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Solving Higherorder Equations : From Logic To Programming (Progress In Theoretical Computer Science),New
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This Monograph Develops Techniques For Equational Reasoning In Higherorder Logic. Due To Its Expressiveness, Higherorder Logic Is Used For Specification And Verification Of Hardware, Software, And Mathematics. In These Applica Tions, Higherorder Logic Provides The Necessary Level Of Abstraction For Con Cise And Natural Formulations. The Main Assets Of Higherorder Logic Are Quan Tification Over Functions Or Predicates And Its Abstraction Mechanism. These Allow One To Represent Quantification In Formulas And Other Variablebinding Constructs. In This Book, We Focus On Equational Logic As A Fundamental And Natural Concept In Computer Science And Mathematics. We Present Calculi For Equa Tional Reasoning Modulo Higherorder Equations Presented As Rewrite Rules. This Is Followed By A Systematic Development From General Equational Rea Soning Towards Effective Calculi For Declarative Programming In Higherorder Logic And Acalculus. This Aims At Integrating And Generalizing Declarative Programming Models Such As Functional And Logic Programming. In These Two Prominent Declarative Computation Models We Can View A Program As A Logical Theory And A Computation As A Deduction.
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