The Science of Functional Programming
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The Science of Functional Programming

A tutorial, with examples in Scala

About the Book

This pedagogical tutorial book presents the theoretical knowledge needed by practitioners of the functional programming paradigm. The main topics covered are: working with functional collections and recursion; the fundamental type and code constructions in functional programming; reasoning about types and code with the Curry-Howard correspondence; laws, structure theorems, and code derivation for functors, monads, and other important typeclasses; free type constructions; and parametricity theorems. Detailed explanations are logically developed and accompanied by full derivations and worked examples tested in the Scala interpreter, as well as exercises. Readers should have a working knowledge of programming; e.g. be able to write code that reads a small text file and prints the number of words in it. The mathematical complexity of the calculations in this book is at the level of undergraduate calculus, similar to simplifying the expressions 1/(x-2) - 1/(x+2) and (d/dx)((x+1)f(x)exp(-x)).

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    • Functional Programming
    • Scala
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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

  • Preface
  • Part I. Beginner level
    • 1 Mathematical formulas as code. I. Nameless functions
    • 2 Mathematical formulas as code. II. Mathematical induction
    • 3 The logic of types. I. Disjunctive types
  • Part II. Intermediate level
    • 4 The logic of types. II. Curried functions
    • 5 The logic of types. III. The Curry-Howard correspondence
    • 6 Functors and contrafunctors
    • 7 Reasoning about code. Techniques of symbolic derivation
    • 8 Typeclasses and functions of types
    • 9 Computations in functor blocks. I. Filterable functors and contrafunctors
    • 10 Computations in functor blocks. II. Semimonads and monads
    • 11 Applicative functors and contrafunctors
    • 12 Traversable functors
  • Part III. Advanced level
    • 14 Computations in functor blocks. III. Monad transformers
  • Part IV. Discussions
    • 16 "Applied functional type theory": A proposal
    • 17 Essay: Software engineers and software artisans
    • 18 Essay: Towards functional data engineering with Scala
    • 19 Essay: Why category theory is useful in functional programming
  • Part V. Appendices
    • A Notations
    • B Glossary of terms
    • C Inferring code from types. The LJT algorithm
    • D Parametricity theorem and naturality laws
    • E Solutions of some exercises
    • F A humorous disclaimer
    • G GNU Free Documentation License

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