A Calculus for and Termination of Rippling

Basin, David; Walsh, Toby

doi:10.1007/978-94-009-1675-3_5

Cited by 16 publications

(7 citation statements)

References 10 publications

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“…Below we provide a short description of rippling. For a full account see [3,9,11]. We implement rippling with an annotate method and a wave method.…”

Section: Rippling Methodsmentioning

confidence: 99%

An Integrated Approach to High Integrity Software Verification

Ireland¹,

Ellis²,

Cook³

et al. 2006

J Autom Reasoning

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Using automated reasoning techniques, we tackle the niche activity of proving that a program is free from run-time exceptions. Such a property is particularly valuable in high integrity software, for example, safety-or security-critical applications. The context for our work is the SPARK Approach for the development of high integrity software. The SPARK Approach provides a significant degree of automation in proving exception freedom. Where this automation fails, however, the programmer is burdened with the task of interactively constructing a proof and possibly also having to supply auxiliary program annotations. We minimize this burden by increasing the automation, through an integration of proof planning and a program analysis oracle. We advocate a 'cooperative' integration, where prooffailure analysis directly constrains the search for auxiliary program annotations. The approach has been successfully tested on industrial data.

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“…Below we provide a short description of rippling. For a full account see [3,9,11]. We implement rippling with an annotate method and a wave method.…”

Section: Rippling Methodsmentioning

confidence: 99%

An Integrated Approach to High Integrity Software Verification

Ireland¹,

Ellis²,

Cook³

et al. 2006

J Autom Reasoning

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“…Since rippling was developed for induction, it is not surprising that it is also applicable to the verification of while-loop programs. For a full account of rippling see (Basin and Walsh, 1996;Bundy et al, 1993).…”

Section: Proof Planningmentioning

confidence: 99%

Combining Proof Plans with Partial Order Planning for Imperative Program Synthesis

Ireland

Stark

2006

Autom Software Eng

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The structured programming literature provides methods and a wealth of heuristic knowledge for guiding the construction of provably correct imperative programs. We investigate these methods and heuristics as a basis for mechanizing program synthesis. Our approach combines proof planning with conventional partial order planning. Proof planning is an automated theorem proving technique which uses high-level proof plans to guide the search for proofs. Proof plans are structured in terms of proof methods, which encapsulate heuristics for guiding proof search. We demonstrate that proof planning provides a local perspective on the synthesis task. In particular, we show that proof methods can be extended to represent heuristics for guiding program construction. Partial order planning complements proof planning by providing a global perspective on the synthesis task. This means that it allows us to reason about the order in which program fragments are composed. Our hybrid approach has been implemented in a semi-automatic system called BERTHA. BERTHA supports partial correctness and has been tested on a wide range of non-trivial programming examples.

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“…Rippling [4,8,9] is a kind of rewriting, used in inductive proofs. It is based on the idea that very often the induction hypothesis and the conclusion are syntactically similar.…”

Section: The Use Of Rippling In the Induction Proofmentioning

confidence: 99%

“…In our system for the first goal, we use sorted logic with a type hierarchy; it allows us to reduce the search space and also to avoid the synthesis of incorrect function branches. Second, we suggest here to plan the proof using a rippling heuristic [1,4,[7][8][9] for constructing the proof path corresponding to recursive branch synthesis.…”

mentioning

confidence: 99%

An approach to automatic deductive synthesis of functional programs

Korukhova

2007

Ann Math Artif Intell

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The work deals with automatic deductive synthesis of functional programs. Formal specification of a program is taken as a mathematical existence theorem and while proving it, we derive a program and simultaneously prove that this program corresponds to given specification. Several problems have to be resolved for automatic synthesis: the choice of synthesis rules that allows us to derive the basic constructions of a functional program, order of rule application and choice of a particular induction rule. The method proposed here is based on the deductive tableau method. The basic method gives rules for functional program construction.To determine the proof strategy we use some external heuristics, including rippling. And for the induction hypothesis formation the combination of rippling and the deductive tableau method became very useful. The proposed techniques are implemented in the system ALISA (Automatic Lisp Synthesizer) and used for automatic synthesis of several functions in the Lisp language.

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A Calculus for and Termination of Rippling

Cited by 16 publications

References 10 publications

An Integrated Approach to High Integrity Software Verification

An Integrated Approach to High Integrity Software Verification

Combining Proof Plans with Partial Order Planning for Imperative Program Synthesis

An approach to automatic deductive synthesis of functional programs

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