Thinking with Types
This book is 100% complete
Completed on 2019-01-10
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
Authors have earned$9,098,746writing, 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
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
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
