1. Introduction to Programming in Haskell Koen Lindström Claessen

2. Programming Exciting subject at the heart of computing Never programmed? –Learn to make the computer obey you! Programmed before? –Lucky you! Your knowledge will help a lot... –...as you learn a completely new way to program Everyone will learn a great deal from this course!

3. Goal of the Course Start from the basics, after Datorintroduktion Learn to write small-to-medium sized programs in Haskell Introduce basic concepts of computer science

4. The Flow You prepare in advance I explain in lecture You learn with exercises You put to practice with lab assignments Tuesdays,Fridays Mondays/Tuesdays Submit end of each week Do not break the flow!

5. Exercise Sessions Mondays or Tuesdays –Depending on what group you are in Come prepared Work on exercises together Discuss and get help from tutor –Personal help Make sure you understand this week’s things before you leave

6. Lab Assignments Work in pairs –(Almost) no exceptions! Lab supervision –Book a time in advance –One time at a time! Start working on lab when you have understood the matter Submit end of each week Feedback –Return: The tutor has something to tell you; fix and submit again –OK: You are done even this week!

7. Getting Help Weekly group sessions –personal help to understand material Lab supervision –specific questions about programming assignment at hand Discussion forum –general questions, worries, discussions

8. Assessment Written exam (3 credits) –Consists of small programming problems to solve on paper –You need Haskell ”in your fingers” Course work (2 credits) –Complete all labs successfully

9. A Risk 7 weeks is a short time to learn programming So the course is fast paced –Each week we learn a lot –Catching up again is hard So do keep up! –Read the text book each week –Make sure you can solve the problems –Go to the weekly exercise sessions –From the beginning

10. Course Homepage The course homepage will have ALL up-to- date information relevant for the course –Schedule –Lab assignments –Exercises –Last-minute changes –(etc.) http://www.cs.chalmers.se/Cs/Grundutb/Kurser/funht/ Or Google for ”chalmers introduction functional programming”

11. Software Software = Programs + Data

12. Data Data is any kind of storable information. Examples: Numbers Letters Email messages Songs on a CD Maps Video clips Mouse clicks Programs

13. Programs compute new data from old data. Example: Baldur’s Gate computes a sequence of screen images and sounds from a sequence of mouse clicks.

14. Building Software Systems A large system may contain many millions of lines of code. Software systems are among the most complex artefacts ever made. Systems are built by combining existing components as far as possible. Volvo buys engines from Mitsubishi. Bonnier buys Quicktime Video from Apple.

15. Programming Languages Programs are written in programming languages. There are hundreds of different programming languages, each with their strengths and weaknesses. A large system will often contain components in many different languages.

16. Programming Languages C Haskell Java ML O’CaML C++ C# Prolog Perl Python Ruby PostScript SQL Erlang PDF bash JavaScript Lisp Scheme BASIC csh VHDL Verilog Lustre Esterel Mercury Curry which language should we teach?

17. Programming Language Features polymorphism higher-order functions statically typed parameterized types overloading type classes object oriented reflection meta- programming compiler virtual machine interpreter pure functions lazy high performance type inference dynamically typed immutable datastructures concurrency distribution real-time Haskell unification backtracking Java C

18. Teaching Programming Give you a broad basis –Easy to learn more programming languages –Easy to adapt to new programming languages Haskell is defining state-of-the-art in programming language development –Appreciate differences between languages –Become a better programmer!

19. Industrial Uses of Functional Languages Intel (microprocessor verification) Hewlett Packard (telecom event correlation) Ericsson (telecommunications) Carlstedt Research & Technology (air-crew scheduling) Hafnium (Y2K tool) Shop.com (e-commerce) Motorola (test generation) Thompson (radar tracking) Microsoft (SDV) Jasper (hardware verification)

20. Why Haskell? Haskell is a very high-level language (many details taken care of automatically). Haskell is expressive and concise (can achieve a lot with a little effort). Haskell is good at handling complex data and combining components. Haskell is not a high-performance language (prioritise programmer-time over computer-time).

