Size-Change Termination and Transition Invariants

Heizmann, Matthias; Jones, Neil D.; Podelski, Andreas

doi:10.1007/978-3-642-15769-1_4

Cited by 22 publications

(29 citation statements)

References 31 publications

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“…A mechanized program logic may let us automate the particularly MSP-specific proof step of showing that erasure preserves semantics. The Erasure Theorem reduces this problem to essentially termination checks, and we can probably capitalize on recent advances in automated termination analysis, for example, those of Heizmann et al (2010).…”

Section: Discussionmentioning

confidence: 99%

Reasoning about multi-stage programs

Inoue¹,

Taha²

2016

J. Funct. Prog.

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We settle three basic questions that naturally arise when verifying code generators written in multi-stage functional programming languages. First, does adding staging to a language compromise any equalities that hold in the base language? Unfortunately it does, and more care is needed to reason about terms with free variables. Second, staging annotations, as the name "annotations" suggests, are often thought to be orthogonal to the behavior of a program, but when is this formally guaranteed to be true? We give termination conditions that characterize when this guarantee holds. Finally, do multi-stage languages satisfy useful, standard extensional properties, for example, that functions agreeing on all arguments are equivalent? We provide a sound and complete notion of applicative bisimulation, which establishes such properties or, in principle, any valid program equivalence. These results yield important insights into staging and allow us to prove the correctness of quite complicated multi-stage programs.

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Section: Discussionmentioning

confidence: 99%

Reasoning about multi-stage programs

Inoue¹,

Taha²

2016

J. Funct. Prog.

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Section: Discussionmentioning

confidence: 99%

Reasoning about Multi-stage Programs

Inoue

Taha

2012

Programming Languages and Systems

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Abstract. We settle three basic questions that naturally arise when verifying multi-stage functional programs. Firstly, does adding staging to a language compromise any equalities that hold in the base language? Unfortunately it does, and more care is needed to reason about terms with free variables. Secondly, staging annotations, as the name "annotations" suggests, are often thought to be orthogonal to the behavior of a program, but when is this formally guaranteed to be true? We give termination conditions that characterize when this guarantee holds. Finally, do multi-stage languages satisfy useful, standard extensional facts-for example, that functions agreeing on all arguments are equivalent? We provide a sound and complete notion of applicative bisimulation, which establishes such facts or, in principle, any valid program equivalence. These results greatly improve our understanding of staging, and allow us to prove the correctness of quite complicated multi-stage programs.

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“…In general, an in-depth comparison between such fairly different methods is an open research topic (e.g. see [13] for the comparison of the transition invariants and the size-change termination methods).…”

Section: Related Workmentioning

confidence: 99%

An Abstract Domain to Infer Ordinal-Valued Ranking Functions

Urban

Miné

2014

Programming Languages and Systems

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Abstract. The traditional method for proving program termination consists in inferring a ranking function. In many cases (i.e. programs with unbounded non-determinism), a single ranking function over natural numbers is not sufficient. Hence, we propose a new abstract domain to automatically infer ranking functions over ordinals.We extend an existing domain for piecewise-defined natural-valued ranking functions to polynomials in ω, where the polynomial coefficients are natural-valued functions of the program variables. The abstract domain is parametric in the choice of the maximum degree of the polynomial, and the types of functions used as polynomial coefficients.We have implemented a prototype static analyzer for a while-language by instantiating our domain using affine functions as polynomial coefficients. We successfully analyzed small but intricate examples that are out of the reach of existing methods.To our knowledge this is the first abstract domain able to reason about ordinals. Handling ordinals leads to a powerful approach for proving termination of imperative programs, which in particular subsumes existing techniques based on lexicographic ranking functions.

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Size-Change Termination and Transition Invariants

Cited by 22 publications

References 31 publications

Reasoning about multi-stage programs

Reasoning about multi-stage programs

Reasoning about Multi-stage Programs

An Abstract Domain to Infer Ordinal-Valued Ranking Functions

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