Predicate transformers and higher order logic

  • R. J. R. Back
  • J. von Wright
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 666)


Predicate transformers are formalized in higher order logic. This gives a basis for mechanized reasoning about total correctness and refinement of programs. The notions of program variables and logical variables are explicated in the formalization. We show how to describe common program constructs, such as assignment statements, sequential and conditional composition, iteration, recursion, blocks and procedures with parameters, are described as predicate transformers in this framework. We also describe some specification oriented constructs, such as assert statements, guards and nondeterministic assignments. The monotonicity of these constructs over the lattice of predicates is proved, as well as the monotonicity of the statement constructors with respect to the refinement ordering on predicate transformers.

Key words

Stepwise refinement weakest preconditions total correctness predicate transformers higher order logic HOL semantics of programming languages state spaces nondeterminism procedures 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • R. J. R. Back
    • 1
  • J. von Wright
    • 2
  1. 1.Department ofComputer ScienceÅbo Akademi UniversityÅboFinland
  2. 2.Swedish School of Economics and Business EducationVasaFinland

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