21. A Haskell Demo Start the GHCi Haskell interpreter: > ghci ___ ___ _ / _ \ /\ /\/ __(_) / /_\// /_/ / / | | GHC Interactive, version 6.6.1, for Haskell 98. / /_\\/ __ / /___| | http://www.haskell.org/ghc/ \____/\/ /_/\____/|_| Type :? for help. Loading package base... linking... done. Prelude> The prompt. GHCi is ready for input.

22. GHCi as a Calculator Prelude> 2+2 4 Prelude> 2-2 0 Prelude> 2*3 6 Prelude> 2/3 0.666666666666667 Type in expressions, and ghci calculates and prints their value. Multiplication and division look a bit unfamiliar – we cannot omit multiplication, or type horizontal lines. 2 3 X

23. Binding and Brackets Prelude> 2+2*3 8 Prelude> (2+2)*3 12 Prelude> (1+2)/(3+4) 0.428571428571429 Multiplication and division ”bind more tightly” than addition and subtraction – so this means 2+6, not 4*3. We use brackets to change the binding (just as in mathematics), so this is 4*3. This is how we write 1+2 3+4

24. Quiz What is the value of this expression? Prelude> 1+2/3+4

25. Quiz What is the value of this expression? Prelude> 1+2/3+4 5.66666666666667

26. Example: Currency Conversion Suppose we want to buy a game costing €53 from a foreign web site. Prelude> 53*9.16642 485.82026 Exchange rate: €1 = 9.16642 SEK Price in SEK Boring to type 9.16642 every time we convert a price!

27. Naming a Value We give a name to a value by making a definition. Definitions are put in a file, using a text editor such as emacs. > emacs Examples.hs The UNIX prompt, not the ghci one! Do this in a separate window, so you can edit and run hugs simultaneously. Haskell files end in.hs

28. Creating the Definition Give the name euroRate to the value 9.16642 variable

29. Using the Definition Prelude> :l Examples Main> euroRate 9.16642 Main> 53*euroRate 485.82026 Main> Load the file Examples.hs into ghci – make the definition available. The prompt changes – we have now loaded a program. We are free to make use of the definition.

30. Functional Programming is based on Functions A function is a way of computing a result from its arguments A functional program computes its output as a function of its input –E.g. Series of screen images from a series of mouse clicks –E.g. Price in SEK from price in euros

31. A Function to convert Euros to SEK -- convert euros to SEK sek x = x*euroRate Function name – the name we are defining. Name for the argument Expression to compute the result A definition – placed in the file Examples.hs A comment – to help us understand the program

32. Using the Function Main> :r Main> sek 53 485.82026 Reload the file to make the new definition available. Call the function Notation: no brackets! C.f. sin 0.5, log 2, not f(x). sek x = x*euroRate x = 53 While we evaluate the right hand side 53*euroRate

33. Binding and Brackets again Main> sek 53 485.82026 Main> sek 50 + 3 461.321 Main> sek (50+3) 485.82026 Main> Different! This is (sek 50) + 3. Functions bind most tightly of all. Use brackets to recover sek 53. No stranger than writing sin  and sin (  +  )

34. Converting Back Again -- convert SEK to euros euro x = x/euroRate Main> :r Main> euro 485.82026 53.0 Main> euro (sek 49) 49.0 Main> sek (euro 217) 217.0 Testing the program: trying it out to see if does the right thing.

35. Automating Testing Why compare the result myself, when I have a computer? Main> 2 == 2 True Main> 2 == 3 False Main> euro (sek 49) == 49 True The operator == tests whether two values are equal Yes they are No they aren’t Let the computer check the result. Note: two equal signs are an operator. One equal sign makes a definition.

36. Defining the Property Define a function to perform the test for us prop_EuroSek x = euro (sek x) == x Main> prop_EuroSek 53 True Main> prop_EuroSek 49 True Performs the same tests as before – but now we need only remember the function name!

