Science of Computer Programming, 22(1-2):21-44, 1994.

Authors: Paul Gardiner, Clare Martin and Oege de Moor
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Abstract

In this paper we present an algebraic construction of monotonic predicate transformers, using a categorical construction which is similar to the algebraic construction of the integers from the natural numbers. When applied to the category of sets and total functions once, it yields a category isomorphic to the category of sets and relations; a second application yields a category isomorphic to the category of monotonic predicate transformers. This hierarchy cannot be extended further: the category of total functions is not itself an instance of the categorical construction, and can only be extended by it twice.

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BIBTEX:

           @article{scp94martin, 
           author = "Paul Gardiner and Clare Martin and De Moor, Oege",
           title = "An algebraic construction of predicate transformers", 
           journal = "Science of Computer Programming",
           volume = "22",
           number = "1-2",
           pages = "21-44",
           year = "1994"}