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Structured Proofs in Isar/HOL
 Types for Proofs and Programs (TYPES 2002), LNCS 2646
, 2003
"... Abstract. Isar is an extension of the theorem prover Isabelle with a language for writing humanreadable structured proofs. This paper is an introduction to the basic constructs of this language. 1 ..."
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Abstract. Isar is an extension of the theorem prover Isabelle with a language for writing humanreadable structured proofs. This paper is an introduction to the basic constructs of this language. 1
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.
UPCOMING AUTOMOTIVE STANDARDS FOR FAULTTOLERANT COMMUNICATION: FLEXRAY AND OSEKTIME FTCOM. ∗
"... A safetycritical system needs faulttolerant communication between its components. This is especially important for automotive domain, as it consists of distributed realtime systems that are based on the results of the communication. To realize distributed systems with predictable time behavior th ..."
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Cited by 3 (3 self)
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A safetycritical system needs faulttolerant communication between its components. This is especially important for automotive domain, as it consists of distributed realtime systems that are based on the results of the communication. To realize distributed systems with predictable time behavior the timetriggered paradigm is used. According to this paradigm, a timetriggered communication protocol, FlexRay, and an operating system OSEKtime with corresponding communication layer FTCom for the faulttolerant communication are introduced. In this paper we present the formal specifications of FlexRay and FTCom that allow us to argue about their properties in a precise, formal manner and also infer the collaboration between their properties. 1.
Proving RealValued Inequalities by Computation in Isabelle/HOL
"... In this thesis we present an automatic proof method on real valued formulas. It translates the formulas into interval arithmetic calculations on floating point numbers. The resulting formulas are then evaluated by utilizing the code generator. These computations are entirely verified in Isabelle/HOL ..."
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In this thesis we present an automatic proof method on real valued formulas. It translates the formulas into interval arithmetic calculations on floating point numbers. The resulting formulas are then evaluated by utilizing the code generator. These computations are entirely verified in Isabelle/HOL itself. To reach that goal, we extend the theory with several missing analytical results about trigonometrical functions, as well as derivation rules for power series. A major new development are the boundary computations for, pi, sin, cos, arctan, exp and ln. Finally the correctness of these computations is verified in Isabelle/HOL. Acknowledgements I am very grateful to Tobias Nipkow, for introducing me to the field of theorem proving, and for all his advice and support. I also want to thank Amine Chaieb for his advice and for reading draft versions of my thesis. A big thankyou goes to Lukas Bulwahn for giving me lots of advice after reading a draft version and for the interesting cocoa breaks. Florian Haftmann helped me a lot with advice to his code generator framework. Thanks are due to the entire Isabelle group at