Thinking with Types
Thinking with Types
Type-Level Programming in Haskell
About the Book
About the Author
Table of Contents
Preface
Acknowledgments
Introduction
I Fundamentals
1 - The Algebra Behind Types
1.1 - Isomorphisms and Cardinalities
1.2 - Sum, Product and Exponential Types
1.3 - Example: Tic-Tac-Toe
1.4 - The Curry--Howard Isomorphism
1.5 - Canonical Representations
2 - Terms, Types and Kinds
2.1 - The Kind System
2.1.1 - The Kind of "Types"
2.1.2 - Arrow Kinds
2.1.3 - Constraint Kinds
2.2 - Data Kinds
2.3 - Promotion of Built-In Types
2.3.1 - Symbols
2.3.2 - Natural Numbers
2.3.3 - Lists
2.3.4 - Tuples
2.4 - Type-Level Functions
3 - Variance
II Lifting Restrictions
4 - Working with Types
4.1 - Type Scoping
4.2 - Type Applications
4.3 - Ambiguous Types and Non-Injectivity
5 - Constraints and GADTs
5.1 - Introduction
5.2 - GADTs
5.3 - Heterogeneous Lists
6 - Rank-N Types
6.1 - Introduction
6.2 - Ranks
6.3 - The Nitty Gritty Details
6.4 - The Continuation Monad
7 - Existential Types
7.1 - Existential Types and Eliminators
7.1.1 - Dynamic Types
7.1.2 - Generalized Constraint Kinded Existentials
7.2 - Scoping Information with Existentials
8 - Roles
8.1 - Coercions
8.2 - Roles
III Computing at the Type-Level
9 - Associated Type Families
9.1 - Building Types from a Schema
9.2 - Generating Associated Terms
10 - First Class Families
10.1 - Defunctionalization
10.2 - Type-Level Defunctionalization
10.3 - Working with First Class Families
10.4 - Ad-Hoc Polymorphism
11 - Extensible Data
11.1 - Introduction
11.2 - Open Sums
11.3 - Open Products
11.4 - Overloaded Labels
12 - Custom Type Errors
13 - Generics
13.1 - Generic Representations
13.2 - Deriving Structural Polymorphism
13.3 - Using Generic Metadata
13.4 - Performance
13.5 - Kan Extensions
14 - Indexed Monads
14.1 - Definition and Necessary Machinery
14.2 - Linear Allocations
15 - Dependent Types
15.1 - Overview
15.2 - Ad-Hoc Implementation
15.3 - Generalized Machinery
15.4 - The Singletons Package
15.5 - Dependent Pairs
15.5.1 - Structured Logging
IV Appendices
Glossary
Solutions
Bibliography
About the Author
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
Do Well. Do Good.
Authors have earned$10,607,028writing, publishing and selling on Leanpub, earning 80% royalties while saving up to 25 million pounds of CO2 and up to 46,000 trees.
Learn more about writing on Leanpub
Free Updates. DRM Free.
If you buy a Leanpub book, you get free updates for as long as the author updates the book! Many authors use Leanpub to publish their books in-progress, while they are writing them. All readers get free updates, regardless of when they bought the book or how much they paid (including free).
Most Leanpub books are available in PDF (for computers), EPUB (for phones and tablets) and MOBI (for Kindle). The formats that a book includes are shown at the top right corner of this page.
Finally, Leanpub books don't have any DRM copy-protection nonsense, so you can easily read them on any supported device.
Learn more about Leanpub's ebook formats and where to read them
Top Books
- #1
Jetpack Compose internals
Jorge CastilloJetpack Compose is the future of Android UI. Master how it works internally and become a more efficient developer with it. You'll also find it valuable if you are not an Android dev. This book provides all the details to understand how the Compose compiler & runtime work, and how to create a client library using them.
- #2
Practical FP in Scala: A hands-on approach
Gabriel VolpeA practical book aimed for those familiar with functional programming in Scala who are yet not confident about architecting an application from scratch.
Together, we will develop a purely functional application using the best libraries in the Cats ecosystem, while learning about design patterns and best practices.
- #3
Functional Programming Made Easier
Charles ScalfaniA Functional Programming book from beginner to advanced without skipping a single step along the way.
