## Axiomatising the logic of computer programming |

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### Contents

FOUNDATIONS l | 1 |

The Logical Structure of Commands | 36 |

Assignments | 108 |

Copyright | |

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### Common terms and phrases

0-algebra A-consistent a-Lemma A-theorems A-theory a]ip algebraic algorithm array variable assignment Assume the result axiomatisation axioms Boolean expression called called by value causes no side Completeness Theorem component constant contains correctness assertions data type defined definition denote Diag(A dynamic logic Edited enumerable equivalent evaluating execution EXERCISES finite number first-order formulae first-order logic flowchart Fma(L follows formal parameter function declaration Fundamental Theorem given gives halting problem Hence Hoare ikip implies induction hypothesis infinitary rule interpretation Iteration Lemma mathematical means modal logic modal operators natural model natural number not-c not-e notion occur procedure program letters proof quantifier relation replaceable result holds rule of inference scalar semantics side effect simple command standard model standard-model condition structure Suppose symbols syntactic temporal logic termination theory true undefined valid Vxi|i Vxip