Extending the HOL theorem prover with a computer algebra system to reason about the reals

Author(s):  
John Harrison ◽  
Laurent Théry
10.29007/r5k7 ◽  
2018 ◽  
Author(s):  
Laura Meikle ◽  
Jacques Fleuriot

In this paper we describe a number of automation techniques which we have developed to assist us in reasoning formally about geometry in the interactive theorem prover Isabelle. These range from simplification rules to a user-centric integration of Isabelle with the computer algebra system QEPCAD-B. We demonstrate the power and limitations of these techniques through illustrative examples taken from our verification of a triangulation algorithm.


1998 ◽  
Vol 37 (03) ◽  
pp. 235-238 ◽  
Author(s):  
M. El-Taha ◽  
D. E. Clark

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.


2021 ◽  
Vol 43 (1) ◽  
pp. 1-46
Author(s):  
David Sanan ◽  
Yongwang Zhao ◽  
Shang-Wei Lin ◽  
Liu Yang

To make feasible and scalable the verification of large and complex concurrent systems, it is necessary the use of compositional techniques even at the highest abstraction layers. When focusing on the lowest software abstraction layers, such as the implementation or the machine code, the high level of detail of those layers makes the direct verification of properties very difficult and expensive. It is therefore essential to use techniques allowing to simplify the verification on these layers. One technique to tackle this challenge is top-down verification where by means of simulation properties verified on top layers (representing abstract specifications of a system) are propagated down to the lowest layers (that are an implementation of the top layers). There is no need to say that simulation of concurrent systems implies a greater level of complexity, and having compositional techniques to check simulation between layers is also desirable when seeking for both feasibility and scalability of the refinement verification. In this article, we present CSim 2 a (compositional) rely-guarantee-based framework for the top-down verification of complex concurrent systems in the Isabelle/HOL theorem prover. CSim 2 uses CSimpl, a language with a high degree of expressiveness designed for the specification of concurrent programs. Thanks to its expressibility, CSimpl is able to model many of the features found in real world programming languages like exceptions, assertions, and procedures. CSim 2 provides a framework for the verification of rely-guarantee properties to compositionally reason on CSimpl specifications. Focusing on top-down verification, CSim 2 provides a simulation-based framework for the preservation of CSimpl rely-guarantee properties from specifications to implementations. By using the simulation framework, properties proven on the top layers (abstract specifications) are compositionally propagated down to the lowest layers (source or machine code) in each concurrent component of the system. Finally, we show the usability of CSim 2 by running a case study over two CSimpl specifications of an Arinc-653 communication service. In this case study, we prove a complex property on a specification, and we use CSim 2 to preserve the property on lower abstraction layers.


1995 ◽  
Vol 10 (3) ◽  
pp. 329-337 ◽  
Author(s):  
John Hutton ◽  
James Hutton

2020 ◽  
Vol 9 (1) ◽  
pp. 53
Author(s):  
Kamhar Ngado ◽  
Rosnawati Rosnawati ◽  
Heri Retnawati ◽  
Sri Andayani

2021 ◽  
Vol 254 ◽  
pp. 02006
Author(s):  
Liubov Feshchenko ◽  
Gleb Vodinchar

The paper describes a technology for the automated compilation of equations for shell models of turbulence in the computer algebra system Maple. A general form of equations for the coefficients of nonlinear interactions is given, which will ensure that the required combination of quadratic invariants and power-law solutions is fulfilled in the model. Described the codes for the Maple system allowing to generate and solve systems of equations for the coefficients. The proposed technology allows you to quickly and accurately generate classes of shell models with the desired properties.


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