Introduction to Higher-Order Categorical Logic [Paperback]

Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.In this volume, Lambek and Scott reconcile two different viewpoints of the foundations of mathematics, namely mathematical logic and category theory. In Part I, they show that typed lambda-calculi, a formulation of higher-order logic, and cartesian closed categories, are essentially the same. Part II demonstrates that another formulation of higher-order logic, (intuitionistic) type theories, is closely related to topos theory. Part III is devoted to recursive functions. Numerous applications of the close relationship between traditional logic and the algebraic language of category theory are given. The authors have included an introduction to category theory and develop the necessary logic as required, making the book essentially self-contained. Detailed historical references are provided throughout, and each section concludeds with a set of exercises.Preface; Part I. Introduction to Category Theory: Part II. Cartesian Closed Categories and Calculus: Part III. Type Theory and Toposes: Part IV. Representing Numerical Functions in Various Categories; Bibliography; Author index; Subject index. ...important monograph...very clearly written... SciTech Book News ...a readable and timely account of important results, most of which were not previously available in book form. London Mathematical Society [The authors] present their material as persuasively and as lucidly as possible. In addition, they have included many useful exercises and illuminating historical and philosophical remarks, which lc*