Using middle-out reasoning to control the synthesis of tail-recursive programs

Hesketh, Jane; Bundy, Alan; Smaill, Alan

doi:10.1007/3-540-55602-8_174

Cited by 6 publications

(4 citation statements)

References 6 publications

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“…[13,15], is that ours ensures termination. Our restricted unification heuristic also efficiently cuts out undesirable unifiers, while previous work had to apply filtering of unwanted results after unification [13], or use heuristics specific to rippling [15].…”

Section: Related Workmentioning

confidence: 95%

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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Section: Related Workmentioning

confidence: 95%

Dynamic Rippling, Middle-Out Reasoning and Lemma Discovery

Johansson

Dixon

Bundy

2010

Verification, Induction, Termination Analysis

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“…Hesketh's work, however, was much broader than ours in that she unified a number of different kinds of generalization. Moreover, she was also able to synthesize tail-recursive functions given equivalent naive recursive definitions (Hesketh et al, 1992).…”

Section: Related Workmentioning

confidence: 99%

Automatic verification of functions with accumulating parameters

Ireland¹,

Bundy²

1999

J. Funct. Prog.

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Proof by mathematical induction plays a crucial role in reasoning about functional programs. A generalization step often holds the key to discovering an inductive proof. We present a generalization technique which is particularly applicable when reasoning about functional programs involving accumulating parameters. We provide empirical evidence for the success of our technique and show how it is contributing to the ongoing development of a parallelizing compiler for Standard ML.

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“…Assuming d denotes a constant then pri(d) evaluates to M 1 (bl 1 c). Substituting this accumulator term for d in (8) gives a schematic conclusion of the form: g(f(c 1 (a; b) " 1 ; M 1 (bl 1 c)); c 1 (a; b) "…”

Section: Primary Accumulator Termsmentioning

confidence: 99%

“…k ; t)))) " 1 7 Note that the conclusion has been -reduced automatically. 8 Again the conclusion has been -reduced automatically.…”

Section: Second Proof Attemptmentioning

confidence: 99%

Extensions to a generalization critic for inductive proof

Ireland

Bundy

1996

Automated Deduction — Cade-13

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In earlier papers a critic for automatically generalizing conjectures in the context of failed inductive proofs was presented. The critic exploits the partial success of the search control heuristic known as rippling. Through empirical testing a natural generalization and extension of the basic critic emerged. Here we describe our extended generalization critic together with some promising experimental results.

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Using middle-out reasoning to control the synthesis of tail-recursive programs

Cited by 6 publications

References 6 publications

Dynamic Rippling, Middle-Out Reasoning and Lemma Discovery

Dynamic Rippling, Middle-Out Reasoning and Lemma Discovery

Automatic verification of functions with accumulating parameters

Extensions to a generalization critic for inductive proof

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