling [9]. ACL2 has a powerful mechanism for generating induction schemes from recursive definitions.…”

Section: Related Workmentioning

confidence: 99%

“…VeriFun [31] is a semi-automatic verification tool for functional programs written in the L [30] programming language. Its induction formula generalisation heuristics have been developed in a long line of research [29,15,1]. The heuristics are inverse applications of sound inferences.…”

Section: Related Workmentioning

confidence: 99%

Generalisation of Induction Formulae based on Proving by Symbolic Execution

Wallenburg

EPiC Series in Computing

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Induction is a powerful method that can be used to prove the total correctness of program loops. Unfortunately the induction proving process in an interactive theorem prover is often very cumbersome. In particular it can be difficult to find the right induction formula. We describe a method for generalising induction formulae by analysing a symbolic proof attempt in a semi-interactive first-order theorem prover. Based on the proof attempt we introduce universally quantified variables, meta-variables and sets of constraints on these. The constraints describe the conditions for a successful proof. By the help of examples, we outline some classes of problems and their associated constraint solutions, and possible ways to automate the constraint solving.

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Improvements in Formula Generalization

Cited by 6 publications

References 7 publications

Case-Analysis for Rippling and Inductive Proof

Case-Analysis for Rippling and Inductive Proof

Dynamic Rippling, Middle-Out Reasoning and Lemma Discovery

Generalisation of Induction Formulae based on Proving by Symbolic Execution

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