Why Functional Programming

Presented Star City Code School

Transcript

1. Why Func)onal Programming?
2. You wouldn't want to write non-func'onal code, would you?
3. What is Func,onal Programming?
4. First, What is Impera/ve Programming? the kind your doing now
5. Impera've Programming Computa(on is performed through successive muta(on of state via statements. • Based on the Von Neumann computer architecture • Models implementa6on details of the computer (or what the computer used to be) • program variables ↔ computer storage cells • control statements ↔ computer test-and-jump instruc6ons • assignment statements ↔ fetching, storing instruc6ons • expressions ↔ memory reference and arithme6c instruc6ons.
6. Impera've Programming Problems • Close coupling of seman1cs to state transi1on • Poorly suited to concurrent and parallel computa1on • Lacks a useful founda1on fom which to reason about computa1on • correctness, testability, etc.
7. Impera've Programming Some Impera*ve languages - C 1 - Java 2 - JavaScript 3 - Ruby 4 - C++ 5 5 object oriented with mul2ple inheritence, sta2c typing, technically weak typing, and a specifica2on full of contradi2ons (see picture, right) 4 object oriented, dynamic typing, strong typing 3 prototypical object oriented, dynamic typing, weak/duck typing 2 object oriented, sta0c typing, strong typing 1 procedural, sta/c typing, weak typing
8. Impera've Programming Example: inner product int calc_inner_product(int[] a, int[] b, int dim) { int c = 0; for(int i = 0; i < dim; ++i) { c = c + a[i] * b[i]; } return c; }
9. Impera've Programming Example: inner product • Operates on invisible state • Dynamic and repe55ve; to understand it you must mentally execute it • Computes the result word-at-a-5me by repe55on of assignment and modifica5on • Entangles housekeeping opera5ons with the rest of the code, making them impossible to extract and reuse
10. c + a[i] * b[i];
11. Func%onal inner product Clojure (reduce + (map * a b)) Haskell foldr (+) 1 (zipWith (*) a b) Ruby a.zip(b).map {|x| x.reduce(:*)}.reduce(:+)
12. Wait, what? Ruby!?
13. #javascript is a func/onal language the same way my sedan is a truck– I use it to haul things around, but it wasn’t built for it.
14. OOP Matrix Mul,plica,on public class Matrix { int n; int m; double[,] a; public Matrix(int n, int m) { if (n <= 0 || m <= 0) throw new ArgumentException("Matrix dimensions must be positive"); this.n = n; this.m = m; a = new double<n, m>; } //indices start from one public double this<int i, int j> { get { return a[i - 1, j - 1]; } set { a[i - 1, j - 1] = value; } } public int N { get { return n; } } public int M { get { return m; } } public static Matrix operator*(Matrix _a, Matrix b) { int n = _a.N; int m = b.M; int l = _a.M; if (l != b.N) throw new ArgumentException("_a.M must be equal b.N"); Matrix result = new Matrix(_a.N, b.M); for(int i = 0; i < n; i++) for (int j = 0; j < m; j++) { double sum = 0.0; for (int k = 0; k < l; k++) sum += _a.a[i, k]*b.a[k, j]; result.a[i, j] = sum; } return result; } }
15. Before we go any further Lisp expression syntax in one slide Instead of this: foo(1, 2, bar(3, 4)); This: (foo 1 2 (bar 3 4))
16. Func%onal Matrix Mul%plica%on (defn dot-product [x y] (reduce + (map * x y))) (defn transpose [coll] (apply map vector coll)) (defn matrix-mult [mat1 mat2] (map (fn [row] (map (partial dot-product row) (transpose mat2))) mat1))
17. What makes a language func0onal?
18. Func%onal Programming6 • Composed of expressions • First-class func6ons • Pure func6ons • Immutable data • Value-based equality seman6cs 6 There are many more features common to FP languages, but these are the essen7als.
19. Composed of expressions • No Statements • No assignment, control structures, or explicit return • Programs are expressed by composing func%ons together • No explicit intermediate state
20. What's wrong with Statements? • They are not composable • You cannot pass them as arguments to a func6on • You cannot build higher abstrac6ons from them • No formal “algebra” by which to op6mize or evaluate the correctness of programs. • statements cannot be reduced (operate on hidden state) • None of their uses are unique to statements • usually used to approximate expression composi6on in an impera6ve way.
