Healthiness Conditions for Predicate Transformers

AbstractThe behavior of a program can be modeled by describing how it transforms input states to output states, the state transformer semantics. Alternatively, for verification purposes one is interested in a 'predicate transformer semantics' which, for every condition on the output, yields the weakest precondition on the input that guarantees the desired property for the output.In the presence of computational effects like nondeterministic or probabilistic choice, a computation will be modeled by a map t:X→TY, where T is an appropriate computational monad. The corresponding predicate transformer assigns predicates on Y to predicates on X. One looks for necessary and, if possible, sufficient conditions (healthiness conditions) on predicate transformers that correspond to state transformers t:X→TY.In this paper we propose a framework for establishing healthiness conditions for predicate transformers. As far as the author knows, it fits to almost all situations in which healthiness conditions for predicate transformers have been worked out. It may serve as a guideline for finding new results; but it also shows quite narrow limitations

SCS 13: Complements to Relations with the Interpolation Properties and Continuous Lattices

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.htm

SCS 19: Several Remarks

Contents: The closed subsemilattices of a continuous lattice form a continuous lattice When do the prime elements of a distributive lattice form a closed subset Remarks on lower semicontinuous function spaces Remarks on the continuity of the congruence lattice of the continuous lattice Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.htm

An Error in the Copower Considerations

Accompanies October 13, 1976 letter from Karl Heinrich Hofmann to Jimmie D. Lawson

SCS 28: The Lattice of Open Subsets of a Topological Space

Also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.htm