# Functional Programming

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1 Functional Programming Björn B. Brandenburg The University of North Carolina at Chapel Hill Based in part on slides and notes by S. Olivier, A. Block, N. Fisher, F. Hernandez-Campos, and D. Stotts.

2 Brief Overview First, some introductory remarks. Then weʼll cover Haskell details in a tutorial style. Take notes. Ask questions. 2

3 What s a functional language? Most functional languages provide: Functions as first-class values Higher-order functions Primitive list type (operators on lists) Recursion Structured function return (return tuples) Garbage collection Polymorphism and type inference Covered next lecture. Functional programming. Also possible in imperative languages. Applying functional style to imperative language can yield very elegant code. 3

4 So Why Functional? Teaches truly recursive thinking. Teaches good programming style. Short, self-contained functions. Implicit Polymorphism. Natural expressiveness for symbolic and algebraic computations. Algorithms clearly map to the code that implements them. 4

5 Origins Lambda-calculus as semantic model (Church) LISP (1958, MIT, McCarthy) Alanzo Church (defun fib (n) (if (or (= n 0) (= n 1)) 1 (+ (fib (- n 1)) (fib (- n 2))))) Naive Fibonacci Implementation in LISP John McCarthy Source: Wikimedia Commons 5

6 Can Programming be Liberated from the von Neumann Style? This is the title of the lecture given by John Backus when he received the Turing Award in In this, he pointed out that a program should be an abstract description of algorithms rather than a sequence of changes in the state of the memory. He called for raising the level of abstraction A way to realize this goal is functional programming Programs written in modern functional programming languages are a set of mathematical relationships between objects. No explicit memory management takes place. 6

7 History Lisp Dynamic Scoping Common Lisp (CL), Scheme Static scoping ML (late 1970ies) Common Lisp Logo (unofficial) Scheme Logo Typing, type inference, fewer parentheses Haskell, Miranda (1980ies) Haskell Logo purely functional Compiler disallows side effects 7

8 Referential Transparency Bindings are immutable. Any name may be substituted by the value bound to that name and not alter the semantics of the expression. no side effects. This means no printf() debugging! Functional programing languages encourage referential transparency. Pure functional programming languages enforce referential transparency. 8

9 Referential Transparency If two expressions are defined to have equal values, then one can be substituted for the other in any expression without affecting the result of the computation. sumofsquares :: Int -> Int -> Int sumofsquares x y = let x2 = x * x y2 = y * y in x2 + y2 sumofsquares' :: Int -> Int -> Int sumofsquares' x y = (x * x) + (y * y) Semantically equivalent. 9

10 Referentially Transparent Functions aka pure functions A function is called referentially transparent if given the same argument(s), it always returns the same result. In mathematics, all functions are referentially transparent. In programming this is not always the case, with use of imperative features in languages. The subroutine/function called could affect some global variable that will cause a second invocation to return a different value. Input/Output 10

11 Evaluation (Scott) Advantages Lack of side effects makes programs easier to understand. Lack of explicit evaluation order (in some languages) offers possibility of parallel evaluation (e.g. Haskell). Programs are often surprisingly concise. Language can be extremely small and yet powerful. Problems Difficult (but not impossible!) to implement efficiently on von Neumann machines. Naive impl.: Lots of copying, inefficient cache use, memory use. Requires a different mode of thinking by the programmer. Not necessarily a bad thing! Difficult to integrate I/O into purely functional model. Haskell: Monads. 11

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