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Calculational Reasoning Revisited  An Isabelle/Isar experience
 THEOREM PROVING IN HIGHER ORDER LOGICS: TPHOLS 2001
, 2001
"... We discuss the general concept of calculational reasoning within Isabelle/Isar, which provides a framework for highlevel natural deduction proofs that may be written in a humanreadable fashion. Setting out from a few basic logical concepts of the underlying metalogical framework of Isabelle, such ..."
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We discuss the general concept of calculational reasoning within Isabelle/Isar, which provides a framework for highlevel natural deduction proofs that may be written in a humanreadable fashion. Setting out from a few basic logical concepts of the underlying metalogical framework of Isabelle, such as higherorder unification and resolution, calculational commands are added to the basic Isar proof language in a flexible and nonintrusive manner. Thus calculational proof style may be combined with the remaining natural deduction proof language in a liberal manner, resulting in many useful proof patterns. A casestudy on formalizing Computational Tree Logic (CTL) in simplytyped settheory demonstrates common calculational idioms in practice.
Mizar Light for HOL Light
 Theorem Proving in Higher Order Logics: TPHOLs 2001, LNCS 2152
, 2001
"... There are two dierent approaches to formalizing proofs in a computer: the procedural approach (which is the one of the HOL system) and the declarative approach (which is the one of the Mizar system). ..."
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There are two dierent approaches to formalizing proofs in a computer: the procedural approach (which is the one of the HOL system) and the declarative approach (which is the one of the Mizar system).
A PROOFTHEORETIC APPROACH TO MATHEMATICAL KNOWLEDGE MANAGEMENT
, 2007
"... Mathematics is an area of research that is forever growing. Definitions, theorems, axioms, and proofs are integral part of every area of mathematics. The relationships between these elements bring to light the elegant abstractions that bind even the most intricate aspects of math and science. As the ..."
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Cited by 7 (0 self)
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Mathematics is an area of research that is forever growing. Definitions, theorems, axioms, and proofs are integral part of every area of mathematics. The relationships between these elements bring to light the elegant abstractions that bind even the most intricate aspects of math and science. As the body of mathematics becomes larger and its relationships become richer, the organization of mathematical knowledge becomes more important and more difficult. This emerging area of research is referred to as mathematical knowledge management (MKM). The primary issues facing MKM were summarized by Buchberger, one of the organizers of the first Mathematical Knowledge Management Workshop [20]. • How do we retrieve mathematical knowledge from existing and future sources? • How do we build future mathematical knowledge bases? • How do we make the mathematical knowledge bases available to mathematicians? These questions have become particularly relevant with the growing power of and interest in automated theorem proving, using computer programs to prove
ComputerAssisted Mathematics at Work  The HahnBanach Theorem in Isabelle/Isar
 TYPES FOR PROOFS AND PROGRAMS: TYPES’99, LNCS
, 2000
"... We present a complete formalization of the HahnBanach theorem in the simplytyped settheory of Isabelle/HOL, such that both the modeling of the underlying mathematical notions and the full proofs are intelligible to human readers. This is achieved by means of the Isar environment, which provides ..."
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We present a complete formalization of the HahnBanach theorem in the simplytyped settheory of Isabelle/HOL, such that both the modeling of the underlying mathematical notions and the full proofs are intelligible to human readers. This is achieved by means of the Isar environment, which provides a framework for highlevel reasoning based on natural deduction. The final result is presented as a readable formal proof document, following usual presentations in mathematical textbooks quite closely. Our case study demonstrates that Isabelle/Isar is capable to support this kind of application of formal logic very well, while being open for an even larger scope.
MMode, a Mizar Mode for the proof assistant Coq
, 2003
"... We present a set of tactics for version 7.4 of the Coq proof assistant which makes it possible to write proofs for Coq in a language similar to the proof language of the Mizar system. These tactics can be used with any interface of Coq, and they can be freely mixed with the normal Coq tactics. ..."
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We present a set of tactics for version 7.4 of the Coq proof assistant which makes it possible to write proofs for Coq in a language similar to the proof language of the Mizar system. These tactics can be used with any interface of Coq, and they can be freely mixed with the normal Coq tactics.
Proving as Programming with DrHOL: A Preliminary Design
"... Abstract. We discuss the design of a new implementation of the HOL system aimed at improved graphical user interface support for formal proof. We call our approach Proving as Programming, since we believe that metalanguage programming is a central aspect of proof construction. Thus we look to contem ..."
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Abstract. We discuss the design of a new implementation of the HOL system aimed at improved graphical user interface support for formal proof. We call our approach Proving as Programming, since we believe that metalanguage programming is a central aspect of proof construction. Thus we look to contemporary programming environments for inspiration on how to provide graphical support for proof. In particular, our implementation builds upon DrScheme, a popular programming environment for Scheme. 1 Proving as Programming We have begun work on DrHOL, a new implementation of the HOL logic. DrHOL is systematically derived from HOL4 [8] and aims at improving user interfaces in many aspects of work in HOL: development of proof procedures, construction of terms and definitions, interactive proof, and embedding of object languages are seen as candidates for better interface support. We believe that programmability is an essential part of all these activities. To support our view, we will discuss the