37. Writing Properties in Files Functions with names beginning ”prop_” are properties – they should always return True Writing properties in files –Tells us how functions should behave –Tells us what has been tested –Lets us repeat tests after changing a definition Properties help us get programs right!

38. Automatic Testing Testing account for more than half the cost of a software project We will use a tool for automatic testing import Test.QuickCheck Add first in the file of definitions – makes QuickCheck available. Capital letters must appear exactly as they do here.

39. Running Tests Main> quickCheck prop_EuroSek Falsifiable, after 10 tests: 3.75 Main> sek 3.75 34.374075 Main> euro 34.374075 3.75 Runs 100 randomly chosen tests It’s not true! The value for which the test fails. Looks OK

40. The Problem There is a very tiny difference between the initial and final values Calculations are only performed to about 15 significant figures The property is wrong! Main> euro (sek 3.75) - 3.75 4.44089209850063e-016 e means £ 10 -16

41. Fixing the Problem The result should be nearly the same The difference should be small – say <0.000001 Main> 2<3 True Main> 3<2 False We can use < to see whether one number is less than another

42. Defining ”Nearly Equal” We can define new operators with names made up of symbols x ~== y = x-y < 0.000001 Define a new operator ~== With arguments x and y Which returns True if the difference between x and y is less than 0.000001

43. Testing ~== Main> 3 ~== 3.0000001 True Main> 3~==4 True OK What’s wrong? x ~== y = x-y < 0.000001

44. Fixing the Definition A useful function Main> abs 3 3 Main> abs (-3) 3 Absolute value x ~== y = abs (x-y) < 0.000001 Main> 3 ~== 4 False

45. Fixing the Property prop_EuroSek x = euro (sek x) ~== x Main> prop_EuroSek 3 True Main> prop_EuroSek 56 True Main> prop_EuroSek 2 True

46. Name the Price Let’s define a name for the price of the game we want price = 53 Main> sek price ERROR - Type error in application *** Expression : sek price *** Term : price *** Type : Integer *** Does not match : Double

47. Every Value has a Type The :i command prints information about a name Main> :i price price :: Integer Main> :i euroRate euroRate :: Double Integer (whole number) is the type of price Double is the type of real numbers Funny name, but refers to double the precision that computers originally used

48. More Types Main> :i True True :: Bool -- data constructor Main> :i False False :: Bool -- data constructor Main> :i sek sek :: Double -> Double Main> :i prop_EuroSek prop_EuroSek :: Double -> Bool The type of truth values, named after the logician Boole The type of a function Type of the argument Type of the result

49. Types Matter Types determine how computations are performed Main> 123456789*123456789 :: Double 1.52415787501905e+016 Main> 123456789*123456789 :: Integer 15241578750190521 Correct to 15 figures Specify which type to use The exact result – 17 figures (but must be an integer) Hugs must know the type of each expression before computing it.

50. Type Checking Infers (works out) the type of every expression Checks that all types match – before running the program

51. Our Example Main> :i price price :: Integer Main> :i sek sek :: Double -> Double Main> sek price ERROR - Type error in application *** Expression : sek price *** Term : price *** Type : Integer *** Does not match : Double

52. Why did it work before? Main> sek 53 485.82026 Main> 53 :: Integer 53 Main> 53 :: Double 53.0 Main> price :: Integer 53 Main> price :: Double ERROR - Type error in type annotation *** Term : price *** Type : Integer *** Does not match : Double Certainly works to say 53 What is the type of 53? 53 can be used with several types – it is overloaded Giving it a name fixes the type

53. Fixing the Problem Definitions can be given a type signature which specifies their type price :: Double price = 53 Main> :i price price :: Double Main> sek price 485.82026

54. Always Specify Type Signatures! They help the reader (and you) understand the program The type checker can find your errors more easily, by checking that definitions have the types you say Type error messages will be easier to understand Sometimes they are necessary (as for price)

55. Example with Type Signatures euroRate :: Double euroRate = 9.16642 sek, euro :: Double -> Double sek x = x*euroRate euro x = x/euroRate prop_EuroSek :: Double -> Bool prop_EuroSek x = euro (sek x) ~== x

