A New Invariant Rule for the Analysis of Loops with Non-standard Control Flows

Steinhöfel, Dominic; Wasser, Nathan

doi:10.1007/978-3-319-66845-1_18

Cited by 13 publications

(12 citation statements)

References 16 publications

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“…Logics that prove total correctness directly (e.g., [25,19]) are used more rarely. This is despite the fact that relatively recent work in automated termination proving (e.g., [5,3,13,6,12]) shows that it is beneficial to use information obtained by proving a program (e.g., invariants) in the termination argument: in [5], a cooperation graph is used to enable the cooperation between a safety prover and the rank synthesis tool, in [3], a variance analysis is introduced that is parametric in an invariance analysis and Ramsey-based termination arguments are improved with lexicographic ordering in [13].…”

Section: Related Workmentioning

confidence: 99%

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Reducing Total Correctness to Partial Correctness by a Transformation of the Language Semantics

Buruiana

Ciobâcă

2019

Electron. Proc. Theor. Comput. Sci.

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We give a language-parametric solution to the problem of total correctness, by automatically reducing it to the problem of partial correctness, under the assumption that an expression whose value decreases with each program step in a well-founded order is provided. Our approach assumes that the programming language semantics is given as a rewrite theory. We implement a prototype on top of the RMT tool and we show that it works in practice on a number of examples.

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Section: Related Workmentioning

confidence: 99%

“…More rarely, logics that can directly prove total correctness (e.g., [25,19]) are used. However, recent work in automated termination proving (e.g., [5,3,13,6,12]) shows that it is beneficial to use information obtained by proving properties of a program (e.g., invariants) in the termination argument.…”

Section: Introductionmentioning

confidence: 99%

Reducing Total Correctness to Partial Correctness by a Transformation of the Language Semantics

Buruiana

Ciobâcă

2019

Electron. Proc. Theor. Comput. Sci.

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“…Another change is that the definition of the rule for the empty loop scope in KeY no longer matches the original rule of [2], where the index was set to true. Now, the index is initialized to true by the loop invariant rule, and the rule processing the empty loop scope checks for its value to decide how to continue:…”

Section: Implementation Of Loop Scope Rules In Keymentioning

confidence: 99%

“…These allow a sound loop invariant rule (which does not require program transformation of the loop body) for programs with non-standard control-flow. In [2] it was shown that an implementation of this new loop invariant rule in KeY [1] also decreases proof size when compared to the existing rule.…”

Section: Introductionmentioning

confidence: 99%

Technical Report: Using Loop Scopes with for-Loops

Wasser,

Steinhöfel

2019

Preprint

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Loop scopes have been shown to be a helpful tool in creating sound loop invariant rules which do not require program transformation of the loop body. Here we extend this idea from while-loops to for-loops and also present sound loop unrolling rules for while-and for-loops, which require neither program transformation of the loop body, nor the use of nested modalities. This approach allows for-loops to be treated as firstclass citizens -rather than the usual approach of transforming for-loops into while-loops -which makes semi-automated proofs easier to follow for the user, who may need to provide help in order to finish the proof.

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“…Indexed loop scopes were introduced in [18] to allow a sound loop invariant rule (which does not require program transformation of the loop body) in dynamic logic [10] for while loops containing statements which complete abruptly [8,Chapter 14.1]. In [16] it was shown that an implementation of this new loop invariant rule in KeY 1 [1] also decreases proof size when compared to the existing rule.…”

Section: Introductionmentioning

confidence: 99%

Treating for-Loops as First-Class Citizens in Proofs

Wasser,

Steinhöfel

2020

Preprint

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Indexed loop scopes have been shown to be a helpful tool in creating sound loop invariant rules in dynamic logic for programming languages with abrupt completion, such as Java. These rules do not require program transformation of the loop body, as other approaches to dealing with abrupt completion do. However, indexed loop scopes were designed specifically to provide a loop invariant rule for while loops and work rather opaquely. Here we propose replacing indexed loop scopes with a more transparent solution, which also lets us extend this idea from while loops to for loops. We further present sound loop unrolling rules for while, do and for loops, which require neither program transformation of the loop body, nor the use of nested modalities. This approach allows for loops to be treated as first-class citizens in proofs -rather than the usual approach of transforming for loops into while loops -which makes semi-automated proofs more transparent and easier to follow for the user, whose interactions may be required in order to close the proofs.

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A New Invariant Rule for the Analysis of Loops with Non-standard Control Flows

Cited by 13 publications

References 16 publications

Reducing Total Correctness to Partial Correctness by a Transformation of the Language Semantics

Reducing Total Correctness to Partial Correctness by a Transformation of the Language Semantics

Technical Report: Using Loop Scopes with for-Loops

Treating for-Loops as First-Class Citizens in Proofs

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