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Programming in System Fω using Dhall

Why is Dhall is the most powerful and safe language for templated configuration files? Because Dhall implements System Fω, the type system at the core of Haskell - the most powerful type system short of adopting full dependent types. I found Dhall to be a delightfully lucid vehicle for learning the core patterns of functional programming. Non-Turing-completeness for the win!

Sergei Winitzki

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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 fixpoints for inductive and co-inductive types.

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Sergei Winitzki

Sergei Winitzki has a PhD degree in theoretical physics and, after an academic career in research, now works as a big data engineer. He is passionate about functional programming, declarative programming, and domain-specific languages.

Table of Contents

0. Preface

1 Overview of Dhall

2 Other features of Dhall's type system

3 Numerical algorithms

4 Programming with functions

5 Typeclasses

6 Leibniz equality types

7 Church encodings of simple types

8 Working with Church-encoded data

9 Church encodings of more complicated types

10 Encoding of greatest fixpoints

11 Translating recursive code into Dhall

12 Combinators for monoids

13 Combinators for functors and contrafunctors

14 Filterable (contra)functors and their combinators

15 Applicative type constructors and their combinators

16 Combinators for foldable and traversable functors

17 Monads and their combinators

18 Monad transformers

19 Free typeclass instances

A Appendix: Deriving a functional language from first principles

B Appendix: Naturality and parametricity

C Appendix: About Dhall code examples in this book

D Appendix: GNU Free Documentation License

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