Lambda calculus is a formal system in mathematical logic for expressing computation based on function abstraction and application. It's foundational in computer science and mathematics, especially in the development of functional programming languages like Haskell and Lisp. 📚

Key Concepts

  • Variables: Symbols representing values (e.g., x, y)
  • Abstraction: Creating functions using the lambda operator (e.g., λx.x is the identity function)
  • Application: Applying functions to arguments (e.g., (λx.x) 5 evaluates to 5)
  • Beta Reduction: Simplifying expressions by substituting arguments into functions (e.g., (λx.x+1) 3 → 4)
  • Eta Conversion: Equating functions that have the same behavior (e.g., λx.(λy.y) x ≡ λy.y)

Applications

Lambda calculus underpins:

  • Functional Programming: Core to languages like Scala and Erlang
  • Type Theory: Basis for modern programming language design
  • Computer Science Theory: Used in automata theory and computability studies

Example

(λx.λy.x+y) 2 3 → λy.2+y → 5

This demonstrates function application and reduction steps. 📈

Further Reading

Explore Functional Programming Basics to deepen your understanding of related concepts. 💡

lambda_calculus
functional_programming