List of functional programming topics explained

This is a list of functional programming topics.

Foundational concepts

• Programming paradigm
• Declarative programming
• Programs as mathematical objects
• Function-level programming
• Purely functional programming
• Total functional programming
• Lambda programming
• Static scoping
• Higher-order function
• Referential transparency

Lambda calculus

• Currying
• Lambda abstraction
• Church–Rosser theorem
• Extensionality
• Church numeral

Combinatory logic

• Fixed point combinator
• SKI combinator calculus
• B, C, K, W system
• SECD machine
• Graph reduction machine

Intuitionistic logic

• Sequent, sequent calculus
• Natural deduction
• Intuitionistic type theory
• BHK interpretation
• Curry–Howard correspondence
• Linear logic
• Game semantics

Type theory

• Typed lambda calculus
• Typed and untyped languages
• Type signature
• Type inference
• Datatype
• Algebraic data type (generalized)
• Type variable
• First-class value
• Polymorphism
• Calculus of constructions

Denotational semantics

• Domain theory
  • Directed complete partial order
  • Knaster–Tarski theorem

Category theory

• Cartesian closed category
• Yoneda lemma

Operational issues

• Graph reduction
  • Combinator graph reduction
• Strict programming language
• Lazy evaluation, eager evaluation
• Speculative evaluation
• Side effect
• Assignment
  • Setq
• Closure
• Continuation
• Continuation passing style
• Operational semantics
• State transition system
• Simulation preorder
• Bisimulation
• Monads in functional programming
• Exception handling
• Garbage collection

Programming languages

• Clean
• Clojure
• Elixir
• Erlang
• FP
• F#
• Haskell
  • Glasgow Haskell Compiler
  • Gofer
  • Hugs
  • Template Haskell
• ISWIM
• JavaScript
• Kent Recursive Calculator
• Lisp
  • AutoLISP
  • Common Lisp
  • Emacs Lisp
  • Scheme
• Mercury
• Miranda
• ML
  • OCaml
  • Standard ML
• Pure, predecessor Q
• Q (programming language from Kx Systems)
• Quantum programming
• Scala
• SISAL
• Ωmega