Algebra-Driven Design
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Algebra-Driven Design

Elegant Solutions from Simple Building Blocks

About the Book

Hi there! My name is Sandy Maguire --- you might know me from my work on Polysemy and Thinking with Types.

One of purely functional programming's greatest strengths is its powerful abstraction capabilities. We proudly exclaim that our functions are referentially transparent, and because of that, our bugs will always be shallow. And this is often true.

10x is often cited as the magic number beyond which technology is good enough to overcome network effects. I'm personally convinced that functional programming is 10x better than any other paradigm I've tried. But if functional programming is so good, why hasn't it yet taken over the world?

This is a very serious question. If we're right about this, why haven't we won?

Algebra-Driven Design is my answer to this question. Functional programming hasn't taken market share because we collectively don't yet know how to write real applications with it. Abstraction is our language's greatest strength, but all of our "best practices" evangelize writing the same procedural code and use the same techniques as we would anywhere else.

Instead of giving up, this book encourages us to take a heavy focus on designing leak-free abstractions, on understanding programs so well that the code and tests can be largely generated automatically, and on finding performance improvements not via intuition, but through algebraic manipulation of the program's underlying equations. Functional programming affords us so many new possibilities for designing and testing better code, but this information is scattered and lost in ancient journals. I'd like to change that.

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    • Software Engineering
    • Software Architecture
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About the Author

Sandy Maguire
Sandy Maguire

Sandy might best be described somewhere between independent researcher and voluntarily-unemployed bum. At the ripe old age of 27 he decided to quit his highly-lucrative engineering job and decide to focus more on living than on grinding for the man. It's what you might call a work in progress.

He regularly writes about Haskell and Agda at

Table of Contents

  • Algebra-Driven Design
    • Preface
    • Foreword by John Hughes
    • Overview
      • Abstraction
      • What is Algebra-Driven Design?
      • Conventions
      • A Note on the Companion Library
    • Designing Algebras
      • Tiles
        • Basic Building Blocks
        • Subdividing Space
        • Observations
        • Generalization
    • What Makes a Good Algebra?
    • Scavenger Hunt
      • Input Filters
      • Simultaneous Challenges
      • Challenge Completion
      • Simplification
      • A Unified Observation
      • Symmetry
      • Clues
      • Generalization
    • Deriving Implementations
      • Tile Implementation
        • The Initial Encoding
        • Generating Tests
        • An Efficient Implementation
      • Scavenger Hunt Implementation
        • The Filter Algebra
        • The Challenge Algebra
        • Testing It
        • Implementation
    • Reference Material
      • Property-Based Testing
        • Basics
        • Writing Good Generators
        • Showing
        • Shrinking
        • Using QuickCheck Interactively
      • Effective QuickSpec
        • Signatures
        • Motivating QuickSpec
        • Background Signatures
        • Predicates
        • Naming Variables
        • Observing Equalities
        • Creating QuickCheck Tests
        • Variable Usage
        • Debugging QuickSpec Output
      • Common Algebraic Components
        • Properties
        • Structures
    • Back Matter
      • Acknowledgements
      • Bibliography
      • Glossary

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