56. What is the type of 53? Main> :i 53 Unknown reference `53' Main> :t sek 53 sek 53 :: Double Main> :t 53 53 :: Num a => a Main> :i * infixl 7 * (*) :: Num a => a -> a -> a -- class member :i only works for names But :t gives the type (only) of any expression If a is a numeric type Then 53 can have type a If a is a numeric type Then * can have type a->a->a

57. What is Num exactly? Main> :i Num -- type class... class (Eq a, Show a) => Num a where (+) :: a -> a -> a (-) :: a -> a -> a (*) :: a -> a -> a... -- instances: instance Num Int instance Num Integer instance Num Float instance Num Double instance Integral a => Num (Ratio a) A ”class” of types With these operations Types which belong to this class

58. Examples Main> 2 + 3.5 5.5 Main> True + 3 ERROR - Cannot infer instance *** Instance : Num Bool *** Expression : True + 3 2, +, and 3.5 can all work on Double Sure enough, Bool is not in the Num class

59. A Tricky One! Main> sek (-10) -91.6642 Main> sek -10 ERROR - Cannot infer instance *** Instance : Num (Double -> Double) *** Expression : sek - 10 What’s going on?

60. Operators Again Main> :i + infixl 6 + (+) :: Num a => a -> a -> a -- class member Main> :i * infixl 7 * (*) :: Num a => a -> a -> a -- class member The binding power (or precedence) of an operator – * binds tighter than + because 7 is greater than 6

61. Giving ~== a Precedence Main> 1/2000000 ~== 0 ERROR - Cannot infer instance *** Instance : Fractional Bool *** Expression : 1 / 2000000 ~== 0 Wrongly interpreted as 1 / (2000000 ~== 0) Instead of (1/2000000) ~== 0

62. Giving ~== a Precedence ~== should bind the same way as == Main> :i == infix 4 == (==) :: Eq a => a -> a -> Bool -- class member Main> 1/2000000 ~== 0 True infix 4 ~== x ~== y = abs (x-y) < 0.000001

63. Summary Think about the properties of your program –... and write them down It helps you understanding –the problem you are solving –the program you are writing It helps others understanding what you did –co-workers –customers –you in 1 year from now

64. Cases and Recursion

65. Example: The squaring function Example: a function to compute -- sq x returns the square of x sq :: Integer -> Integer sq x = x * x

66. Evaluating Functions To evaluate sq 5: –Use the definition—substitute 5 for x throughout sq 5 = 5 * 5 –Continue evaluating expressions sq 5 = 25 Just like working out mathematics on paper sq x = x * x

67. Example: Absolute Value Find the absolute value of a number -- absolute x returns the absolute value of x absolute :: Integer -> Integer absolute x = undefined

68. Example: Absolute Value Find the absolute value of a number Two cases! –If x is positive, result is x –If x is negative, result is -x -- absolute x returns the absolute value of x absolute :: Integer -> Integer absolute x | x > 0 = undefined absolute x | x < 0 = undefined Programs must often choose between alternatives Think of the cases! These are guards

69. Example: Absolute Value Find the absolute value of a number Two cases! –If x is positive, result is x –If x is negative, result is -x -- absolute x returns the absolute value of x absolute :: Integer -> Integer absolute x | x > 0 = x absolute x | x < 0 = -x Fill in the result in each case

70. Example: Absolute Value Find the absolute value of a number Correct the code -- absolute x returns the absolute value of x absolute :: Integer -> Integer absolute x | x >= 0 = x absolute x | x < 0 = -x >= is greater than or equal, ¸

71. Evaluating Guards Evaluate absolute (-5) –We have two equations to use! –Substitute absolute (-5) | -5 >= 0 = -5 absolute (-5) | -5 < 0 = -(-5) absolute x | x >= 0 = x absolute x | x < 0 = -x

