Titlebook: Refinement Calculus; A Systematic Introdu Ralph-Johan Back,Joakim Wright Textbook 1998 Springer Science+Business Media New York 1998 calcul

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Truth Values. In this chapter we present the constants and inference rules that are needed for reasoning about logical formulas. We have shown earlier that the truth values form a complete Boolean lattice. Here we describe the general inference rules that are available for reasoning about Boolean lattices. The

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Boolean Expressions and Conditionalsst, they are used to describe control structures with branching, like conditional statements and loops. Second, they are used to express correctness conditions for programs. In both cases, the predicates are expressed in terms of program variables, so they are really Boolean expressions. In this cha

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Relationsally the same set of inference rules as predicates. We can define new operations on relations, giving additional properties. In particular, relations combine a lattice and a category structure. Relations also provide us with a more expressive way of describing state changes, where the effect can be

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Predicate Transformersle to expect contracts to have. We did not, however, say what kind of mathematical entities contracts are. The interpretation of contracts depends on what features are considered essential and what are inessential. We now make the assumption that the essential feature of a contract is what can be ac

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Statements as Gamesre mathematical entities, functions from predicates (sets) to predicates, and as such have no direct computational interpretation. The way in which statements are assumed to be executed as programs has only been explained informally. Because both angelic and demonic nondeterminism is involved in sta

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Choice Semanticset of predicates over the final state space. This means that we have altogether three different semantics for statements: an (operational) game semantics, a (backward) predicate transformer semantics, and a (forward) choice semantics. We show that these semantics are consistent with each other (we h