Leanpub The Leanpub Logo is a Registered Trademark
Created with Sketch.
Gentle Introduction to Dependent Types with Idris
Gentle Introduction to Dependent Types with Idris
Free!
Minimum price
$11.95
Suggested price
  • 122

    Pages

  • English

  • PDF

  • EPUB

  • MOBI

  • APP

Gentle Introduction to Dependent Types with Idris

Last updated on 2019-03-19

About the Book

You can purchase a printed edition of this book on Amazon

Dependent types are a powerful concept that allows us to write proof-carrying code. Idris is a programming language that supports dependent types. We will learn about the mathematical foundations, and then write correct software and mathematically prove properties about it.

This book aims to be accessible to novices that have no prior experience beyond high school mathematics. Thus, this book is designed to be self-contained.

The reason for writing this book is that I could not find a book that explained how things work, so I had to do a lot of research on the internet through white-papers, forums, and example code in order to come up with a complete picture of what dependent types are and what they are good for.

The first part of this book serves as an introduction to the theory behind Idris, while the second part is a practical introduction to Idris with examples.

Contributions are welcome on GitHub.

About the Author

Boro Sitnikovski
Boro Sitnikovski

Boro Sitnikovski has 10+ years of experience working professionally as a Software Engineer. He started programming with the Assembly programming language on an Intel x86 at the age of 10. While in high school, he has won several prizes on competitive programming, varying from 4th, 3rd, and 1st place.

He has a Bachelor of Engineering in Informatics degree, and his thesis was titled “Programming in Haskell using algebraic data structures”. His research interests include: programming languages, mathematics, logic, algorithms, and writing correct software.

He is a strong believer in the open source philosophy, and contributes to various open source projects.

In his spare time he enjoys some time-off with his family.

Table of Contents

  •  
    • Preface and acknowledgements
    • Introduction
  • Part I: Theoretical introduction
    • 1. Formal systems
      • 1.1. MU puzzle example
    • 2. Classic mathematical logic
      • 2.1. Hierarchy of mathematical logic and definitions
        • 2.1.1. Propositional logic
        • 2.1.2. First-order logic
        • 2.1.3. Higher-order logic
      • 2.2. Set theory abstractions
      • 2.3. Substitution and mathematical proofs
        • 2.3.1. Proofs by truth tables
        • 2.3.2. Three-column proofs
        • 2.3.3. Formal proofs
        • 2.3.4. Proof techniques
        • 2.3.5. Mathematical induction
    • 3. Type theory
      • 3.1. Lambda calculus
        • 3.1.1. Term reduction
      • 3.2. Lambda calculus with types
      • 3.3. Dependent types
      • 3.4. Intuitionistic theory of types
        • 3.4.1. Intuitionistic logic
  • Part II: Practical introduction
    • 4. Programming in Idris
      • 4.1. Basic syntax and definitions
        • 4.1.1. Defining functions
        • 4.1.2. Defining and inferring types
        • 4.1.3. Anonymous lambda functions
        • 4.1.4. Recursive functions
        • 4.1.5. Recursive data types
        • 4.1.6. Total and partial functions
        • 4.1.7. Higher-order functions
        • 4.1.8. Dependent types
        • 4.1.9. Implicit parameters
        • 4.1.10. Strict evaluation
        • 4.1.11. Pattern matching expressions
        • 4.1.12. Interfaces and implementations
      • 4.2. Curry-Howard isomorphism
    • 5. Proving in Idris
      • 5.1. Weekdays
        • 5.1.1. First proof (auto-inference)
        • 5.1.2. Second proof (rewrite)
        • 5.1.3. Third proof (impossible)
      • 5.2. Natural numbers
        • 5.2.1. First proof (auto-inference and existence)
        • 5.2.2. Second proof (introduction of a new given)
        • 5.2.3. Third proof (induction)
        • 5.2.4. Ordering
        • 5.2.5. Safe division
        • 5.2.6. Maximum of two numbers
        • 5.2.7. List of even naturals
        • 5.2.8. Partial orders
      • 5.3. Computations as types
      • 5.4. Trees
        • 5.4.1. Depth
        • 5.4.2. Map and size
        • 5.4.3. Length of mapped trees
    • Conclusion
    • Further reading
    • Appendix A: Metamath
    • Appendix B: IO, Codegen targets, compilation, and FFI
      • IO
      • Codegen
      • Compilation
      • Foreign Function Interface
    • About the author
  • Notes

Causes Supported

Free Software Foundation

http://www.fsf.org

The Free Software Foundation (FSF) is a nonprofit with a worldwide mission to promote computer user freedom. We defend the rights of all software users.

As our society grows more dependent on computers, the software we run is of critical importance to securing the future of a free society. Free software is about having control over the technology we use in our homes, schools and businesses, where computers work for our individual and communal benefit, not for proprietary software companies or governments who might seek to restrict and monitor us.

The Leanpub 45-day 100% Happiness Guarantee

Within 45 days of purchase you can get a 100% refund on any Leanpub purchase, in two clicks.

See full terms...

Write and Publish on Leanpub

Authors, publishers and universities use Leanpub to publish amazing in-progress and completed books and courses, just like this one. You can use Leanpub to write, publish and sell your book or course as well! Leanpub is a powerful platform for serious authors, combining a simple, elegant writing and publishing workflow with a store focused on selling in-progress ebooks. Leanpub is a magical typewriter for authors: just write in plain text, and to publish your ebook, just click a button. It really is that easy.

Learn more about writing on Leanpub

Leanpub is copyright © 2010-2019 Ruboss Technology Corp. All rights reserved.