Lambda Calculus & Functional programming
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This document provides an overview of functional programming and its history and applications. It discusses early concepts like the lambda calculus developed by Alonzo Church in the 1930s. It also outlines languages and tools that apply functional programming principles, like Lisp, ML, Haskell, and proof assistants. Some benefits of the functional paradigm discussed are purity, immutability, modularity, and simplicity. The document concludes by noting real-world applications of functional programming.
Lambda Calculus & Functional programming
- 2. onad
- 3. • Algorithm • David Hilbert (1928) — Entscheidungsproblem • Halting Problem
- 5. Alonzo Church (1903 – 1995)
- 6. Alonzo Church (1936) — Lambda Calculus
- 7. Alonzo Church (1932) — λ-calculus L, M, N ::= x | (λx. N) | (L M)
- 9. Rules • Alpha equivalence • Beta reduction λx.x λy.y (λx.x) y == y
- 10. λ-calculus λx.xIdentity λs.s sSelf Apply x => x s => s(s)
- 11. λ-calculus (s => s(s))(x => x) (x => x)(x => x) (x => x)
- 12. λ-calculus Recursion (s => s(s))(s => s(s)) (λs.s s)(λs.s s)
- 13. Church Encoding λx. λy. x λx. λy. y True False λp. λx. λy. p x yIf λp. λq. p q pAnd λp. λq. p p qOr
- 14. Church Encoding λf. λx. x λf. λx. f x 0 1 2 λf. λx. f (f x) λm. λn. λf. λx. m f (n f x)m + n
- 15. Church Encoding λx. λy. λz. z x yPair First λp. p (λx. λy. x) Second λp. p (λx. λy. y)
- 16. Modus Ponens
- 17. Alonzo Church (1940) — Typed λ-calculus
- 18. Howard 1980
- 19. Curry-Howard Correspondence • Proposition • Proof • Normalization • Type • Program • Evaluation
- 20. Correspondence
- 21. Languages • Lisp (McCarthy, 1960) • Scheme • Racket (1994) • Clojure (Hickey, 2007) • ML (Milner, 1979) • Haskell (1987) • O’Caml (Leroy, 1996) • Erlang (Armstrong, 1996) • Scala (Odersky, 2004) • F# (Syme, 2006)
- 22. ML Example
- 23. Proof Assistants • Automath (de Bruijn, 1970) • Type Theory (Martin Löf, 1975) • Coq (Huet and Coquand, 1988) • Isabelle (Paulson, 1993) • Epigram (McBride and McKinna, 2004) • Agda (Norell, 2005) • Idris
- 24. Functional Programming • First-class Functions / Higher Order Functions • Pure Functions / Referential Transparency • Immutability • Recursion
- 25. Benefits • Guaranties! • Modularity • Composability • Conciseness • Concurrency / Distribution • Simplicity • Beauty
- 26. Real World
- 28. Resources • "Propositions as Types" by Philip Wadler https://www.youtube.com/watch?v=FiflFiZ6pPI&t=1430s • Category Theory for the Working Hacker by Philip Wadler https://www.youtube.com/watch?v=V10hzjgoklA • The Value of Values with Rich Hickey https://www.youtube.com/watch?v=-6BsiVyC1kM • Why Functional Programming Matters by John Hughes https://www.youtube.com/watch?v=XrNdvWqxBvA • Robert C Martin - Functional Programming; What? Why? When? https://www.youtube.com/watch?v=7Zlp9rKHGD4 • Persistent Data Structures. MIT 6.851 Advanced Data Structures https://www.youtube.com/watch?v=T0yzrZL1py0 • Simon Peyton Jones - Haskell is useless https://www.youtube.com/watch?v=iSmkqocn0oQ&t=199s • Brian Beckman: Don't fear the Monad https://www.youtube.com/watch?v=ZhuHCtR3xq8 • Erik Meijer: Functional Programming https://www.youtube.com/watch?v=z0N1aZ6SnBk • http://learnyouahaskell.com/ • Scala for the Impatient – http://www.horstmann.com/scala/