Hidden verification for computational mathematics

Gottliebsen, Hanne; Kelsey, Tom; Martin, Ursula

doi:10.1016/j.jsc.2004.12.005

Cited by 6 publications

(2 citation statements)

References 32 publications

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“…Going in the opposite direction, CAS users may want to access ATP or ITP systems. Adams et al [1] use PVS to verify side conditions generated in computations in Maple; Gottliebsen, Kelsey, and Martin [21] make use of similar ideas. Systems such as Analytica [5] and Theorema [11] provide ATP-or ITP-style behavior from within Mathematica.…”

Section: Related Workmentioning

confidence: 99%

A bi-directional extensible interface between Lean and Mathematica

Lewis¹,

Wu²

2021

Preprint

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We implement a user-extensible ad hoc connection between the Lean proof assistant and the computer algebra system Mathematica. By reflecting the syntax of each system in the other and providing a flexible interface for extending translation, our connection allows for the exchange of arbitrary information between the two systems.We show how to make use of the Lean metaprogramming framework to verify certain Mathematica computations, so that the rigor of the proof assistant is not compromised. We also use Mathematica as an untrusted oracle to guide proof search in the proof assistant and interact with a Mathematica notebook from within a Lean session. In the other direction, we import and process Lean declarations from within Mathematica. The proof assistant library serves as a database of mathematical knowledge that the CAS can display and explore.

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Section: Related Workmentioning

confidence: 99%

A bi-directional extensible interface between Lean and Mathematica

Lewis¹,

Wu²

2021

Preprint

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“…One approach would be to extend the type checker with computer algebra capabilities. Works dealing with a combination of CASs and automated theorem provers have been presented in recent years . Thus, a combination of the Haskell type checker with a CAS, such as Maple, could be seen as a distant goal for the application of type theory to conceptual modelling.…”

Section: Conceptual Approaches To Mathematical Modellingmentioning

confidence: 99%

Conceptual modelling: Towards detecting modelling errors in engineering applications

Gürlebeck

Legatiuk

Nilsson

et al. 2019

Math Methods in App Sciences

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Rapid advancements of modern technologies put high demands on mathematical modelling of engineering systems. Typically, systems are no longer "simple" objects, but rather coupled systems involving multiphysics phenomena, the modelling of which involves coupling of models that describe different phenomena. After constructing a mathematical model, it is essential to analyse the correctness of the coupled models and to detect modelling errors compromising the final modelling result. Broadly, there are two classes of modelling errors: (a) errors related to abstract modelling, eg, conceptual errors concerning the coherence of a model as a whole and (b) errors related to concrete modelling or instance modelling, eg, questions of approximation quality and implementation. Instance modelling errors, on the one hand, are relatively well understood. Abstract modelling errors, on the other, are not appropriately addressed by modern modelling methodologies. The aim of this paper is to initiate a discussion on abstract approaches and their usability for mathematical modelling of engineering systems with the goal of making it possible to catch conceptual modelling errors early and automatically by computer assistant tools. To that end, we argue that it is necessary to identify and employ suitable mathematical abstractions to capture an accurate conceptual description of the process of modelling engineering systems.

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Designing a Solver for Arithmetic Constraints to Support Education in Mathematics

Tomás

Moreira

Pereira

IFIP International Federation for Information Processing

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Abstract. We present a conditional rewrite system for arithmetic and membership univariate constraints over real numbers, designed for computer assisted learning (CAL) in elementary math. Two fundamental principles guided the design of the proposed rewrite rules: cognitive fidelity (emulating steps students should take) and correctnesSf aiming that step-by-step solutions to problems look like ones carried out by students. In order to gain more flexibility to modify rules, add new ones and customize solvers, the rules are written in a specification language and then compiled to Prolog. The rewrite system is complete for a relevant subset of problems found in high-school math textbooks.

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Hidden verification for computational mathematics

Cited by 6 publications

References 32 publications

A bi-directional extensible interface between Lean and Mathematica

A bi-directional extensible interface between Lean and Mathematica

Conceptual modelling: Towards detecting modelling errors in engineering applications

Designing a Solver for Arithmetic Constraints to Support Education in Mathematics

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