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</script>Not only monotonicity, but also other homomorphism properties of predicate transformers turn out to be important in modeling programming constructs. In this chapter we study homomorphic predicate transformers, i.e., predicate transformers that preserve some of the predicate lattice structure. We consider the four basic homomorphism properties — bottom, top, meet, and join homomorphism — to see to what extent the constructs in our statement language preserve these properties. These homomorphism properties are closely linked to distributivity properties of statements.
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