An Interactive Algebra Course with Formalised Proofs and Definitions

Asperti, Andrea; Geuvers, Herman; Loeb, Iris; Mamane, Lionel; Coen, Claudio Sacerdoti

doi:10.1007/11618027_21

Cited by 2 publications

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“…Ideally, one would like to extract a mathematical document from a formalization, but things are not that simple (see [6] for an example study). The outcome is a quite direct 'pretty printed' translation of the computer code, containing too many details.…”

Section: Mathematical Knowledge Managementmentioning

confidence: 99%

Proof assistants: History, ideas and future

Geuvers

2009

Sadhana

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In this paper we will discuss the fundamental ideas behind proof assistants: What are they and what is a proof anyway? We give a short history of the main ideas, emphasizing the way they ensure the correctness of the mathematics formalized. We will also briefly discuss the places where proof assistants are used and how we envision their extended use in the future. While being an introduction into the world of proof assistants and the main issues behind them, this paper is also a position paper that pushes the further use of proof assistants. We believe that these systems will become the future of mathematics, where definitions, statements, computations and proofs are all available in a computerized form. An important application is and will be in computer supported modelling and verification of systems. But their is still along road ahead and we will indicate what we believe is needed for the further proliferation of proof assistants.

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Section: Mathematical Knowledge Managementmentioning

confidence: 99%

Proof assistants: History, ideas and future

Geuvers

2009

Sadhana

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Point-and-Write – Documenting Formal Mathematics by Reference

Tankink

Lange

Urban

2012

Lecture Notes in Computer Science

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This paper describes the design and implementation of mechanisms for light-weight inclusion of formal mathematics in informal mathematical writings, particularly in a Web-based setting. This is conceptually done in three stages: (i) by choosing a suitable representation layer (based on RDF) for encoding the information about available resources of formal mathematics, (ii) by exporting this information from formal libraries, and (iii) by providing syntax and implementation for including formal mathematics in informal writings. We describe the use case of an author referring to formal text from an informal narrative, and discuss design choices entailed by this use case. Furthermore, we describe an implementation of the use case within the Agora prototype: a Wiki for collaborating on formalized mathematics.

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An Interactive Algebra Course with Formalised Proofs and Definitions

Cited by 2 publications

References 4 publications

Proof assistants: History, ideas and future

Proof assistants: History, ideas and future

Point-and-Write – Documenting Formal Mathematics by Reference

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