Treatise on Intuitionistic Type Theory

Intuitionistic type theory can be described, somewhat boldly, as a fulfillment of the dream of a universal language for science. In particular, intuitionistic type theory is a foundation for mathematics and a programming language. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.

Autorentext

Johan G. Granström (1977) holds an Uppsala doctorate in mathematical logic (2009). He had the privilege of having Em.Prof. Per Martin-Löf, the father of dependent types, as doctoral supervisor (2003-2009), along with Prof. Erik Palmgren, a renowned expert in constructive mathematics.

Dr. Granström has been a short-term research fellow at Ludwig-Maximilians-Universität München (2006-2007) and a research associate in formal methods for MDA at King's College London (2009). Before entering into doctoral studies he was employed in the computer industry as systems developer, consultant, and software architect (1998-2003). He worked as Systems and Solutions Architect at Svea Ekonomi (2009-2011) and is currently employed by Google, Zürich (2011- ).

Zusammenfassung
Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.

Inhalt

List of Figures

List of Tables

Introduction

Chapter I. Prolegomena

Chapter II. Truth and Knowledge

Chapter III. The Notion of Set

Chapter IV. Reference and Computation

Chapter V. Assumption and Substitution

Chapter VI. Intuitionism

Bibliography

Index of Proper Names

Index of Subjects.