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Introduction
to Haskell
Luca Molteni
Haskell ITA Meeting 17/10/2015
Topics
Basic Concepts
Currying
Functors
• Functions are first-class, that is, functions are
values which can be used in exactly the same
ways as any other sort of ...
3 * (9 + 5)
=> 3 * 14
=> 42
3 * (9 + 5)
=> 3 * 9 + 3 * 5
=> 27 + 3 * 5
=> 27 + 15
=> 42
simple x y z = x * (y + z)
simple 3 9 5
=> 3 * (9 + 5)
=> 3 * 14
=> 42
“An expression is said to be referentially
transparent if it can be replaced with its value
without changing the behavior ...
simple a b c = simple a c b
simple a b c
=> { unfold }
a * (b + c)
=> { commutativity }
a * (c + b)
=> { fold }
simple a c b
x = x + 1
x = x + 1
x
=> x + 1
=> (x + 1) + 1
=> ((x + 1) + 1) +1
=> (((x + 1) +1) +1) +1
...
“Because a referentially transparent expression
can be evaluated at any time, it is not
necessary to define sequence points...
totalArea r1 r2 r3
= pi * r1 ^ 2 +
pi * r2 ^ 2 +
pi * r3 ^ 2
Sum of the areas of three circles
with radii r1, r2, r3
circleArea r = pi * r ^ 2
totalArea r1 r2 r3
= circleArea r1 +
circleArea r2 +
circleArea r3
Sum of the areas of three cir...
r1 = 3
r2 = 4
r3 = 5
radii = r1 : r2 : r3 : []
Sum of the areas of n circles?
radii :: [Float]
radii = r1 : r2 : r3 : []
Sum of the areas of n circles?
List
data List a = []
| a : List a
totalArea :: [Float] -> Float
totalArea [] = 0
Sum of the areas of three circles
with radii r1, r2, r3
totalArea :: [Float] -> Float
totalArea [] = 0
totalArea (x : xs) =
circleArea x + totalArea xs
Sum of the areas of three ...
square :: [Int] -> [Int]
square [] = []
square (x : xs) = (x ^ 2) : square xs
Square of list
Map
map :: (a -> b) -> [a] -> [b]
totalArea :: [Float] -> [Float]
totalArea = map circleArea
Sum of the areas of three circles
with radii r1, r2, r3
totalArea :: [Float] -> Float
totalArea = sum . map circleArea
Sum of the areas of three circles
with radii r1, r2, r3
Currying
simple :: (Int -> Int -> Int) -> Int
simple (x y z)
Currying
simple :: Int -> Int -> Int -> Int
simple x y z = x * ( y + z)
(((simple x) y) z)
Currying
simple 5
Partial Application
simple 5 :: Int -> Int -> Int
simple 5
Partial Application
simple :: Int -> Int -> Int -> Int
simple 5 :: Int -> Int -> Int
simple 5 2 :: Int -> Int
simple 5 2 3 :: Int
Partial Appl...
Point free programming
Tacit programming (point-free programming) is a
programming paradigm in which a function definition
...
Point free programming
map (x -> increment x) [2,3,4]
[3,4,5]
map increment [2,3,4]
[3,4,5]
map (x -> x + 1) [2,3,4]
[3,4,...
Point free programming
mf criteria operator list = filter criteria (map operator list)
mf = (. map) . (.) . filter
Functors
Functors
map :: (a -> b) -> [a] -> [b]
data List a = []
| a : List a
Functors
treeMap :: (a -> b) -> Tree a -> Tree b
data Tree a = Leaf a
| Branch (Tree a) (Tree a)
Functors
treeMap :: (a -> b) -> Tree a -> Tree b
map :: (a -> b) -> [a] -> [b]
Functors
thingMap :: (a -> b) -> f a -> f b
Functors
A typeclass is a class of types that behave
similarly.
Functors
class Functor f where
fmap :: (a -> b) -> f a -> f b
Functors
instance Functor [] where
fmap = map
Functors / Maybe
data Maybe a = Just a | Nothing
Functors
instance Functor Maybe where
fmap _ Nothing = Nothing
fmap f (Just a) = Just (f a)
Functors / Maybe
fmap (* 2) (Just 2)
Just 4
fmap (+ 5) (Just 2)
Just 7
fmap (+ 5) (Nothing)
Nothing
The End
@volothamp
It’s not about the destination.
It’s about the journey.
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Introduction to haskell

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A simple introduction to Haskell during the 17/10/2015 Haskell ITA meetup in Bologna.
It shows basic Haskell concepts, currying and functors.

