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Dijkstra Monads in Monadic Computation

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8446)

Abstract

The Dijkstra monad has been introduced recently for capturing weakest precondition computations within the context of program verification, supported by a theorem prover. Here we give a more general description of such Dijkstra monads in a categorical setting. We first elaborate the recently developed view on program semantics in terms of a triangle of computations, state transformers, and predicate transformers. Instantiations of this triangle for different monads \(T\) show how to define the Dijkstra monad associated with \(T\), via the logic involved. Technically, we provide a morphism of monads from the state monad transformation applied to \(T\), to the Dijkstra monad associated with \(T\). This monad map is precisely the weakest precondition map in the triangle, given in categorical terms by substitution.

Keywords

Complete Lattice Effect Algebra Monoidal Category Monoid Structure Weak Precondition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

Thanks to Sam Staton, Mathys Rennela, and Bas Westerbaan for their input & feedback.

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Copyright information

© IFIP International Federation for Information Processing 2014

Authors and Affiliations

  1. 1.Institute for Computing and Information Sciences (iCIS)Radboud University NijmegenNijmegenThe Netherlands

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