Programming Language Constructs for Which It Is Impossible To Obtain Good Hoare Axiom Systems
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Theoretical Computer Science
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Clarke has shown that it is impossible to obtain a relatively complete axiomatization of a block-structured programming language if it has features such as static scope, recursive procedure calls with procedure parameters, and global variables, provided that we take first-order logic as the underlying assertion language [Cl]. We show that if we take a more powerful assertion language, and hence a more powerful notion of expressiveness, such a complete axiomatization is possible. The crucial point is that we need to be able to express weakest preconditions of commands with free procedure parameters. The axioms presented here are natural and reflect the syntax of the programming language. Such an axiom system provides a tool for understanding how to reason about languages with powerful control features.