Programming in System Fω using Dhall
Programming in System Fω using Dhall
About the Book
This book is an advanced-level tutorial on functional programming (FP) in Dhall for software engineers already familiar with the FP paradigm, as practiced in languages such as OCaml, Haskell, Scala, and others.
Although most code examples are in Dhall, much of the material of the book has a wider applicability. The book studies a certain flavor of purely functional programming without side effects and with guaranteed termination, which is known in the academic literature as "System Fω".
From that point of view, Dhall is an industrial-strength interpreter for System Fω with some additional features and a Haskell-like syntax.
The book focuses on issues arising in practical programming and contains many code examples, which can be evaluated by the Dhall interpreter after exporting them into a single Dhall file.
The Appendix of the book contains some theoretical material that proves the correctness of certain code constructions, notably the Church encodings of fix-point inductive and co-inductive types.
About the Author
Table of Contents
0. Preface
1. Overview of Dhall
2 Some features of the Dhall type system
3 Arithmetic with Natural numbers
4 Programming with functions
5 Typeclasses
6 Programming with Leibniz equality types
7 Church encoding for recursive types and type constructors
8 Working with Church-encoded data
9 Church encodings for more complicated types
10 Co-inductive types
11 Translating recursive code into Dhall
12 Combinators for functors and contrafunctors
13 Filterable functors and contrafunctors, and their combinators
14 Applicative functors and contrafunctors, and their combinators
15 Monoids and their combinators
16 Traversable functors and their combinators
17 Monads and their combinators
18 Monad transformers
19 Free typeclasses
20 Nested types and GADTs
21 Dhall as a scripting DSL
A Appendix: Naturality, parametricity, and proofs of type equivalence
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