From Logic to Logic Programming (Foundations of Computing) Review

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From Logic to Logic Programming (Foundations of Computing) ReviewThis book is an excellent introduction to logic as it is applied to logic programming. It begins with a set of mathematical preliminaries, mathematical induction, trees, multisets, ordinals and cardinals. This is a ten-page refresher that most readers will be able to skip. Chapter two covers propositional logic, but this is not a standard overview of the subject. Advanced theorems such as the Soundness and Completeness theorems are stated and succinctly proven.
First-order logic is the topic of chapter three, and the coverage is thorough with it being aimed directly at the topic of chapter four, which is program-definability. In any complex programming project, one of the most difficult problems to resolve is how the data is to be represented in the computer. Chapter four explains how domains such as the natural numbers, binary notation and lists can be represented using the Herbrand Universe model.
The final three chapters cover linear resolution, infinite derivations, computability and negation. Mathematical proofs can be based on either verification of a positive or affirmation of a negative. Linear resolution can only deduce positive information from programs, infinite derivations and negation can be used to affirm a negative, indirectly deducing the opposite positive. Exercises are included at the end of each chapter, but no solutions are given.
This book is the best place to begin if you want to understand the mathematical foundations of logic programming. However, at least one course in mathematical logic is a precondition to that understanding.
From Logic to Logic Programming (Foundations of Computing) Overview

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The Definition of Standard ML - Revised Review

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The Definition of Standard ML - Revised ReviewTo explain it in the words of the authors: "The keystone of the method [used to define Standard ML in this book], then, is a certain kind of assertion that takes the form B |- P => M and may be pronounced: 'Against the background B, the phrase P evaluates to the meaning M.' The formal purpose of this Definition is no more, and no less, than to decree exactly which assertions of this form are true."
Standard ML is a very powerful language because of the abilities it grants and the restrictions it enforces. While reading this book will not teach you SML, it will help reinforce its subtle elegance. If you have developed an infatuation with this language, you will not be able to resist the only book that truly contains it.
While not necessary to enjoy this volume, a prerequisite to have any understanding of its contents is some sort of background in type theory and mathematical logic that a course like this one taught by Harper... can only begin to provide.
And remember, ML loves you!The Definition of Standard ML - Revised Overview

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