Results 1 
6 of
6
Locales: A sectioning concept for Isabelle
 IN BERTOT ET AL
, 1999
"... Locales are a means to define local scopes for the interactive proving process of the theorem prover Isabelle. They delimit a range in which fixed assumption are made, and theorems are proved that depend on these assumptions. A locale may also contain constants defined locally and associated with pr ..."
Abstract

Cited by 35 (10 self)
 Add to MetaCart
Locales are a means to define local scopes for the interactive proving process of the theorem prover Isabelle. They delimit a range in which fixed assumption are made, and theorems are proved that depend on these assumptions. A locale may also contain constants defined locally and associated with pretty printing syntax. Locales can be seen as a simple form of modules. They are similar to reasoning and similar applications of theorem provers. This paper motivates the concept of locales by examples from abstract algebraic reasoning. It also discusses some implementation issues.
Modular Reasoning in Isabelle
, 1999
"... The concept of locales for Isabelle enables local definition and assumption for interactive mechanical proofs. Furthermore, dependent types are constructed in Isabelle/HOL for first class representation of structure. These two concepts are introduced briefly. Although each of them has proved use ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
The concept of locales for Isabelle enables local definition and assumption for interactive mechanical proofs. Furthermore, dependent types are constructed in Isabelle/HOL for first class representation of structure. These two concepts are introduced briefly. Although each of them has proved useful in itself, their real power lies in combination. This paper illustrates by examples from abstract algebra how this combination works and argues that it enables modular reasoning.
A Formal Proof of Sylow's Theorem  An Experiment in Abstract Algebra with Isabelle HOL
 Journal of Automated Reasoning
, 1999
"... The theorem of Sylow is proved in Isabelle HOL. We follow the proof by Wielandt that is more general than the original and uses a nontrivial combinatorial identity. The mathematical proof is explained in some detail leading on to the mechanization of group theory and the necessary combinatorics in ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
The theorem of Sylow is proved in Isabelle HOL. We follow the proof by Wielandt that is more general than the original and uses a nontrivial combinatorial identity. The mathematical proof is explained in some detail leading on to the mechanization of group theory and the necessary combinatorics in Isabelle. We present the mechanization of the proof in detail giving reference to theorems contained in an appendix. Some weak points of the experiment with respect to a natural treatment of abstract algebraic reasoning give rise to a discussion of the use of module systems to represent abstract algebra in theorem provers. Drawing from that, we present tentative ideas for further research into a section concept for Isabelle.
Towards a formal mathematical vernacular
 Utrecht University
, 1992
"... Contemporary proof veri cators often use a command language to construct proofs. These commands are often called tactics. This new generation of theorem provers is a substantial improvement over earlier ones such asAUTOMATH. Based on experience with these new provers we feel the need to study these ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Contemporary proof veri cators often use a command language to construct proofs. These commands are often called tactics. This new generation of theorem provers is a substantial improvement over earlier ones such asAUTOMATH. Based on experience with these new provers we feel the need to study these languages further, especially, because we think that these may be improved in their adequateness to express proofs closer to the established mathematical vernacular. We also feel that a systematic treatment of these vernaculars may lead to an improvement towards the automatic inference of trivial proof steps. In any case a systematic treatment will lead to a better understanding of the command languages. This exercise is carried out in the setting of Pure Type Systems (PTSs) in which a whole range of logics can be embedded. We rstidentify a subclass of PTSs, called the PTSs for logic. For this class we de ne a formal mathematical vernacular and we prove elementary sound and completeness. Via an elaborate example we try to assess how easy proofs in mathematics can be written down in our vernacular along the lines of the original proofs. 1
A refinement of de Bruijn's formal language of mathematics
 Journal of Logic, Language and Information
, 2004
"... We provide a syntax and a derivation system for a formal language of mathematics called Weak Type Theory (WTT). We give the metatheory of WTT and a number of illustrative examples. WTT is a refinement of de Bruijn's Mathematical Vernacular (MV) and hence: WTT is faithful to the mathematician's lang ..."
Abstract
 Add to MetaCart
We provide a syntax and a derivation system for a formal language of mathematics called Weak Type Theory (WTT). We give the metatheory of WTT and a number of illustrative examples. WTT is a refinement of de Bruijn's Mathematical Vernacular (MV) and hence: WTT is faithful to the mathematician's language yet is formal and avoids ambiguities.
First Year Report
, 2003
"... syntax. The MathLang abstract syntax (that is to say the way we represent MathLang data) is de ned in the following sections. The abstract syntax will only be used in the WTC The BackusNaur form (BNF) is a metasyntax to formally describe languages. ..."
Abstract
 Add to MetaCart
syntax. The MathLang abstract syntax (that is to say the way we represent MathLang data) is de ned in the following sections. The abstract syntax will only be used in the WTC The BackusNaur form (BNF) is a metasyntax to formally describe languages.