© m. winter cosc 4p41 – functional programming 1.11.1 cosc 4p41 functional programming...

© M. Winter

COSC 4P41 – Functional Programming

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COSC 4P41Functional Programming

• Instructor: Michael Winter– Office J323– Office Hours: Wed & Fri 1:00pm – 3:00pm– email: [email protected]

• Webpage: http://www.cosc.brocku.ca/~mwinter/Courses/4P41/

• Course Description (Brock Calendar): Introduction to functional programming using the languages Haskell. Topics include all data types, type inference, pattern-matching, recursion, polymorphism, higher-order functions, lazy vs eager evaluation, modules and monads.

• Prerequisites: three and one-half COSC credits or permission of the instructor.

• Haskell:http://www.haskell.org

© M. Winter


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Textbooks

• Main Text– Haskell, The Craft of Functional Programming, 3rd

edition, S. Thompson, Addison - Wesley (2011), ISBN 0-201-88295-7

• Supplemental Texts– The Haskell 2010 Report, Simon Marlow, online. – Real World Haskell, Bryan O'Sullivan, John

Goerzen, Don Steward, O'Reilly (2009), ISBN 978-0-596-51498-3

– The Haskell School of Expression, P. Hudak, Cambridge University Press (2000), ISBN 0-521-64408-9

© M. Winter


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Course Work

• Marking Scheme– Lab Tests (3x20%) 60%– Final Lab Exam 40%

• Tests & Exam (D205) Lab Test 1 January 31 @ 3:30pm – 5:00pm Lab Test 2 February 28 @ 3:30pm – 5:00pm Lab Test 3 March 21 @ 3:30pm-5:00pm Exam April 07 @ tba

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• A mark of at least 40% on the final exam is required to achieve a passing grade in this course.

• Consideration regarding illness for test dates will only be considered if accompanied with the completed Departmental Medical Excuse form.

• Academic misconduct is a serious offence. The principle of academic integrity, particularly of doing one's own work, documenting properly (including use of quotation marks, appropriate paraphrasing and referencing/citation), collaborating appropriately, and avoiding misrepresentation, is a core principle in university study. Students should consult Section VII, 'Academic Misconduct", in the "Academic Regulations and University Polices“ entry in the Undergraduate Calendar, available at brocku.ca/webcal to view a fuller description of prohibited actions, and the procedures and penalties.

© M. Winter


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Course OutlineWeek

Date Book/Chapt. Topics

1 Jan 08/10 [1] 1–3 Introduction to Functional Programming

2 Jan 15/17 [1] 4–5 Recursion and Data Types

3 Jan 22/24 [1] 6–7 Lists

4 Jan 29/31 [1] 9-10 Patterns of Computation, Functions as Values

5 Feb 05/07 [1] 12-13 Overloading, Type Classes, Type Checking

6 Feb 12/14 [1] 14-15 Algebraic Types

7 Feb 26/28*

[1] 16 Abstract Data Types

8 Mar 05/07 [1] 17 Lazy Evaluation

9 Mar 12/14 [1] 18 Programming with Actions

10 Mar 19/21 [1] 8, 14.7 & 17.9

Reasoning about Programs

11 Mar 26/28 [1] 8, 14.7 & 17.9

Reasoning about Programs II

12 Apr 02/04 [2] 7 Language extensions, Review

*Feb 17-21 is Reading Week.

© M. Winter


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Imperative languages

• Von Neumann model:– store with addressable locations

• machine code: – effect achieved by changing contents of store locations– instructions executed in sequence, flow of control altered

by jumps• imperative language:

– variable corresponds to store location– instructions executed in sequence, flow of control altered

by conditional and loop statements– efficient implementation since close to design of

conventional computers

© M. Winter


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Functional languages

• computational model: lambda calculus• mathematical functions: domain, range• functional languages achieve effect by applying functions• functional vs. imperative languages

– store location– assignment statement vs. application of a function

(expressions)• side-effects• aliasing• referential transparency

© M. Winter


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Features of functional languages

• usually strongly typed (modern languages)• algebraic type definitions

– mathematical based notation– no (implicit) pointers

• higher-order functions– can accept functions as parameters– can return functions as results

• recursion as a basic principle• application of rewrite rule:

– function call replaced by code body• run-time overhead garbage collection• slogan: define “what to do”, not “how to do”

© M. Winter


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What is a function?

+1234 46

inputsoutput

A functional program is basically a list of definitions of functions.

+Int

IntInt

A function is something which produces an output value depending on the input value(s).

A type is a collection of values. Usually functions are considered to take values of specific types as input, and produce values of another type.

© M. Winter


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Definitions

Haskell definitions are of the form:name :: type

name = expression

Examples:size :: Int

size = (12+13)*4

square :: Int -> Int

square n = n*n

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{-#########################################################

FirstScript.hs

Simon Thompson, June 1998

The purpose of this script is - to illustrate some simple definitions

over integers (Int); - to give a first example of a script.

#########################################################-}

-- The value size is an integer (Int), defined to be -- the sum of twelve and thirteen.

size :: Int size = 12+13

-- The function to square an integer.

square :: Int -> Int square n = n*n

-- The function to double an integer.

double :: Int -> Int double n = 2*n

-- An example using double, square and size.

example :: Int example = double (size - square (2+2))

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###########################################################

FirstLiterate.lhs

Simon Thompson, June 1998

The purpose of this script is - to illustrate some simple definitions over integers (Int); - to give a first example of a literate script.

###########################################################

The value size is an integer (Int), defined to be the sum of twelve and thirteen.

> size :: Int > size = 12+13

The function to square an integer.

> square :: Int -> Int > square n = n*n

The function to double an integer.

> double :: Int -> Int > double n = 2*n

An example using double, square and size.

> example :: Int > example = double (size - square (2+2))

© M. Winter


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The Booleans

• type Bool• operations

exOr :: Bool -> Bool -> Bool

exOr x y = (x || y) && not (x && y)

&& and

|| or

not not

© M. Winter


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The integers

• type Int: range –2147483648…2147483647• type Integer: range unbounded• operations + sum

* product

^ raise to the power

- difference

div whole number division

mod remainder

abs absolute value

negate change sign

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Relational operators and overloading

(==) for integers and Booleans. This means that (==) will have the type

Int -> Int -> Bool

Bool -> Bool -> Bool

Indeed t -> t -> Bool if the type t carries an equality.

(==) :: Eq a => a -> a -> Bool

> greater than

>= greater than or equal to

== equal to

/= not equal to

<= less than or equal to

< less than

© M. Winter


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The rational numbers

• type Rational (import Ratio)• operations

and +, *, -, negate, abs

% Integer -> Integer -> Rational

numerator the numerator

denominator the denominator

fromInteger Integer -> Rational

© M. Winter


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The characters

• type Char

‘a’

‘\t’ tab‘\n’ newline‘\\’ backslash‘\’’ single quote‘\”’ double quote‘\97’ character with ASCII code 97, i.e., ‘9’

© M. Winter


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Layout

mystery x = x*x

+x

+2

next x = …

fun v1 v2 … vn

| g1 = e1

| g2 = e2

…

| otherwise = er

© M. Winter


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Operators and Do-it-yourself operators

(+) :: Int -> Int -> Int

(+) 2 3 = 2 + 3

2 `max` 3 = max 2 3

Operator symbols !,#,$,%,&,*,+,.,/,<,=,>,?,\,^,|,:,-,~

(&&&) :: Int -> Int -> Int

x &&& y

| x > y = y

| otherwise = x

© m. winter cosc 4p41 – functional programming 1.11.1 cosc 4p41 functional programming...

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