Magical Haskell: A Friendly Approach to Modern Functional Programming, Type Theory, and Artificial Intelligence

About the Author ................................................................................................xiAbout the Technical Reviewer ...............................................................................xiiiAcknowledgments ...............................................................................................xvIntroduction .......................................................................................................xviiHow This Book Came to Be: Instead of an Introduction ............................................xixChapter 1: Wizards, Types, and Functions ....1Solving Problems As Wizards Do ....3Let’s Fall in Love with Types! ....7A Char and an Int Walk into a Bar and Make a Function ....8How FunTypical! ....12Curry and Recurse! ....15Conclusion ....19Chapter 2: Type Construction ....21House of Cards with a Little Help from Algebra ....22Algebraic Data Types ....25Records ....27Type Functions Are Functions, Maybe? ....30Advanced: On Data Constructors and Types ....37List, Recursion on Types and Patterns ....39Length of a List ....42Map a Function Over a List of Values ....44Conclusion ....50Chapter 3: Very Gentle Type Theory and Category Theory Intro ....51Types and Functions ....52Maybe and Advanced Generalized Functions ....54Dependent Function Types (Pi-Types) ....59Sum, Product, and Dependent Pair (Sigma) Types ....61Very Gentle Category Theory Introduction ....63Typeclasses ....66Conclusion ....70Chapter 4: Basic Typeclasses or “Show Me a Monoid” ....71Show Typeclass ....72Algebra Is Cool ....73Typeclass Hierarchy in Haskell ....76Lift Me Up! ....79Conclusion ....83Chapter 5: Functor, Bifunctor, and Applicative Functor Enteran Elevator … ....85Functor Typeclass Definition ....86Three-Dimensional Vector Example ....89Tracking Players in Our Game ....91You Are Either Functor or a Bifunctor ....92We Need a Bigger Lift ....98Action! Apply! Cut! ....104Applicative Typeclass ....107Conclusion ....111Chapter 6: O, Monad, Help Me Compose! ....113Can We Play Cards in This State? ....117Monad Typeclass and Basic Monads ....128Reader–Writer–State Triple ....132The State Monad ....132The Reader Monad ....135The Writer Monad ....140Conclusion ....145Chapter 7: Input, Transformer Stack, Output ....147Do Notation ....153Monad Transformer Stacks ....158Conclusion ....169Chapter 8: Blackjack: Full Haskell Program ....171Preparation ....174Initial “Pure” Design ....177Building the First Floor: IO ....183Building the Top Floor: StateT IO ....188Final Game and Recap ....197Conclusion ....201Chapter 9: Let’s AI ....203Agentic AI and Large Language Models ....203LLMs in a Nutshell ....205Haskell and LLMs ....210Big Picture of the Haskell AI Framework ....211Terminal Chatbot ....212Conclusion ....231Conclusion ....234Chapter 10: Terminal AI Chat Agent ....237Terminal UI Skeleton ....238Adding a Nicer Response Function ....239Initialization ....241Building the Monad Transformer Stack ....242Main Program ....245Building Muscles ....248Logging ....248Usage Stats in the Writer Monad ....253Chat History ....255Conclusion ....263Chapter 11: Web-Enabled AI Framework and GHC “Guts” ....265Terminal UI Improvements ....265Example Jarvis Scenarios ....270“M” Subchapter: Under the Hood of GHC ....278Adding a Web API ....283Mutable Variables ....294IORef: Simple Mutable Variables in the IO Monad ....295MVar: Mutable Variables with Concurrency Control ....296TVar: The Power of Software Transactional Memory (STM) ....298Conclusion ....300Chapter 12: Down the Rabbit Hole ....303MongoDB as a Persistence Layer ....304MongoDB Initialization ....308Adding a System Prompts Collection ....310Redesigning Architecture: MRWST Monad Transformer ....313Vectors and Type Families ....321Type Synonym Families ....322Data Families ....323Associated Type and Data Families ....325Vectors As Arrays in Haskell ....330More AI: Vector RAG ....340In-Memory Vector Engine ....344Conclusion ....358Chapter 13: AI Multi-agents, Arrows, and the Future ....359Arrows: The Last Abstraction ....361Arrows Definition and Basic Examples ....364Arrows Interface ....367AI Multi-agents and Arrows ....373AI Multi-agents Examples ....377Arrows to Support Quick AI Multi-agent Creation ....379Final Improvements for the AI Framework ....390Web Authentication with JWTs ....390Error Handling: Embracing the Try–Catch Approach ....396Multiple LLMs and Agents Support ....399Conclusion ....404Index ....407