21. We don't need statements if(predicate, then, else) Takes a predicate expression and, if true, returns the result of evalua6ng the then expression; otherwise, returns the result of evalua6ng the else expression eq(a, b) If a is func)onally equivalent to b, returns true; otherwise, false
22. Expression Algebra if(a, eq(x, b), eq(x, c)) ≡ eq(x, if(a, b, c)) This is possible because if is an expression and expressions adhere to simple, well-defined rules of composi9on
23. First-class Func-ons Func%ons are a primi%ve en%ty type in the language • Func&ons can be passed as arguments to other func&ons • Higher Order func&ons: • Func&ons that take func&ons as arguments or return func&ons as results
24. Higher Order Func.ons (defn make-adder [n] (fn [x] (+ n x))) (map (make-adder 3) [1 2 3 4]) result: [4 5 6 7]
25. Higher Order Func.ons (filter odd? (range 10)) result: [1 3 5 7 9]
26. Higher Order Func.ons (defn prime? [num] (let [p (fn [x] (= (mod num x) 0))] (not (some p (range 2 num))))) (def count-if (comp count filter)) (count-if prime? (range 3000)) result: 432
27. Laziness Higher order func.ons make lazy evalua.on possible: The range func)on produces a lazy-sequence of all posi)ve integers. (def all-primes (filter prime? (range))) (take 20 all-primes) result: [0 1 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61]
28. Laziness ... just don't run this: (last all-primes) result: ...
29. Pure Func)ons A rela'on between a set of inputs and a set of poten'al outputs with the property that each input is related to exactly one output. • Implies no side-effects • Enables referen%al transparency • an expression can be replaced with its value without changing the behavior of a program • Makes many op7miza7ons possible (e.g., memoiza7on) • Work hand-in-hand with immutable data
30. Immutable Data Data that cannot be modified a/er it is created • New values are func%ons of old values • Values can always be observed and new values calculated from old values without coordina8on • Values will never change "in hand" • Values can be safely shared between threads • No need for defensive copying (or any copying)
31. Persistent Immutable Datastructures Immutable data structures that share structure under the hood • safe to do share data between data- structures because all data is immutable • Unreachable data can be garbage- collected at op7mal granularity • Crea7ng new data-structures from exis7ng ones requires li=le or no copying of member data
32. Persistent Immutable Datastructures
33. Value-based equality seman1cs Equality is determined by an objects values, not by its iden6ty (e.g., instance)
34. State, Iden*ty, and Value • Values don't change (if they did, they'd be different values) • e.g., 72, {–, ‖, —, ―}, "cat", [2, 3, 5, 7] • An IdenGty is an enGty that is associated with different values over Gme • State is a value at a point in Gme • IdenGGes give us conGnuity across state changes
35. Func%onal Programming is Inevitable • Virtually every mainstream language has been adding or seen widespread adop7on the aforemen7oned features at an increasingly rapid pace • Java Lambdas • Ruby Lazy Sequences • JavaScript ImmutableJS • For the past 50+ years impera7ve languages have been slowly adding func7onal features • Adding func7onal features to impera7ve languages is a double-edged sword (complexity, sub-op7mal implementa7on)
36. Try a Func*onal Language • Wri%ng func%onal code in a func%onal language, rather than using a func%onal style in an impera%ve language is: • Simpler, and o;en easier • Allows you to lean on features (e.g., pure func%ons and immutable data) • O;en more performant (e.g., persistent immutable datastructures)
37. Try a Func*onal Language Haskell - Purely func0onal, sta0cally-typed (ML family) Clojure - (mostly) Purely func4onal, dynamically-typed, runs on the JVM and JavaScript VMs (Lisp family) F# - sta(cally-typed, runs on .net run(me (OCaml Family)
38. About me Joseph Smith So,ware Engineer Cognitect, Inc. (Clojure, Datomic, etc.)