Algebra Driven Design

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