## Foundations of Computing: System Development with Set Theory and LogicSet theory and logic are the twin pillars of computing science. Their mastery is an essential part of the software engineer's education. This book provides a clear introduction to the key ideas of these two subjects and shows how they can be applied successfully in formal system development. Highlights of the book include: - A presentation of set theory as a modelling language of universal applicability
- A wealth of practical examples demonstrating the remarkable simplicity and naturalness of set theory as a description tool
- A description of logic as a formal language, and as a simple way of introducing the key concepts of formal syntax, semantics and deduction calculus
- A practical methodology of system development based on set theory and illustrated by several substantial case studies
The book starts from first principles and requires no prior knowledge of mathematics. It will be equally valuable for students of computing science and software engineers wishing to develop the skills required to apply formal methods successfully. |

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### Contents

Prologue | 3 |

Set Theory and Induction | 33 |

Relations and Functions | 89 |

Copyright | |

16 other sections not shown

### Common terms and phrases

Alloc application arity axioms base set bijection Bool called cartesian product Chapter codomain computing condition Consequently Consider construction couple cursor deduction defined definition denoted described determined dictionary disjoint domain elements empty empty set equivalent establish example Exercise extension Feature Notation finite first-order logic Forest formal ForOrd ForOVl FPts function F function symbol given Gr(F Gr(R graph implies induction principle inductive set instance introduced isomorphism KReTypes KTasks L'Pts language ListPtd0 ListVl LPts n-ary n-ary function n-tuple natural numbers Note objects occur operations parse tree precondition predicate symbol proof propositional logic relation represented rule satisfied secondary features Section semantics set theory specified string structural induction subset substitutable successor function task tautology theorem total function TPts TreePtd0 true truth assignment truth table unary Vals variable features Wfes