Introduction to Programming in Haskell

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

Or Google for chalmers introduction functional
programming
http//www.cs.chalmers.se/Cs/Grundutb/Kurser/funht
/
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
Programs compute new data from old
data. Example Baldurs 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.
Bonnier buys Quicktime Video from Apple.
Volvo buys engines from Mitsubishi.
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
which language should we teach?
Scheme
C
Lisp
BASIC
C
Haskell
Java
C
ML
Python
JavaScript
csh
Curry
Perl
OCaML
bash
Erlang
Ruby
Prolog
Lustre
Mercury
PostScript
VHDL
Esterel
PDF
SQL
Verilog
17
Programming Language Features
dynamically typed
pure functions
higher-order functions
statically typed
type inference
real-time
immutable datastructures
polymorphism
overloading
concurrency
high performance
distribution
parameterized types
lazy
virtual machine
Java
reflection
type classes
object oriented
compiler
interpreter
meta-programming
Haskell
unification
C
backtracking
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

• gt ghci
• ___ ___ _
• / _ \ /\ /\/ __(_)
• / /_\// /_/ / / GHC Interactive,
  version 6.6.1, for Haskell 98.
• / /_\\/ __ / /___ http//www.haskell.org/
  ghc/
• \____/\/ /_/\____/_ Type ? for help.
• Loading package base ... linking ... done.
• Preludegt

The prompt. GHCi is ready for input.
22
GHCi as a Calculator
Type in expressions, and ghci calculates and
prints their value.
Preludegt 22 4 Preludegt 2-2 0 Preludegt
23 6 Preludegt 2/3 0.666666666666667
Multiplication and division look a bit unfamiliar
we cannot omit multiplication, or type
horizontal lines.
X
2
3
23
Binding and Brackets
Preludegt 223 8 Preludegt (22)3 12 Prelude
gt (12)/(34) 0.428571428571429
Multiplication and division bind more tightly
than addition and subtraction so this means
26, not 43.
We use brackets to change the binding (just as in
mathematics), so this is 43.
This is how we write 12 34
24
Quiz

• What is the value of this expression?
• Preludegt 12/34

25
Quiz

• What is the value of this expression?
• Preludegt 12/34
• 5.66666666666667

26
Example Currency Conversion

• Suppose we want to buy a game costing 53 from a
  foreign web site.

Preludegt 539.16642 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.
• gt emacs Examples.hs

Do this in a separate window, so you can edit and
run hugs simultaneously.
Haskell files end in .hs
The UNIX prompt, not the ghci one!
28
Creating the Definition
Give the name euroRate to the value 9.16642
variable
29
Using the Definition
Load the file Examples.hs into ghci make the
definition available.
The prompt changes we have now loaded a program.
Preludegt l Examples Maingt euroRate 9.16642 Maingt
53euroRate 485.82026 Maingt
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
A definition placed in the file Examples.hs
A comment to help us understand the program
-- convert euros to SEK sek x xeuroRate
Function name the name we are defining.
Expression to compute the result
Name for the argument
32
Using the Function
Reload the file to make the new definition
available.
Maingt r Maingt sek 53 485.82026
Call the function Notation no brackets! C.f. sin
0.5, log 2, not f(x).
sek x xeuroRate
x 53 While we evaluate the right hand side
53euroRate
33
Binding and Brackets again
Different! This is (sek 50) 3. Functions bind
most tightly of all.
Maingt sek 53 485.82026 Maingt sek 50
3 461.321 Maingt sek (503) 485.82026 Maingt
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
Maingt r Maingt euro 485.82026 53.0 Maingt euro
(sek 49) 49.0 Maingt 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?

The operator tests whether two values are equal
Maingt 2 2 True Maingt 2 3 False Maingt euro
(sek 49) 49 True
Yes they are
No they arent
Note two equal signs are an operator. One equal
sign makes a definition.
Let the computer check the result.
36
Defining the Property

• Define a function to perform the test for us

prop_EuroSek x euro (sek x) x
Maingt prop_EuroSek 53 True Maingt 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
Capital letters must appear exactly as they do
here.
Add first in the file of definitions makes
QuickCheck available.
39
Running Tests
Runs 100 randomly chosen tests
Maingt quickCheck prop_EuroSek Falsifiable, after
10 tests 3.75 Maingt sek 3.75 34.374075 Maingt
euro 34.374075 3.75
Its 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!

Maingt 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 lt0.000001

Maingt 2lt3 True Maingt 3lt2 False
We can use lt 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 lt 0.000001
With arguments x and y
Which returns True if the difference between x
and y is less than 0.000001
Define a new operator
43
Testing
Maingt 3 3.0000001 True Maingt 34 True
OK
Whats wrong?
x y x-y lt 0.000001
44
Fixing the Definition

• A useful function

Maingt abs 3 3 Maingt abs (-3) 3
Absolute value
x y abs (x-y) lt 0.000001
Maingt 3 4 False
45
Fixing the Property
prop_EuroSek x euro (sek x) x
Maingt prop_EuroSek 3 True Maingt prop_EuroSek
56 True Maingt prop_EuroSek 2 True
46
Name the Price

• Lets define a name for the price of the game we
  want

price 53
Maingt 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

Integer (whole number) is the type of price
Maingt i price price Integer Maingt i
euroRate euroRate Double
Double is the type of real numbers Funny name,
but refers to double the precision that computers
originally used
48
More Types
The type of truth values, named after the
logician Boole
Maingt i True True Bool -- data
constructor Maingt i False False Bool --
data constructor Maingt i sek sek Double -gt
Double Maingt i prop_EuroSek prop_EuroSek
Double -gt Bool
The type of a function
Type of the result
Type of the result
Type of the argument
49
Types Matter

