Essays about Programming in Joy

These essays are adapted from Jupyter notebooks. I hope to have those hosted somewhere where people can view them “live” and interact with them, possibly on MS Azure. For now, Sphinx does such a great job rendering the HTML that I am copying over some notebooks in ReST format and hand-editing them into these documents.

• Developing a Program in Joy
  • Project Euler, first problem: “Multiples of 3 and 5”
  • Generator Version
  • A little further analysis renders iteration unnecessary.
  • The Simplest Program
• Quadratic formula
  • Write a straightforward program with variable names.
  • Derive a definition.
• Replacing Functions in the Dictionary
  • A long trace
  • Replacing size with a Python version
  • A shorter trace
• Recursion Combinators
  • Designing Recursive Functions
  • Primitive Recursive Functions
  • Hylomorphism
  • Hylomorphism in Joy
  • Derivation of hylomorphism combinator
  • Four Specializations
  • Anamorphism
  • Catamorphism
  • Example: Factorial Function
  • Example: tails
  • Conclusion: Patterns of Recursion
  • Appendix: Fun with Symbols
• Treating Trees I: Ordered Binary Trees
  • Adding Nodes to the Tree
  • Interlude: cmp combinator
  • A Function to Traverse this Structure
  • Interlude: A Set-like Datastructure
  • A Version of Tree-iter that does In-Order Traversal
  • Getting values by key
  • Tree-delete
  • Appendix: The source code.
• Treating Trees II: treestep
  • Derive the recursive function.
  • Extract the givens to parameterize the program.
  • Define treestep
  • Examples
  • Redefining the Ordered Binary Tree in terms of treestep.
  • With treegrind?
  • treegrind with step
  • Do we have the flexibility to reimplement Tree-get?
  • Putting it together
• Using x to Generate Values
  • direco
  • Making Generators
  • Generating Multiples of Three and Five
  • Project Euler Problem One
  • A generator for the Fibonacci Sequence.
  • Project Euler Problem Two
  • How to compile these?
  • An Interesting Variation
• Newton’s method
  • A Generator for Approximations
  • Finding Consecutive Approximations within a Tolerance
• Square Spiral Example Joy Code
  • Original Form
  • Translation to Joy
  • Putting the Pieces Together
  • Turning it into a Generator with x
  • Conclusion
• Traversing Datastructures with Zippers
  • Trees
  • Zipper in Joy
  • dip and infra
  • Z
  • Addressing
  • Determining the right “path” for an item in a tree.
• The Blissful Elegance of Typing Joy
  • Part I: Pöial’s Rules
  • Part II: Implementation
  • Part III: Compiling Yin Functions
  • Part IV: Types and Subtypes of Arguments
  • Part V: Functions that use the Stack
  • Part VI: Multiple Stack Effects
  • Part VII: Typing Combinators
  • Conclusion
  • Appendix: Joy in the Logical Paradigm
• Type Checking
  • An Example
  • Unification Works “in Reverse”
  • Failing a Check
• No Updates
• Categorical Programming
• The Four Fundamental Operations of Definite Action
  • Sequence
  • Branch
  • Loop
  • Parallel
• ∂RE
  • Brzozowski’s Derivatives of Regular Expressions
  • Implementation
  • Let’s try it out…
  • Larger Alphabets
  • State Machine
  • Reversing the Derivatives to Generate Matching Strings