72. Evaluating Guards Evaluate absolute (-5) –We have two equations to use! –Evaluate the guards absolute (-5) | False = -5 absolute (-5) | True = -(-5) absolute x | x >= 0 = x absolute x | x < 0 = -x Discard this equation Keep this one

73. Evaluating Guards Evaluate absolute (-5) –We have two equations to use! –Erase the True guard absolute (-5) = -(-5) absolute x | x >= 0 = x absolute x | x < 0 = -x

74. Evaluating Guards Evaluate absolute (-5) –We have two equations to use! –Compute the result absolute (-5) = 5 absolute x | x >= 0 = x absolute x | x < 0 = -x

75. Notation We can abbreviate repeated left hand sides Haskell also has if then else absolute x | x >= 0 = x absolute x | x < 0 = -x absolute x | x >= 0 = x | x < 0 = -x absolute x = if x >= 0 then x else -x

76. Example: Computing Powers Compute (without using built-in x^n)

77. Example: Computing Powers Compute (without using built-in x^n) Name the function power

78. Example: Computing Powers Compute (without using built-in x^n) Name the inputs power x n = undefined

79. Example: Computing Powers Compute (without using built-in x^n) Write a comment -- power x n returns x to the power n power x n = undefined

80. Example: Computing Powers Compute (without using built-in x^n) Write a type signature -- power x n returns x to the power n power :: Integer -> Integer -> Integer power x n = undefined

81. How to Compute power? We cannot write –power x n = x * … * x n times

82. A Table of Powers Each row is x* the previous one Define power x n to compute the nth row npower x n 01 1x 2x*x 3x*x*x

83. A Definition? Testing: Main> power 2 2 ERROR - stack overflow power x n = x * power x (n-1) Why?

84. A Definition? Testing: –Main> power 2 2 –Program error: pattern match failure: power 2 0 power x n | n > 0 = x * power x (n-1)

85. A Definition? Testing: –Main> power 2 2 –4 power x 0 = 1 power x n | n > 0 = x * power x (n-1) First row of the table The BASE CASE

86. Recursion First example of a recursive function –Defined in terms of itself! Why does it work? Calculate: –power 2 2 = 2 * power 2 1 –power 2 1 = 2 * power 2 0 –power 2 0 = 1 power x 0 = 1 power x n | n > 0 = x * power x (n-1)

87. Recursion First example of a recursive function –Defined in terms of itself! Why does it work? Calculate: –power 2 2 = 2 * power 2 1 –power 2 1 = 2 * 1 –power 2 0 = 1 power x 0 = 1 power x n | n > 0 = x * power x (n-1)

88. Recursion First example of a recursive function –Defined in terms of itself! Why does it work? Calculate: –power 2 2 = 2 * 2 –power 2 1 = 2 * 1 –power 2 0 = 1 power x 0 = 1 power x n | n > 0 = x * power x (n-1) No circularity!

89. Recursion First example of a recursive function –Defined in terms of itself! Why does it work? Calculate: –power 2 2 = 2 * power 2 1 –power 2 1 = 2 * power 2 0 –power 2 0 = 1 power x 0 = 1 power x n | n > 0 = x * power x (n-1) The STACK

90. Recursion Reduce a problem (e.g. power x n) to a smaller problem of the same kind So that we eventually reach a ”smallest” base case Solve base case separately Build up solutions from smaller solutions Powerful problem solving strategy in any programming language!

91. Counting the regions n lines. How many regions? remove one line... problem is easier! when do we stop?

92. The Solution Always pick the base case as simple as possible! regions :: Integer -> Integer regions 0 = 1 regions n | n > 0 = regions (n-1) + n

93. Course Text Book The Craft of Functional Programming (second edition), by Simon Thompson. Available at Cremona. An excellent book which goes well beyond this course, so will be useful long after the course is over. Read Chapter 1 to 4 before the laboratory sessions on Wednesday, Thursday and Friday. uses Hugs instead of GHCi

94. Course Web Pages URL: http://www.cs.chalmers.se/Cs/Grundutb/Kurser/funht/ Updated almost daily! These slides Schedule Practical information Assignments Discussion board