Structured Formal Development with Quotient Types in Isabelle/HOL

  • Maksym Bortin
  • Christoph Lüth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6167)

Abstract

General purpose theorem provers provide sophisticated proof methods, but lack some of the advanced structuring mechanisms found in specification languages. This paper builds on previous work extending the theorem prover Isabelle with such mechanisms. A way to build the quotient type over a given base type and an equivalence relation on it, and a generalised notion of folding over quotiented types is given as a formalised high-level step called a design tactic. The core of this paper are four axiomatic theories capturing the design tactic. The applicability is demonstrated by derivations of implementations for finite multisets and finite sets from lists in Isabelle.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Maksym Bortin
    • 1
  • Christoph Lüth
    • 2
  1. 1.Department of Mathematics and Computer ScienceUniversität Bremen 
  2. 2.Deutsches Forschungszentrum für Künstliche Intelligenz, Bremen 

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