Certified Computer Algebra on Top of an Interactive Theorem Prover

Kaliszyk, Cezary; Wiedijk, Freek

doi:10.1007/978-3-540-73086-6_8

Cited by 27 publications

(24 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By this prototype we have demonstrated in that it is possible to build a computer algebra system in a proof assistant [18]. Such architecture guarantees that the system will make no mistakes.…”

Section: Approach Towards Cas-like Functionalitymentioning

confidence: 97%

“…There are various reasons for the mistakes found in mainstream CAS systems: assumptions can be lost, types of expressions can be forgotten or algorithms of the system themselves may contain implementation errors [18]. Simple mistakes have been found and fixed over the years.…”

Section: Approach Towards Cas-like Functionalitymentioning

confidence: 99%

“…as an oracle, whereas in other approaches the prover takes the output of a CAS and then tries to build a verified theorem out of it. A longer list of frameworks for information exchange and bridges between systems can be found in [18].…”

Section: Related Workmentioning

confidence: 99%

See 2 more Smart Citations

CTP-based programming languages?

Haftmann

Kaliszyk

Neuper

2010

ACM Commun. Comput. Algebra

Self Cite

View full text Add to dashboard Cite

This paper discusses plans for joint work in order to gain early feedback from the community. Three lines of work pursued independently so far shall be joined: (1) narrowing the gap between declarative program specification and program generation already working in Isabelle, (2) reusing work, which embedded an input-response-loop resembling Computer Algebra Systems (CAS) into HOL Light, and (3) reconstructing an experimental language for applied mathematics by exploiting established as well as emerging features of Isabelle/Isar.These plans have to be seen as part of a variety of highly active research areas -on "integration of the deduction and the computational power" of Computer Theorem Proving (CTP) and CAS respectively (Calculemus), on "innovative theoretical and technological solutions for content-based systems" (MKM), on "Programming Languages for Mechanized Mathematics Systems" (PLMMS), just to cite from some related interest groups.Facing the abundant variety of approaches, of intermediate results and of ongoing developments, and taking under consideration the many difficulties in integrating such approaches, we pursue pragmatic goals:Design a component indispensable for working engineers, a programming language for engineering applications. Use Isabelle for an experimental embedding of the language, which is useful at least in engineering education as soon as possible.

show abstract

Section: Approach Towards Cas-like Functionalitymentioning

confidence: 97%

Section: Approach Towards Cas-like Functionalitymentioning

confidence: 99%

See 1 more Smart Citation

CTP-based programming languages?

Haftmann

Kaliszyk

Neuper

2010

ACM Commun. Comput. Algebra

Self Cite

View full text Add to dashboard Cite

show abstract

“…Alternatively, one can build a CAS inside a proof assistant without reflection, such that proof terms are carried through the computation. Kaliszyk and Wiedijk [13] implement such a system in HOL Light, exhibiting techniques for simplification, numeric approximation, and antiderivation.…”

Section: 1 Related Workmentioning

confidence: 99%

An Extensible Ad Hoc Interface between Lean and Mathematica

Lewis

2017

Electron. Proc. Theor. Comput. Sci.

View full text Add to dashboard Cite

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.Comment: In Proceedings PxTP 2017, arXiv:1712.0089

show abstract

“…C. Kaliszyk etc [5] present a prototype of a computer algebra system that is on top of a proof assistant HOL Light. This method makes sure that the algebraic calculation will make no mistake since the proof assist will check the correctness of all simplifications and the operation performed.…”

Section: Introductionmentioning

confidence: 99%

A preliminary framework for geometric basis computing pattern

Wang

2010

2010 IEEE International Conference on Progress in Informatics and Computing

View full text Add to dashboard Cite

Geometric problems are usually solved by algebraic methods, which narrows the capacity of geometry. We represent a preliminary framework for geometric basis computing pattern.The pattern is based on He's theory and solves the problems in the synthetic way. We define the geometric basis and use an axiomatic prover to generate a sequence of geometric bases.Computing is made according to the sequence. We also give an example to demonstration the feasibility of our approach.

show abstract

Certified Computer Algebra on Top of an Interactive Theorem Prover

Cited by 27 publications

References 14 publications

CTP-based programming languages?

CTP-based programming languages?

An Extensible Ad Hoc Interface between Lean and Mathematica

A preliminary framework for geometric basis computing pattern

Contact Info

Product

Resources

About