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Introduction to haskell

  1. 1. Introduction to Haskell Luca Molteni Haskell ITA Meeting 17/10/2015
  2. 2. Topics Basic Concepts Currying Functors
  3. 3. • Functions are first-class, that is, functions are values which can be used in exactly the same ways as any other sort of value. • The meaning of Haskell programs is focused around evaluating expressions rather than executing instructions.
  4. 4. 3 * (9 + 5) => 3 * 14 => 42
  5. 5. 3 * (9 + 5) => 3 * 9 + 3 * 5 => 27 + 3 * 5 => 27 + 15 => 42
  6. 6. simple x y z = x * (y + z)
  7. 7. simple 3 9 5 => 3 * (9 + 5) => 3 * 14 => 42
  8. 8. “An expression is said to be referentially transparent if it can be replaced with its value without changing the behavior of a program (in other words, yielding a program that has the same effects and output on the same input).” Referential transparency
  9. 9. simple a b c = simple a c b
  10. 10. simple a b c => { unfold } a * (b + c) => { commutativity } a * (c + b) => { fold } simple a c b
  11. 11. x = x + 1
  12. 12. x = x + 1 x => x + 1 => (x + 1) + 1 => ((x + 1) + 1) +1 => (((x + 1) +1) +1) +1 ...
  13. 13. “Because a referentially transparent expression can be evaluated at any time, it is not necessary to define sequence points nor any guarantee of the order of evaluation at all. Programming done without these considerations is called purely functional programming.” Referential transparency
  14. 14. totalArea r1 r2 r3 = pi * r1 ^ 2 + pi * r2 ^ 2 + pi * r3 ^ 2 Sum of the areas of three circles with radii r1, r2, r3
  15. 15. circleArea r = pi * r ^ 2 totalArea r1 r2 r3 = circleArea r1 + circleArea r2 + circleArea r3 Sum of the areas of three circles with radii r1, r2, r3
  16. 16. r1 = 3 r2 = 4 r3 = 5 radii = r1 : r2 : r3 : [] Sum of the areas of n circles?
  17. 17. radii :: [Float] radii = r1 : r2 : r3 : [] Sum of the areas of n circles?
  18. 18. List data List a = [] | a : List a
  19. 19. totalArea :: [Float] -> Float totalArea [] = 0 Sum of the areas of three circles with radii r1, r2, r3
  20. 20. totalArea :: [Float] -> Float totalArea [] = 0 totalArea (x : xs) = circleArea x + totalArea xs Sum of the areas of three circles with radii r1, r2, r3
  21. 21. square :: [Int] -> [Int] square [] = [] square (x : xs) = (x ^ 2) : square xs Square of list
  22. 22. Map map :: (a -> b) -> [a] -> [b]
  23. 23. totalArea :: [Float] -> [Float] totalArea = map circleArea Sum of the areas of three circles with radii r1, r2, r3
  24. 24. totalArea :: [Float] -> Float totalArea = sum . map circleArea Sum of the areas of three circles with radii r1, r2, r3
  25. 25. Currying
  26. 26. simple :: (Int -> Int -> Int) -> Int simple (x y z) Currying
  27. 27. simple :: Int -> Int -> Int -> Int simple x y z = x * ( y + z) (((simple x) y) z) Currying
  28. 28. simple 5 Partial Application
  29. 29. simple 5 :: Int -> Int -> Int simple 5 Partial Application
  30. 30. simple :: Int -> Int -> Int -> Int simple 5 :: Int -> Int -> Int simple 5 2 :: Int -> Int simple 5 2 3 :: Int Partial Application
  31. 31. Point free programming Tacit programming (point-free programming) is a programming paradigm in which a function definition does not include information regarding its arguments, using combinators and function composition [...] instead of variables.
  32. 32. Point free programming map (x -> increment x) [2,3,4] [3,4,5] map increment [2,3,4] [3,4,5] map (x -> x + 1) [2,3,4] [3,4,5] map (+1) [2,3,4] [3,4,5] increment :: Int -> Int increment x = x + 1
  33. 33. Point free programming mf criteria operator list = filter criteria (map operator list) mf = (. map) . (.) . filter
  34. 34. Functors
  35. 35. Functors map :: (a -> b) -> [a] -> [b] data List a = [] | a : List a
  36. 36. Functors treeMap :: (a -> b) -> Tree a -> Tree b data Tree a = Leaf a | Branch (Tree a) (Tree a)
  37. 37. Functors treeMap :: (a -> b) -> Tree a -> Tree b map :: (a -> b) -> [a] -> [b]
  38. 38. Functors thingMap :: (a -> b) -> f a -> f b
  39. 39. Functors A typeclass is a class of types that behave similarly.
  40. 40. Functors class Functor f where fmap :: (a -> b) -> f a -> f b
  41. 41. Functors instance Functor [] where fmap = map
  42. 42. Functors / Maybe data Maybe a = Just a | Nothing
  43. 43. Functors instance Functor Maybe where fmap _ Nothing = Nothing fmap f (Just a) = Just (f a)
  44. 44. Functors / Maybe fmap (* 2) (Just 2) Just 4 fmap (+ 5) (Just 2) Just 7 fmap (+ 5) (Nothing) Nothing
  45. 45. The End @volothamp It’s not about the destination. It’s about the journey.

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