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functional-programming-anatomy.md

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Concepts

L1 Concepts

  • Immutable Data
  • Second-Order Functions
  • Constructing & Destructuring
  • Function Composition First-Class Functions & Lambdas

L2 Concepts

  • Algebraic Data Types
  • Pattern Matching
  • Parametric Polymorphism
  • General Recursion
  • Type Classes, Instances, & Laws
  • Lower-Order Abstractions (Equal, Semigroup, Monoid, etc)
  • Referential Transparency & Totality
  • Higher-Order Functions
  • Partial-Application, Currying, & Point-Free Style

L3 Concepts

  • Generalized Algebraic Data Types
  • Higher-Kinded Types
  • Rank-N Types
  • Folds & Unfolds
  • Higher-Order Abstractions (Category, Functor, Monad)
  • Basic Optics
  • Efficient Persistent Data Structures
  • Existential Types
  • Embedded DSlLs using Combinators

L4 Concepts

  • Codata

  • (Co)Recursion Schemes

  • Advanced Optics

  • Dual Abstractions (Comonad)

  • Monad Transformers

  • Free Monads & Extensible Effects

  • Functional architecture

  • Advanced Functors (Exponential, Profunctors, Contravariant)

  • Embedded DSlLs using GADTs, Finally Tagless

  • Advanced Monads (Continuation, Logic)

  • Type Families, Functional Dependencies

L5 Concepts

  • High-Performance
  • Kind Polymorphism
  • Generic Programming
  • Type-Level Programming
  • Dependent-Types, Singleton Types
  • Category Theory
  • Graph Reduction
  • Higher-Order Abstract Syntax
  • Compiler Design for Functional Languages
  • Profunctor Optics

Skills and Exercises

L1 Skills and Exercises

  • Use second-order functions (map, cite fold) on immutable data structures
  • Destructure values to access their components
  • Use data types to represent optionality
  • Read basic type signatures
  • Pass lambdas to second-order functions

L2 Skills and Exercises

  • Solve problems without nulls, exceptions, or type casts
  • Process & transform recursive data structures using recursion
  • Able to use functional programming “in the small”
  • Write basic monadic code for a concrete monad
  • Create type class instances for custom data types
  • Model a business domain with ADts
  • write functions that take and return functions
  • Reliably identify & isolate pure code from impure code
  • Avoid introducing unnecessary lambdas & named parameters

L3 Skills and Exercises

  • Able to use functional programming “in the large”
  • Test code using generators and properties
  • Write imperative code in a purely functional way through monads
  • Use popular purely functional libraries to solve business problems
  • Separate decision from effects
  • Write a simple custom lawful monad
  • Write production medium-sized projects
  • Use lenses & prisms to manipulate data
  • Simplify types by hiding irrelevant data with existentials

L4 Skills and Exercises

  • Design a minimally-powerful monad transformer stack
  • Write concurrent and streaming programs
  • Use purely functional mocking in tests
  • Use type classes to modularly model different effects
  • Recognize type patterns & abstract over them
  • Use functional libraries in novel ways
  • Use optics to manipulate state
  • write custom lawful monad transformers
  • Use free monads / extensible effects to separate concerns
  • Encode invariants at the type level
  • Effectively use FDs / type families to create safer code

L5 Skills and Exercises

  • Design a generic, lawful library with broad appeal
  • Prove properties manually using equational reasoning
  • Design & implement a new functional programming language
  • Create novel abstractions with laws
  • Write distributed systems with certain guarantees
  • Use proof systems to formally prove properties of code
  • Create libraries that do not permit invalid states
  • Use dependent-typing to prove more properties at compile-time
  • Understand deep relationships between different Concepts
  • Profile, debug, & optimize purely functional code with minimal sacrifices