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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 ..."
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Cited by 45 (10 self)
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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.
A Refinement of de Bruijn’s Formal Language of Mathematics
 Journal of Logic, Language and Information
, 2004
"... Abstract. 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 mathematici ..."
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Cited by 31 (15 self)
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Abstract. 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. WTT is close to the usual way in which mathematicians express themselves in writing. ¡ WTT has a syntax based on linguistic categories instead of set/type theoretic constructs. More so than MV however, WTT has a precise abstract syntax whose derivation rules resemble those of modern type theory enabling us to establish important desirable properties of WTT such as strong normalisation, decidability of type checking and subject reduction. The derivation system allows one to establish that a book written in WTT is wellformed following the syntax of WTT, and has great resemblance with ordinary mathematics books. WTT (like MV) is weak as regards correctness: the rules of WTT only concern linguistic correctness, its types are purely linguistic so that the formal translation into WTT is satisfactory as a readable, wellorganized text. In WTT, logicomathematical aspects of truth are disregarded. This separates concerns and means that WTT can be easily understood by either a mathematician, a logician or a computer scientist. acts as an intermediary between the language of mathematicians and that of logicians.
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 ..."
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Cited by 13 (2 self)
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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 ..."
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Cited by 5 (3 self)
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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 ..."
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Cited by 2 (0 self)
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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
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. ..."
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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.
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&a ..."
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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.