Book Chapter10.1007/978-3-319-22102-1_11
Proof-Producing Reflection for HOL
Benja Fallenstein,Ramana Kumar +1 more
- 24 Aug 2015
- pp 170-186
10
TL;DR: In this article, the authors present a reflection principle of the form "If the cardinality of a cardinal is provable, then the cardinal has the same meaning both inside and outside of the HOL4 theorem prover".
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Abstract: We present a reflection principle of the form “If \(\ulcorner \varphi \urcorner \) is provable, then \(\varphi \)” implemented in the HOL4 theorem prover, assuming the existence of a large cardinal. We use the large-cardinal assumption to construct a model of HOL within HOL, and show how to ensure \(\varphi \) has the same meaning both inside and outside of this model. Soundness of HOL implies that if \(\ulcorner \varphi \urcorner \) is provable, then it is true in this model, and hence \(\varphi \) holds. We additionally show how this reflection principle can be extended, assuming an infinite hierarchy of large cardinals, to implement model polymorphism, a technique designed for verifying systems with self-replacement functionality.
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Citations
QED at Large: A Survey of Engineering of Formally Verified Software
TL;DR: A survey of the literature on proof engineering for program correctness can be found in this article, covering impact in practice, foundations, proof automation, proof organization, and practical proof development.
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Tom Everitt
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Formalising Liveness Properties in Event-B with the Reflexive EB4EB Framework
TL;DR: In this paper , the authors propose a formalisation and operationalisation of proof obligations associated to liveness properties expressed in linear temporal logic (LTL) for Event-B models.
Standalone Event-B Models Analysis Relying on the EB4EB Meta-theory
TL;DR: In this article , the EB4EB framework is extended to support new system analysis mechanisms associated to properties that are not natively present in Event-B. This methodology is used to define three analyses: deadlock-freeness, invariant weakness analysis and reachability.
Model Transformation as Conservative Theory-Transformation
TL;DR: This work presents a new technique to construct tool support for domain-specific languages (DSLs) inside the interactive theorem prover environment Isabelle, based on modeling the DSL formally in higher-order logic (HOL), modeling the API of Isabelle inside it, and defining the transformation between these two.
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