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Formal Proof: Reconciling Correctness and Understanding

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Intelligent Computer Mathematics (CICM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5625))

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Abstract

Hilbert’s concept of formal proof is an ideal of rigour for mathematics which has important applications in mathematical logic, but seems irrelevant for the practice of mathematics. The advent, in the last twenty years, of proof assistants was followed by an impressive record of deep mathematical theorems formally proved. Formal proof is practically achievable. With formal proof, correctness reaches a standard that no pen-and-paper proof can match, but an essential component of mathematics — the insight and understanding — seems to be in short supply. So, what makes a proof understandable? To answer this question we first suggest a list of symptoms of understanding. We then propose a vision of an environment in which users can write and check formal proofs as well as query them with reference to the symptoms of understanding. In this way, the environment reconciles the main features of proof: correctness and understanding.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Auckland, New Zealand

    Cristian S. Calude & Christine Müller

  2. Department of Computer Science, Jacobs University Url: kwarc.info/cmueller, Bremen, Germany

    Christine Müller

Authors
  1. Cristian S. Calude
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  2. Christine Müller
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Editor information

Editors and Affiliations

  1. Department of Computing and Software, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    Jacques Carette

  2. Informatics, 2.02 Informatics Forum, University of Edinburgh, 10 Crichton street, EH8 9AB, Edinburgh, UK

    Lucas Dixon

  3. Department of Computer Science, University of Bologna, via Mura Anteo Zamboni, 7, 40127, Bologna, Italy

    Claudio Sacerdoti Coen

  4. Department of Computer Science MC 375, University of Western Ontario, N6A 5B7, London, ON, Canada

    Stephen M. Watt

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Calude, C.S., Müller, C. (2009). Formal Proof: Reconciling Correctness and Understanding. In: Carette, J., Dixon, L., Coen, C.S., Watt, S.M. (eds) Intelligent Computer Mathematics. CICM 2009. Lecture Notes in Computer Science(), vol 5625. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02614-0_20

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  • DOI: https://doi.org/10.1007/978-3-642-02614-0_20

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