# Functional Programming Lecture 1: Introduction

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1 Functional Programming Lecture 1: Introduction Viliam Lisý Artificial Intelligence Center Department of Computer Science FEE, Czech Technical University in Prague

2 Acknowledgements This course is based on materials created by: Jiří Vyskočil, Michal Pěchouček ČVUT, Czech Republic Koen Claessen and Emil Axelsson Chalmers University of Technology, Sweden

3 What is functional programming? Wikipedia: Functional programming is a programming paradigm a style of building the structure and elements of computer programs that treats computation as the evaluation of mathematical functions.

4 Goal of the course 1. Improve your programming skills! master recursion master problem decomposition rethink side effects different perspective to the same problems 2. Learn principles of functional programming has clear benefits for SOME problems it is used in many other languages

5 Why do I care? quickly learn new programming languages programming paradigms change and develop no side effects is great for parallelization and verification understanding fundamentals of computation

7 Imperative vs. Declarative Instructions to change the computer s state x:=x+1 deletefile( slides.pdf ) Are executed have effects Run program by following instructions top-down Functions used to declare dependences between data values: z = g(y) y = f(x) Expressions are evaluated result to a value Run program by evaluating dependencies

8 Pure functional programming No side effects output of a function depends only on its inputs function does not change anything in evaluation can be evaluated in any order (many times, never) No mutable data More complex function based on recursion no for/while cycles natural problem decomposition mathematical induction

9 Pure functional programming Forbids most of what you use in (C/Java) we will show you do really not loose anything it can be useful for many tasks it often leads to more compact code!?! Substantially less time spent debugging encapsulation, repeatability, variety of mistakes Focus on operations with symbols Easier parallelization and verification Generally less computationally efficient

10 Brief History Lambda calculus (1930s) formal theory of computation older than TM Lisp = List processor (1950s) early practical programming language second oldest higher level language after Fortran ML = Meta language (1970s) Lisp with types, used in compilers Haskell = first name of Curry (1990s) standard for functional programming research Python, Scala, Java8, C++ 11,.

11 What will we learn? Lisp (Scheme) Lambda calculus Haskell

12 Why LISP? Extremely simple Reasonably popular Allows deriving all concepts from principles Directly matches lambda calculus

13 Why Haskell? Purely functional language promotes understanding the paradigm Rich syntactic sugar (contrast to Lisp) Most popular functional language Fast prototyping of complex systems Why not Scala?

14 Course organization Web: cw.fel.cvut.cz/wiki/courses/fup Lectures + Labs Homework every 2 weeks (50 %) 3x10 Scheme 2x10 Haskell must have at least 1 point from each and >= 25 Programming exam (30 %) Test (20 %)

15 Suggested literature R. Kent Dybvig: The Scheme Programming Language, Fourth Edition, MIT Press, Greg Michaelson: An Introduction to Functional Programming Through Lambda Calculus, Dover edition, 2011.

16 Scheme Dialect of Lisp (such as Common Lisp, Racket) Created in 1970 at MIT by Steele and Sussman Last standard from 2007 The Revised 6 Report on the Algorithmic Language Scheme (R6RS) Supports imperative programming we will not use it (we want to learn FP) DrRacket: racket-lang.org text editor + REPL (read-evaluate-print loop)

17 Scheme syntax Scheme program is a collection of expressions Expression Evaluates to 5 5 "abc" "abc" #t #t + #<procedure:+> a?

18 Prefix notation Infix notation 1+2*5 Prefix notation + 1 * 2 5 In Scheme, there are no operator preferences (+ 1 (* 2 5))

19 S - expression (fn arg1 arg2 argn) ( operator of calling a function fn expression that evaluates to a procedure argx arguments of the function ) end of function call

20 Conventions Special suffixes? for predicates! for procedures with side effects -> in procedures that transform a type of an object Prefix of character / string / vector procedures char-, string-, and vector-

21 Basics data types Numbers (infinite precision, complex, etc.) +, -, *, /, abs, sqrt Logical values #t, #f, >, <, and, or, boolean? Strings "abc", "Hello!!!", string?, substring Other types symbol?, char?, procedure?, pair?, port?, vector?

22 Quote Do not evaluate, just to return the argument (quote exp) Abbreviated by ' A quoted expression can be evaluated by eval (eval (quote (+ 1 2)) Evaluate part of the argument (quasiquote (* (unquote (+ 2 2)) 4 5) Abbreviated by ` and, respectively

23 Identifiers Keywords, variables, and symbols may be formed from the following set of characters: the lowercase letters a through z, the uppercase letters A through Z, the digits 0 through 9, and the characters?!. + - * / < = > : \$ % ^ & _ cannot start with 0-9, +,

24 Define Naming expressions (define id exp) Defining functions (define (name <formals>) <body>)

25 Comments ; starts a comment until the end of the line on the line before the explained expression ;;; still start a comment until the end of the line used to comment a function or code segment # # delimit block comments

26 Conditional expressions if (if test-exp then-exp else-exp) cond (cond (test-exp1 exp) (test-exp2 exp) (#t exp)...)

27 Recursion A function calling itself (define (fact n) (cond ((= 0 n) 1) ((= 1 n) 1) (#t (* n (fact (- n 1)))) ) )

28 Avoiding infinite recursion 1. First expression of the function is a cond 2. The first test is a termination condition 3. The "then" of the first test is not recursive 4. The cond pairs are in increasing order of the amount of work required 5. The last cond pair is a recursive call 6. Each recursive call brings computations closer to the termination condition

29 Recursion Tail recursion Last thing a function does is the recursive call Analytic / synthetic Return value from termination condition / composed Tree recursion Function is called recursively multiple times (qsort) Indirect recursion Function A calls function B which calls A

30 Lists The key data structure of Lisp S-expressions are just lists '( ) Lists can be created by a function (list item1 item2 itemn) List are linked lists of pairs with '() at the end sometimes abbreviated by. (cons 1 2), (cons 1 (cons 2 '()) 1 2 '()

31 Lists Pairs forming the lists can be decomposed by car [car] first element of the pair cdr [could-er] second element of the pair (caddr x) shortcut for (car (cdr (cdr x ))) Empty list is a null pointer null? tests whether the argument is the empty list

32 Last Return the last element of a list (define (last list) (cond ((null? (cdr list)) (car list)) (#t (last (cdr list))) ) )

33 What have we learned? Functional programming is an alternative programming paradigm no side effects no mutable data structures focus on symbols Recursion is the key programming method Lists are a key data structure

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