Programming in System Fω using Dhall
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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.

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About the Author

Sergei Winitzki
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 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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