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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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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.
A Framework for Interactive Proof
"... Abstract. This paper introduces Proof General Kit, a framework for software components tailored to interactive proof development. The goal of the framework is to enable flexible environments for managing formal proofs across their lifecycle: creation, maintenance and exploitation. The framework con ..."
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Abstract. This paper introduces Proof General Kit, a framework for software components tailored to interactive proof development. The goal of the framework is to enable flexible environments for managing formal proofs across their lifecycle: creation, maintenance and exploitation. The framework connects together different kinds of component, exchanging messages using a common communication infrastructure and protocol called PGIP. The main channel connects provers to displays. Provers are the backend interactive proof engines and displays are components for interacting with the user, allowing browsing or editing of proofs. At the core of the framework is a broker middleware component which manages proofinprogress and mediates between components. 1 Introducing Proof General Kit The use of interactive machine proof is becoming more widespread, and larger and more complex formalisations are being undertaken in application areas such as hardware or software verification, and formalisation of mathematics, even up
Proof General meets IsaWin — combining textbased and graphical user interfaces
 In International Workshop on User Interfaces for Theorem Provers (UITP’03), volume 104 of Electronic Notes in Theoretical Computer Science
, 2004
"... We describe the design and prototype implementation of a combination of theorem prover interface technologies. On one side, we take from Proof General the idea of a proverindependent interaction language and its proposed implementation within the PG Kit middleware architecture. On the other side, w ..."
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Cited by 2 (0 self)
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We describe the design and prototype implementation of a combination of theorem prover interface technologies. On one side, we take from Proof General the idea of a proverindependent interaction language and its proposed implementation within the PG Kit middleware architecture. On the other side, we take from IsaWin a sophisticated graphical metaphor using direct manipulation for developing proofs. We believe that the resulting system will provide a powerful, robust and generic environment for developing proofs within interactive proof assistants that also opens the way for studying and implementing new mechanisms for managing interactive proof development. 1
Parsing, Editing, Proving: . . .
, 2005
"... This paper describes how proof texts are constructed and edited in the Proof General Kit framework. Proof texts are the central object of development within our framework and we want to allow flexible ways to construct them, both explicitly via text editing and implicitly by graphical manipulation o ..."
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This paper describes how proof texts are constructed and edited in the Proof General Kit framework. Proof texts are the central object of development within our framework and we want to allow flexible ways to construct them, both explicitly via text editing and implicitly by graphical manipulation or metamanipulation. To this end, the framework allows for useroriented display components, connected to provers via a central broker component. The display components and the broker exchange messages in a format specified by the PGIP display protocol, which facilitates parsing, editing and proving of proof texts. The design of this part of the framework is new; the remainder of the framework, which connects the prover components to the broker, is based more closely on refining work of the previous Proof General project, and was described in [4].