Algebra Driven Design: Elegant Software from Simple Building Blocks, Version 1.1.2

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. Dedication Foreword Preface Overview Abstraction What is Algebra-Driven Design? Conventions Why Haskell? Reading Haskell Understanding Haskell Types Equational Laws A Note on the Companion Library I 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 II Deriving Implementations Tile Implementation The Initial Encoding Generating Tests An Efficient Implementation Scavenger Hunt Implementation The Filter Algebra The Challenge Algebra Testing It Implementation III Reference Material Property-Based Testing Basics Writing Good Generators Showing Shrinking Using QuickCheck Interactively Effective QuickSpec Signatures Motivating QuickSpec QuickSpec for Designing Greenfield Projects QuickSpec for Analyzing Existing Projects Background Signatures Predicates Naming Variables Observing Equalities Creating QuickCheck Tests Variable Usage Debugging QuickSpec Output Common Warnings Insane Laws Poorly-Typed Laws Unsimplified Laws Common Algebraic Components Properties Associativity Identity Idempotency Invertibility Distributivity Commutativity Annihilation Structures Semigroups Monoids Groups Semilattices Functors Applicative Functors Back Matter Acknowledgements Bibliography Glossary