List of functional programming topics

This is a list of functional programming topics.

Contents 1 Foundational concepts 2 Lambda calculus 3 Combinatory logic 4 Intuitionistic logic 5 Type theory 6 Denotational semantics 7 Category theory 8 Operational issues 9 Languages

Foundational concepts

• Programming paradigm
• Declarative programming
• Programs as mathematical objects
• Function-level programming
• Purely functional
• 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
• Linear logic
• Game semantics

Type theory

• Typed lambda calculus
• Typed and untyped languages
• Type signature
• Type inference
• Datatype
• Algebraic data type
• 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
• Non-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 (computer science)

Languages

• Abstract Rewriting Machine
• Clean programming language
• Clojure programming language
• Erlang programming language
• FP programming language
• F# programming language
• Haskell programming language
  • Glasgow Haskell Compiler
  • Gofer
  • Hugs
  • Template Haskell
• ISWIM
• Kent Recursive Calculator
• Kogut programming language
• Lisp
  • AutoLISP
  • Common Lisp
  • Emacs Lisp
  • Scheme programming language
  • Lush programming language
• Mercury programming language
• Miranda programming language
• ML programming language (Category:ML programming language family)
  • Mythryl
  • Objective Caml
  • Standard ML
• Pure
• Q (equational programming language)
• Q (programming language from Kx Systems)
• Quantum programming
• Scala
• SISAL
• Ωmega