Intelligent Computer Mathematics

Libbrecht, Paul; Rebholz, Sandra; Herding, Daniel; Müller, Wolfgang; Tscheulin, Felix

doi:10.1007/978-3-642-31374-5

Cited by 9 publications

(5 citation statements)

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“…Auto-active verifiers, such as Dafny [6,7] and AutoProof [23] hide verification and interaction with the verification tool entirely behind annotations in the analyzed code. Interactive theorem provers, such as Coq [2] and Isabelle/HOL [14], primarily interact with users through scripts, such as structured proofs in Isabelle/Isar [13] and hide only little of the proof complexity behind other means of presentation even in advanced editors [25] or when proofs are found automatically, e.g., with Sledgehammer [15]. Many (hybrid systems) theorem provers (e.g., [1,18,20,24]) opt for implementing their proof calculus using axiom schemata or with trusted rules, which renders the features presented here soundness-critical.…”

Section: Discussionmentioning

confidence: 99%

Implicit and Explicit Proof Management in KeYmaera X

Mitsch¹

2021

Electron. Proc. Theor. Comput. Sci.

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Hybrid systems theorem proving provides strong correctness guarantees about the interacting discrete and continuous dynamics of cyber-physical systems. The trustworthiness of proofs rests on the soundness of the proof calculus and its correct implementation in a theorem prover. Correctness is easier to achieve with a soundness-critical core that is stripped to the bare minimum, but, as a consequence, proof convenience has to be regained outside the soundness-critical core with proof management techniques. We present modeling and proof management techniques that are built on top of the soundness-critical core of KeYmaera X to enable expanding definitions, parametric proofs, lemmas, and other useful proof techniques in hybrid systems proofs. Our techniques steer the uniform substitution implementation of the differential dynamic logic proof calculus in KeYmaera X to allow users choose when and how in a proof abstract formulas, terms, or programs become expanded to their concrete definitions, and when and how lemmas and sub-proofs are combined to a full proof. The same techniques are exploited in implicit sub-proofs (without making such sub-proofs explicit to the user) to provide proof features, such as temporarily hiding formulas, which are notoriously difficult to get right when implemented in the prover core, but become trustworthy as proof management techniques outside the core. We illustrate our approach with several useful proof techniques and discuss their presentation on the KeYmaera X user interface.

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Section: Discussionmentioning

confidence: 99%

Implicit and Explicit Proof Management in KeYmaera X

Mitsch¹

2021

Electron. Proc. Theor. Comput. Sci.

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“…Interactive theorem provers, such as Coq [20] and Isabelle [22], primarily interact with users through tactic scripts, such as structured proofs in Isabelle/Isar [21]. Their user interfaces (e. g., CoqIDE [20], ProofGeneral [5], jEdit [31]) focus on text editing support for writing tactics and let users inspect the proof state and open goals by placing the cursor in the tactic script. Navigation with cursors introduced a limited form of proof by pointing [4] to fold or unfold equations.…”

Section: Related Workmentioning

confidence: 99%

The KeYmaera X Proof IDE - Concepts on Usability in Hybrid Systems Theorem Proving

Mitsch

Platzer

2017

Electron. Proc. Theor. Comput. Sci.

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Hybrid systems verification is quite important for developing correct controllers for physical systems, but is also challenging. Verification engineers, thus, need to be empowered with ways of guiding hybrid systems verification while receiving as much help from automation as possible. Due to undecidability, verification tools need sufficient means for intervening during the verification and need to allow verification engineers to provide system design insights.This paper presents the design ideas behind the user interface for the hybrid systems theorem prover KeYmaera X. We discuss how they make it easier to prove hybrid systems as well as help learn how to conduct proofs in the first place. Unsurprisingly, the most difficult user interface challenges come from the desire to integrate automation and human guidance. We also share thoughts how the success of such a user interface design could be evaluated and anecdotal observations about it.

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“…This case is out of the scope of this paper, it requires semantic alignment. Several approaches to align semantics have proposed in the literature, they are based on the definition of institutions as models [72][73][74].…”

Section: Modeling Languagesmentioning

confidence: 99%

Making explicit domain knowledge in formal system development

Aït‐Ameur

Méry

2016

Science of Computer Programming

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Constraints description constructs are offered by the ontology modeling language to define constraints on classes, properties or on whole ontology. In the engineering domain, the more the constraint description language is rich, the more the expressed concepts of the ontologies are precisely described. Checking these constraints depend on the used constraint solving techniques associated to the ontology modeling language.

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Intelligent Computer Mathematics

Abstract: The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Cited by 9 publications

References 0 publications

Implicit and Explicit Proof Management in KeYmaera X

Implicit and Explicit Proof Management in KeYmaera X

The KeYmaera X Proof IDE - Concepts on Usability in Hybrid Systems Theorem Proving

Making explicit domain knowledge in formal system development

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