System Description: GCLCprover + GeoThms

“…Along the proof, this equality is transformed step-by-step, until it becomes trivial. For more details about this prover, see [17]. -theorem provers based on the Gröbner bases method and on the Wu's method.…”

Section: Built-in Theorem Proversmentioning

confidence: 99%

Geometry Constructions Language

Janicic

2009

J Autom Reasoning

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Geometry Constructions Language (gcl) is a language for explicit descriptions of constructions in Euclidean plane and of their properties. Other mathematical objects can also be described in the language. The language gcl is intuitive and simple, yet it supports arrays, flow control structures, user-defined procedures, etc. The processors for the gcl language -applications gclc and Wingclc-enable visualization of described objects and producing of mathematical illustrations, provide different semantical information and support for automated proving of properties of the constructed objects. These features make the tools gclc and Wingclc powerful mechanized geometry systems and they have thousands of users worldwide.

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“…This description of the area method should be sufficient for a complete understanding of the method, and for making a new implementation a straightforward task. This paper also summarises our results, experiences, and descriptions of our software systems related to the area method [30,33,43,45,50,52].…”

Section: Introductionmentioning

confidence: 98%

“…-within a generic proof assistant (Coq [59])-implemented by Narboux [43]; -within a dynamic geometry tool (GCLC [29])-implemented by Janičić and Quaresma [33];…”

Section: Introductionmentioning

confidence: 99%

The Area Method

2010

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The area method for Euclidean constructive geometry was proposed by Chou, Gao and Zhang in the early 1990's. The method can efficiently prove many non-trivial geometry theorems and is one of the most interesting and most successful methods for automated theorem proving in geometry. The method produces proofs that are often very concise and human-readable. In this paper, we provide a first complete presentation of the method. We provide both algorithmic and implementation details that were omitted in the original presentations. We also give a variant of Chou, Gao and Zhang's axiom system. Based on this axiom system, we proved formally all the lemmas needed by the method and its soundness using the Coq proof assistant. To our knowledge, apart from the original implementation by the authors who first proposed the method, there are only three implementations more. Although the basic idea of the method is simple, implementing it is a very challenging task because of a number of details that has to be dealt with. With the description of the method given in this paper, implementing the method should be still complex, but a straightforward task. In the paper we describe all these implementations and also some of their applications. 490 P. Janičić et al.

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System Description: GCLCprover + GeoThms

Cited by 22 publications

References 4 publications

Formalization of Wu’s Simple Method in Coq

Formalization of Wu’s Simple Method in Coq

Geometry Constructions Language

The Area Method

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