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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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Cited by 13 (5 self)
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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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Cited by 9 (3 self)
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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).
ComputerAssisted Mathematics at Work  The HahnBanach Theorem in Isabelle/Isar
 TYPES FOR PROOFS AND PROGRAMS: TYPESâ€™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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Cited by 7 (4 self)
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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.