• Types determine how computations are performed

Specify which type to use
Maingt 123456789123456789 Double 1.524157875019
05e016 Maingt 123456789123456789
Integer 15241578750190521
Correct to 15 figures
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
Maingt i price price Integer Maingt i sek sek
Double -gt Double Maingt sek price ERROR - Type
error in application Expression sek
price Term price Type
Integer Does not match Double
52
Why did it work before?
Certainly works to say 53 What is the type of 53?
Maingt sek 53 485.82026 Maingt 53
Integer 53 Maingt 53 Double 53.0 Maingt price
Integer 53 Maingt price Double ERROR - Type
error in type annotation Term
price Type Integer Does not
match Double
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
Maingt i price price Double Maingt 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 -gt Double sek x xeuroRate euro x
x/euroRate prop_EuroSek Double -gt
Bool prop_EuroSek x euro (sek x) x
56
What is the type of 53?
i only works for names
Maingt i 53 Unknown reference 53' Maingt t sek
53 sek 53 Double Maingt t 53 53 Num a gt
a Maingt i infixl 7 () Num a gt a -gt a
-gt a -- class member
But t gives the type (only) of any expression
Then 53 can have type a
If a is a numeric type
If a is a numeric type
Then can have type a-gta-gta
57
What is Num exactly?
Maingt i Num -- type class ... class (Eq a,
Show a) gt Num a where () a -gt a -gt a (-)
a -gt a -gt a () a -gt a -gt a ... --
instances instance Num Int instance Num
Integer instance Num Float instance Num
Double instance Integral a gt Num (Ratio a)
A class of types
With these operations
Types which belong to this class
58
Examples
Maingt 2 3.5 5.5 Maingt 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!
Maingt sek (-10) -91.6642 Maingt sek -10 ERROR -
Cannot infer instance Instance Num
(Double -gt Double) Expression sek - 10
Whats going on?
60
Operators Again
Maingt i infixl 6 () Num a gt a -gt a -gt a
-- class member Maingt i infixl 7 ()
Num a gt a -gt a -gt a -- class member
The binding power (or precedence) of an
operator binds tighter than because 7 is
greater than 6
61
Giving a Precedence
Maingt 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

Maingt i infix 4 () Eq a gt a -gt a -gt
Bool -- class member
infix 4 x y abs (x-y) lt 0.000001
Maingt 1/2000000 0 True
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 -gt
Integer sq x x x
66
Evaluating Functions

• To evaluate sq 5
• Use the definitionsubstitute 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 -gt 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

Programs must often choose between alternatives
-- absolute x returns the absolute value of
x absolute Integer -gt Integer absolute x x gt
0 undefined absolute x x lt 0 undefined
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 -gt Integer absolute x x gt
0 x absolute x x lt 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 -gt Integer absolute x x
gt 0 x absolute x x lt 0 -x
gt is greater than or equal,
71
Evaluating Guards

• Evaluate absolute (-5)
• We have two equations to use!
• Substitute
• absolute (-5) -5 gt 0 -5
• absolute (-5) -5 lt 0 -(-5)

absolute x x gt 0 x absolute x x lt 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)

Discard this equation
Keep this one
absolute x x gt 0 x absolute x x lt 0 -x
73
Evaluating Guards

• Evaluate absolute (-5)
• We have two equations to use!
• Erase the True guard
• absolute (-5) -(-5)

absolute x x gt 0 x absolute x x lt 0 -x
74
Evaluating Guards

• Evaluate absolute (-5)
• We have two equations to use!
• Compute the result
• absolute (-5) 5

absolute x x gt 0 x absolute x x lt 0 -x
75
Notation

• We can abbreviate repeated left hand sides
• Haskell also has if then else

absolute x x gt 0 x absolute x x lt 0 -x
absolute x x gt 0 x x lt 0 -x
absolute x if x gt 0 then x else -x
76
Example Computing Powers

• Compute (without using built-in xn)

77
Example Computing Powers

• Compute (without using built-in xn)
• Name the function

power
78
Example Computing Powers

• Compute (without using built-in xn)
• Name the inputs

power x n undefined
79
Example Computing Powers

• Compute (without using built-in xn)
• 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 xn)
• Write a type signature

-- power x n returns x to the power n power
Integer -gt Integer -gt 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

n
power x n
0
1
1
x
2
xx
3
xxx
83
A Definition?
power x n x power x (n-1)

• Testing
• Maingt power 2 2
• ERROR - stack overflow

Why?
84
A Definition?

• Testing
• Maingt power 2 2
• Program error pattern match failure power 2 0

power x n n gt 0 x power x (n-1)
85
A Definition?
First row of the table

• Testing
• Maingt power 2 2
• 4

power x 0 1 power x n n gt 0 x power x
(n-1)
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 gt 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 gt 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 gt 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 gt 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 -gt Integer regions 0
1 regions n n gt 0 regions (n-1) n
93
Course Text Book
uses Hugs instead of GHCi
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.
94
Course Web Pages
Updated almost daily!
URL http//www.cs.chalmers.se/Cs/Grundutb/Kurser
/funht/

• These slides
• Schedule
• Practical information
• Assignments
• Discussion board