In my 40 years of programming, I've felt that programming books always let me down, especially Functional Programming books. So, I wrote the book I wish I had 5 years ago.
Functional Programming will never be easy, but it can be easier.
- #4
Discrete Mathematics for Computer Science
Alexander Shen, Alexander S. Kulikov, Vladimir Podolskii, and Alexander GolovnevThis book supplements the DM for CS Specialization at Coursera and contains many interactive puzzles, autograded quizzes, and code snippets. They are intended to help you to discover important ideas in discrete mathematics on your own. By purchasing the book, you will get all updates of the book free of charge when they are released.
- #5
C++20 - The Complete Guide
Nicolai M. JosuttisAll the new language and library features of C++20 (for those who know previous versions).
The book presents all new language and library features of C++20. Learn how this impacts day-to-day programming, to benefit in practice, to combine new features, and to avoid all new traps.
Buy early, pay less, free updates.
Other books:
- #6
Thinking with Types
Sandy MaguireThis book aims to be the comprehensive manual for type-level programming. It's about getting you from here to there---from a competent Haskell programmer to one who convinces the compiler to do their work for them.
- #7
Algebra-Driven Design
Sandy MaguireA how-to field guide on building leak-free abstractions and algebraically designing real-world applications.
- #8
Ansible for DevOps
Jeff GeerlingAnsible is a simple, but powerful, server and configuration management tool. Learn to use Ansible effectively, whether you manage one server—or thousands.
- #9
Stratospheric
Tom Hombergs, Björn Wilmsmann, and Philip RiecksFrom Zero to Production with Spring Boot and AWS. All you need to know to get a Spring Boot application into production with AWS. No previous AWS knowledge required.
- #10
The Technological Future of Medical Specialties - 2021 Edition
Dr. Bertalan MeskoHow will the appearance of AI, sensors, wearables, VR/AR or robots affect each medical specialty? How can physicians of the various professions successfully prepare for the sweeping changes coming with the waves of technology? Read the eBook to find out
45-day Money-back guarantee: If you're not satisfied, simply return the book & get a full refund
Top Bundles
- #1
Software Architecture for Developers: Volumes 1 & 2 - Technical leadership and communication
2 Books
"Software Architecture for Developers" is a practical and pragmatic guide to modern, lightweight software architecture, specifically aimed at developers. You'll learn:The essence of software architecture.Why the software architecture role should include coding, coaching and collaboration.The things that you really need to think about before... - #2
CCIE Service Provider Ultimate Study Bundle
2 Books
Piotr Jablonski, Lukasz Bromirski, and Nick Russo have joined forces to deliver the only CCIE Service Provider training resource you'll ever need. This bundle contains a detailed and challenging collection of workbook labs, plus an extensively detailed technical reference guide. All of us have earned the CCIE Service Provider certification... - #3
All the Books of The Medical Futurist
6 Books
We put together the most popular books from The Medical Futurist to provide a clear picture about the major trends shaping the future of medicine and healthcare. Digital health technologies, artificial intelligence, the future of 20 medical specialties, big pharma, data privacy, digital health investments and how technology giants such as Amazon... - #5
Retromat eBook Bundle for Agile Retrospectives
2 Books
If you facilitate retrospectives this bundle is for you: "Plans for Retrospectives" helps beginners learn the lay of the land with tried-and-true plans. Once you know your way around, "Run great agile retrospectives" contains all 135+ activities in Retromat for you to mix and match. - #6
Growing Agile: The Complete Coach's Guide
7 Books
Growing Agile: Coach's Guide Series This bundle provides a collection of training and workshop plans for a variety of agile topics. The series is aimed at agile coaches, trainers and ScrumMasters who often find themselves needing to help teams understand agile concepts. Each book in the series provides the plans, slides, handouts and activity... - #8
9 Books-Bundle: Shut Up and Code!
9 Books
"Shut up and code." Laughter in the audience. The hacker had just plugged in his notebook and started sharing his screen to present his super-smart Python script. "Shut up and code" The letters written in a white literal coding font on black background was the hackers' home screen background mantra. At the time, I was a first-year computer...
