© 2011

Treatise on Intuitionistic Type Theory


Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 22)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Johan Georg Granström
    Pages 1-11
  3. Johan Georg Granström
    Pages 13-51
  4. Johan Georg Granström
    Pages 53-76
  5. Johan Georg Granström
    Pages 77-106
  6. Johan Georg Granström
    Pages 107-154
  7. Johan Georg Granström
    Pages 155-173
  8. Back Matter
    Pages 175-196

About this book


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 Ample historical references are given throughout the book.


intuitionism intuitionistic type theory lingua characteristica notion of knowledge notion of truth

Authors and affiliations

  1. 1.SträngnäsSweden
  2. 2.UppsalaSweden

About the authors

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- ).

Bibliographic information