The weakest precondition calculus: Recursion and duality

@article{Bonsangue2005TheWP,
  title={The weakest precondition calculus: Recursion and duality},
  author={Marcello M. Bonsangue and Joost N. Kok},
  journal={Formal Aspects of Computing},
  year={2005},
  volume={6},
  pages={788-800}
}
An extension of Dijkstra's guarded command language is studied, including unbounded demonic choice and a backtrack operator. We consider three orderings on this language: a refinement ordering defined by Back, a new deadlock ordering, and an approximation ordering of Nelson. The deadlock ordering is in between the two other orderings. All operators are monotonic in Nelson's ordering, but backtracking is not monotonic in Back's ordering and sequential composition is not monotonic for the… 
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References

SHOWING 1-10 OF 32 REFERENCES
A Cook's Tour of Countable Nondeterminism
TLDR
This work provides four semantics for a small programming language involving unbounded (but countable) nondeterminism and introduces a Hoare-like proof system for total correctness.
A generalization of Dijkstra's calculus
  • Greg Nelson
  • Computer Science
    ACM Trans. Program. Lang. Syst.
  • 1989
TLDR
This paper gives a self-contained account of the generalized calculus from first principles through the semantics of recursion through the fixpoint method from denotational semantics.
Countable nondeterminism and random assignment
TLDR
Four semantics for a small programming language involving unbounded (but countable) nondeterminism are provided and a Hoare-like proof system for total correctness is introduced and its soundness and completeness in an appropriate sense are shown.
Refinement Calculus, Part I: Sequential Nondeterministic Programs
TLDR
A lattice theoretic framework for the calculus of program refinement is presented, which permits miraculous, angelic and demonic statements to be used in the description of program behavior.
Predicate-transformer semantics of general recursion
TLDR
The semantics of a language with arbitrary atomic statements, unbounded nondeterminacy, and mutual recursion is developed, and the universal conjunctivity of the weakest liberal preconditions and the connection between the weakest precondition and the weakest liberalism are proved to remain valid.
Dijkstra's Predicate Transformer, Non-Determinism, Recursion and Termination
TLDR
A method for expressing total correctness of non-deterministic recursive procedures by means of inductive assertion patterns is presented and shown to be adequate (complete), thus refining work of de BAKKER's and MEERTENS'.
A simple fixpoint argument without the restriction to continuity
TLDR
It is shown that, even in the case of unbounded nondeterminacy, the fundamental theorem about the repetition can be proved by a simple and quite elementary argument.
Power Domains
  • M. Smyth
  • Mathematics
    J. Comput. Syst. Sci.
  • 1978
On Correct Refinement of Programs
  • R. Back
  • Computer Science, Chemistry
    J. Comput. Syst. Sci.
  • 1981
...
1
2
3
4
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