The document provides an introduction to functional programming concepts. It defines functional programming as consisting entirely of functions. It discusses key functional programming concepts like immutable variables, recursion, higher-order functions, and common functional patterns like map, filter and fold. It provides examples of functions in Haskell and Python and illustrates how these concepts can be applied to problems like processing bank account data.

1. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
An Introduction to Functional Programming
Andreas Pauley – @apauley
Lambda Luminaries
DeveloperUG
March 11, 2014

2. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
@lambdaluminary
We meet once a month, on the second Monday of the month.
http://www.meetup.com/lambda-luminaries/

3. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Jemstep
Retirement portfolio analysis in Scala.
http://www.jemstep.com/

4. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now

5. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now

6. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
“ No matter what language you work in,
programming in a functional style provides benefits.
You should do it whenever it is convenient, and you
should think hard about the decision when it isn’t
convenient. ”
— John Carmack, ID Software [2]

7. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Quake

8. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
But what exactly is
“Functional Programming”?

9. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Functional Programming, noun:
Functional Programming is a
list of things you CAN’T do.
[7]

10. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
You can’t vary your variables
1> X = 42.
42
2> X = X + 1.
** exception error:
no match of right hand
side value 43

11. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
No while/for loops. Sorry :-(
int i;
for (i=1; i<=3; i++) {
System.out.println(i);
}

12. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
You can’t mutate/change your data structures
Python
>>> list1 = [1,2,3]
>>> list2 = list1
>>> print list1.reverse()
None
>>> list1
[3, 2, 1]
>>> list2
[3, 2, 1]
Haskell
> let list1 = [1,2,3]
> let list2 = list1
> reverse(list1)
[3,2,1]
> list1
[1,2,3]
> list2
[1,2,3]

13. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
You can’t have any side effects

14. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Are you kidding me?
How can anyone program like this???

15. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
GOTO 10
This sounds like
“You can’t have GOTO statements”
See Hughes and Dijkstra [1, 3]

16. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
It’s not about what we cannot
do.

17. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
We need a better definition of
Functional Programming.

18. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Programming Paradigms
(Very Simplified)
Imperative Declarative

19. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Functional Programming, noun:
“ Functional programming is so called because a
program consists entirely of functions. ”
— John Hughes, Why Functional Programming Matters [1, p. 1]

20. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
OK... so what exactly is a function?

21. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
An example function
f(x) = 2x2 − 2x + 3
−1 1 2 3
4
6
8
10
12
14
x
y

22. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Variables in functions
f(x) = 2x2 − 2x + 3
When we evaluate the function:
f(2) = 8 − 4 + 3 = 7
• The value of x will not change inside the function body.

23. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Variables in functions
f(x) = 2x2 − 2x + 3
When we evaluate the function:
f(2) = 8 − 4 + 3 = 7
• The value of x will not change inside the function body.
• Same input, same output. Every time. (Referential
Transparency)

24. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Variables in functions
f(x) = 2x2 − 2x + 3
When we evaluate the function:
f(2) = 8 − 4 + 3 = 7
• The value of x will not change inside the function body.
• Same input, same output. Every time. (Referential
Transparency)
• We can call f multiple times without any side effects
(Idempotence).

25. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Variables in functions
f(x) = 2x2 − 2x + 3
When we evaluate the function:
f(2) = 8 − 4 + 3 = 7
• The value of x will not change inside the function body.
• Same input, same output. Every time. (Referential
Transparency)
• We can call f multiple times without any side effects
(Idempotence).
• We don’t have to recalculate f(2), we can replace any
occurrence of f(2) with 7 (Memoization).

26. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Varying variables does not make sense
x = x + 1
x − x = 1
0 = 1
∴ x = x + 1

27. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Functions can call other functions
g(x) = f(x) + 1

28. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Values are functions
Constant values are just functions with no input parameters
x = 42
Python function definition:
def x():
return 42
Haskell function definition:
x = 42

29. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Functions can be composed
h(x) = (f ◦ g)(x) = f(g(x))
or
h = f ◦ g

30. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Higher-order Functions
Functions can take functions as input.
Functions can return functions as the result.
h(f, g, x) = f(x) + g(2)

31. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Higher-order Functions
The derivative of f(x) returns another function.
f(x) = 2x2
− 2x + 3
d
dxf(x) = 4x − 2
−1 1 2 3
5
10
15
x
y

32. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
A functional program consists entirely of functions
def main():
time = datetime.now()
args = sys.argv[1:]
print outputString(time, args)
def outputString(time, args):
return str(time) + " " + joinArgs(args)
def joinArgs(args):
return "-".join(args)
$ ./justfunctions.py Hello from Python
2014-02-15 10:36:42.062697 Hello-from-Python

33. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
A functional program consists entirely of functions
main :: IO()
main = do
time <- getCurrentTime
args <- getArgs
putStrLn (outputString time args)
outputString :: UTCTime -> [String] -> String
outputString time args =
show(time) ++ " " ++ joinArgs(args)
joinArgs :: [String] -> String
joinArgs = intercalate "-"
$ ./justfunctions Hello from Haskell
2014-02-15 08:36:50.822728 UTC Hello-from-Haskell

34. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Some Haskell Syntax
Python:
def outputString(time, args):
return str(time) + " " + joinArgs(args)
Haskell:
outputString :: UTCTime -> [String] -> String
outputString time args =
show(time) ++ " " ++ joinArgs(args)

35. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Recursive function: Haskell
doubleAll :: [Int] -> [Int]
doubleAll [] = []
doubleAll (x:xs) = x*2 : doubleAll xs
Example use in the interactive interpreter:
Prelude Main> doubleAll [8,2,3]
[16,4,6]

36. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Recursive function expanded
doubleAll [] = []
doubleAll (x:xs) = x*2 : doubleAll xs
doubleAll [8,2,3]
16 : (doubleAll [2,3])
16 : 4 : (doubleAll [3])
16 : 4 : 6 : (doubleAll [])
16 : 4 : 6 : []
16 : 4 : [6]
16 : [4,6]
[16,4,6]

37. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Recursive function: Python
def doubleAll(numbers):
if numbers == []:
return []
else:
first = numbers[0]
rest = numbers[1:]
return [first * 2] + doubleAll(rest)
Example use in the interactive interpreter:
>>> doubleAll([8,2,3])
[16, 4, 6]

38. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Pattern Matching: Haskell
doubleAll :: [Int] -> [Int]
doubleAll [] = []
doubleAll (x:xs) = x*2 : doubleAll xs

39. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Higher-order Functions
3 Basic List Operations
Map Convert each element of a list into some other value.

40. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Higher-order Functions
3 Basic List Operations
Map Convert each element of a list into some other value.
Filter Get a subset of a list based on some condition.

41. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Higher-order Functions
3 Basic List Operations
Map Convert each element of a list into some other value.
Filter Get a subset of a list based on some condition.
Fold Reduce a list of items to a single value.

42. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Map
Apply a function to each element of a list, and you get a new list.
a1 a2 a3 ... an
b1 b2 b3
... bn
f(a1) f(an)

43. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Map
The built-in Haskell map function:
map :: (a -> b) -> [a] -> [b]
map _ [] = []
map f (x:xs) = f x : map f xs

44. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Map
The builtin Haskell map function:
map :: (a -> b) -> [a] -> [b]
map _ [] = []
map f (x:xs) = f x : map f xs
Hmmm, looks very similar to our previous doubleAll function:
doubleAll :: [Int] -> [Int]
doubleAll [] = []
doubleAll (x:xs) = x*2 : doubleAll xs

45. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Map
So our doubleAll can actually be simplified.
In Haskell:
doubleAll = map (*2)
In Python:
def doubleAll(numbers):
return map(lambda x: x * 2, numbers)

46. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Map
doubleAll :: Num a => [a] -> [a]
doubleAll = map (*2)
8 2 3
16 4 6
∗2 ∗2 ∗2

47. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Account Data
data Bank = ABSA | Capitec | FNB | Nedbank | SBSA
data Account = Account {bank :: Bank,
accNum :: String,
owner :: String,
balance :: Amount}

48. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Account Data
[Account {accNum="4076814233",
owner="J. Doe",
balance=(Amount 123000.23),
bank=ABSA},
Account {accNum="6868773585",
owner="J. Black",
balance=(Amount 5782347.99),
bank=FNB},
Account {accNum="4055892156",
owner="A. Kay",
balance=(Amount 100),
bank=ABSA},
Account {accNum="6584539813",
owner="S. Jones",
balance=(Amount 2937361.45),
bank=FNB}]

49. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Map
Map on account data:
balances :: [Account] -> [Amount]
balances accounts = map balance accounts
acc1 acc2 acc3 acc4 acc5
bal1 bal2 bal3 bal4 bal5
balance(acc1) balance(acc5)

50. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Filter
acc1 acc2 acc3 acc4 acc5
acc1 acc3 acc5
in? in? in? in? in?

51. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Filter
Filter on account data:
topAccounts :: [Account] -> [Account]
topAccounts accounts = filter isRich accounts
isRich :: Account -> Bool
isRich acc = balance acc >= (Amount 1000000)
Output:
*Main> topAccounts accounts
[FNB 6868773585 (J. Black) R5782347.99,
FNB 6584539813 (S. Jones) R2937361.45]

52. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Fold/Reduce/Inject
foldl (+) 0 [8,2,3]
13
0 8 2 3
8 2 3
10 3
13

53. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Fold/Reduce/Inject
balanceSum :: [Account] -> Amount
balanceSum accounts = foldl (+) 0 (balances accounts)
0 bal1 bal2 bal3
sum bal2 bal3
sum bal3
sum

54. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Function Composition
balanceSum :: [Account] -> Amount
balanceSum accounts = foldl (+) 0 (balances accounts)
0 bal1 bal2 bal3
sum bal2 bal3
sum bal3
sum
s2 :: [Account] -> Amount
s2 = balances |> (foldl(+)0)
h(x) = (f ◦ g)(x) = f(g(x))
h = f ◦ g
s3 = f1 ◦ balances
s3 :: [Account] -> Amount
s3 = (foldl(+)0) . balances

55. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
balancesPerBank
foldl insertBalance Map.empty accounts
{} acc1 acc2 acc3
map acc2 acc3
map acc3
map

56. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Fold
type BankMap = Map Bank Amount
balancesPerBank :: [Account] -> BankMap
balancesPerBank = foldl insertBalance Map.empty
Output:
*Main> balancesPerBank accounts
fromList [(ABSA,R123100.23),(FNB,R8719709.44)]

57. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Fold
type BankMap = Map Bank Amount
balancesPerBank :: [Account] -> BankMap
balancesPerBank = foldl insertBalance Map.empty
insertBalance :: BankMap -> Account -> BankMap
insertBalance bankmap account =
Map.insert key value bankmap
where key = bank account
value = addBalance bankmap account
addBalance :: BankMap -> Account -> Amount
addBalance bankmap account =
case (Map.lookup (bank account) bankmap) of
Nothing -> balance account
Just bal -> (balance account) + bal

58. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Programming Paradigms
(Very Simplified)
Imperative Declarative

59. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
In imperative programming:
• Your variables can vary any time!

60. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
In imperative programming:
• Your variables can vary any time!
• You have to use locks to be thread-safe!

61. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
In imperative programming:
• Your variables can vary any time!
• You have to use locks to be thread-safe!
• You have to write your own loops for the most basic list
operations!

62. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
In imperative programming:
• Your variables can vary any time!
• You have to use locks to be thread-safe!
• You have to write your own loops for the most basic list
operations!
• Your data structures are mutable!

63. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
In imperative programming:
• Your variables can vary any time!
• You have to use locks to be thread-safe!
• You have to write your own loops for the most basic list
operations!
• Your data structures are mutable!
• You have to defensively make copies of data to prevent bugs!

64. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
In imperative programming:
• Your variables can vary any time!
• You have to use locks to be thread-safe!
• You have to write your own loops for the most basic list
operations!
• Your data structures are mutable!
• You have to defensively make copies of data to prevent bugs!
• You have to defensively check for null values!

65. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
In imperative programming:
• Your variables can vary any time!
• You have to use locks to be thread-safe!
• You have to write your own loops for the most basic list
operations!
• Your data structures are mutable!
• You have to defensively make copies of data to prevent bugs!
• You have to defensively check for null values!
• You have to think about implicit state! (this, self)

66. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
In imperative programming:
• Your variables can vary any time!
• You have to use locks to be thread-safe!
• You have to write your own loops for the most basic list
operations!
• Your data structures are mutable!
• You have to defensively make copies of data to prevent bugs!
• You have to defensively check for null values!
• You have to think about implicit state! (this, self)
• Code is generally riddled with side effects!

67. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Are you kidding me?
How can anyone program like this???

68. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now

69. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Join the anti-for campaign
Less loops, more
map/filter/fold
http://weblogs.asp.net/podwysocki/archive/2009/06/26/
the-anti-for-campaign.aspx

70. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Treat side effects as a first-class concern

71. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Learn a functional language
“ A language that doesn’t affect the way you think
about programming, is not worth knowing. ”
— Alan Perlis[5]

72. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Disclaim your inheritance
Write non-trivial code without
using objects and inheritance.
Get re-usability with higher-order functions.
Try to minimise moving parts instead of
encapsulating moving parts. [4]

73. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Join our group
@lambdaluminary
We meet once a month, on the second Monday of the month.
http://www.meetup.com/lambda-luminaries/

74. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Get out of your comfort zone
Functional Programming is unfamiliar territory for
most.
“ If you want everything to be familiar you will
never learn anything new. ”
— Rich Hickey, author of Clojure[6]

75. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Companies In South Africa
Jemstep, Sandton Using Scala for Fund Analysis
Allan Gray, Cape Town Using Scala for backend logic and system
integration.
Yuppiechef, Cape Town Using Clojure for their Warehouse
Management System.
Cognician, Cape Town Using Clojure to create coaching/learning
modules.
Eldo Energy, Johannesburg Using Clojure for automated meter
reading and intelligent monitoring of consumer
energy.
Rheo Systems, Pretoria Using Clojure for supply chain integration.

76. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Companies In South Africa
Pattern Matched Technologies, Midrand Using Erlang for all
systems, eg. processing high volumes of financial
transactions.
Effective Control Systems, Kyalami Using Erlang for printer
management.
Mira Networks, Somerset West Using Erlang for billing
administration and mobile development.
Kotive Using Scala for designing workflow processes.

77. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Online Courses
Functional Thinking by Neal Ford
O’ Reilly
http://shop.oreilly.com/product/0636920030393.do
Functional Programming Principles in Scala
EPFL University
https://www.coursera.org/course/progfun
School of Haskell
FP Complete
https://www.fpcomplete.com/school
Programming Languages
University of Washington
https://www.coursera.org/course/proglang

78. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
Books
Miran Lipovaˇca
Learn You a Haskell for Great Good!
http://learnyouahaskell.com/
Fred H´ebert
Learn You Some Erlang for Great Good!
http://learnyousomeerlang.com/
Yaron Minski, Anil Madhavapeddy, Jason Hickey
Real World OCaml
https://realworldocaml.org/
Paul Chiusano, R´unar Bjarnason
Functional Programming in Scala
http://www.manning.com/bjarnason/

79. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
References I
John Hughes
Why Functional Programming Matters
http://www.cs.kent.ac.uk/people/staff/dat/miranda/
whyfp90.pdf
John Carmack
Functional Programming in C++
http://www.altdevblogaday.com/2012/04/26/
functional-programming-in-c/
Edsger W. Dijkstra
Go To Statement Considered Harmful
http://www.u.arizona.edu/~rubinson/copyright_
violations/Go_To_Considered_Harmful.html

80. Introduction Definition Function Recap Common Idioms Imperative Comparison Challenges! Industry Use Now
References II
Tweet by Michael Feathers
https://twitter.com/mfeathers/status/29581296216
Alan Jay Perlis
http://www.cs.yale.edu/quotes.html
Rich Hickey
http:
//www.infoq.com/presentations/Simple-Made-Easy
Andreas Pauley
An Introduction to Functional Programming
https://github.com/apauley/fp_presentation