Summary
A very general lattice-based language of commands, based on the primitive operations of substitution and test for equality, is constructed. This base language permits unbounded nondeterminism, demonic and angelic nondeterminism. A dual language permitting miracles is constructed. Combining these two languages yields an extended base language which is complete, in the sense that all monotonic predicate tranformers can be constructed in it. The extended base language provides a unifying framework for various specification languages; we show how two Dijkstra-style specification languages can be embedded in it.
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Back, R.J.R., von Wright, J. Duality in specification languages: a lattice-theoretical approach. Acta Informatica 27, 583–625 (1990). https://doi.org/10.1007/BF00259469
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DOI: https://doi.org/10.1007/BF00259469