Reasoning algebraically about loops

@article{Back1999ReasoningAA,
  title={Reasoning algebraically about loops},
  author={R. Back and J. V. Wright},
  journal={Acta Informatica},
  year={1999},
  volume={36},
  pages={295-334}
}
  • R. Back, J. V. Wright
  • Published 1999
  • Mathematics, Computer Science
  • Acta Informatica
  • Abstract. We show how to formalise different kinds of loop constructs within the refinement calculus, and how to use this formalisation to derive general transformation rules for loop constructs. The emphasis is on using algebraic methods for reasoning about equivalence and refinement of loop constructs, rather than operational ways of reasoning about loops in terms of their execution sequences. We apply the algebraic reasoning techniques to derive a collection of transformation rules for… CONTINUE READING
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    References

    SHOWING 1-10 OF 49 REFERENCES
    A Theoretical Basis for Stepwise Refinement and the Programming Calculus
    • J. Morris
    • Computer Science
    • Sci. Comput. Program.
    • 1987
    • 420
    • PDF
    Data Refinement of Predicate Transformers
    • 104
    • PDF
    Refinement Calculus: A Systematic Introduction
    • 871
    • PDF
    Predicate Calculus and Program Semantics
    • 764
    Stepwise Refinement of Parallel Algorithms
    • 103
    • PDF
    Stepwise Refinement of Action Systems
    • 208
    Reduction: a method of proving properties of parallel programs
    • 466
    • PDF
    The specification statement
    • 310
    • PDF
    Superposition Refinement of Parallel Algorithms
    • 24
    • PDF
    The Lattice of Data Reenement
    • 13