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# Reading Simple

[![Haskell](https://www.haskell.org/static/img/haskell-logo.svg)](https://haskell-lang.org)

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Reading Simple Haskell

  • Markdown format available here.

Haskell

Haskell is a general purpose programming language, and can be used to build:

Haskell's main compiler is GHC.


Module Structure

  • Compiler extensions - we won't talk about those in this talk
  • Comments - -- for single line comment, {- -} for block comments
  • Module name
  • Exports
  • Imports
  • Definitions

Definitions - Simple Values

  • Left-hand side is the name of the value
  • = is used to declare the expression that is bound to the name on the left side (value definition)
five = 5

Definitions - Functions

  • Add argument names after a name
  • Call functions without parentheses
  • Function call is left associative
  • Function call takes precendence over operators
increment n = n + 1

six = increment five

seven = increment (increment five)

incAndAdd x y = increment x + increment y

Definitions - Operators

  • You can also define operators
x +- y = (x + x) - (y + y)

Function Calls - Partial Application

  • We can supply only some of the arguments to a function
  • If we have a function that takes N arguments and we supply K arguments, we'll get a function that takes the remaining (N - K) arguments
-- takes 3 arguments, so in this case N = 3
sum3 x y z = x + y + z

-- only supplies 2 arguments (K = 2), 0 and 1.
-- so newIncrement is a function that takes (N - K = 1) arguments
newIncrement = sum3 0 1

-- three is the value 3
three = newIncrement 2

let/where

  • We can name part of the computation using let or where
  • let [<definition>] in <expression> is an expression and can be used anywhere
  • where is special syntax
sumOf3 x y z =
  let temp = x + y
  in temp + z

-- or:
sumOf3 x y z = temp + z
  where temp = x + y

Defining Types

  • Concrete types starts with an uppercase letter
  • Use type to give a new alias to an existing type. They can be used interchangingly.
type Nickname = String

Type Signatures

We can give values a type signature using ::

myNickname :: Nickname
myNickname = "suppi"

Defining Types - Sum Types

  • We can define our own types using the keyword data
  • Sum types are alternative possible values of a given type
  • Similar to enums in other languages
  • We use | to say "alternatively"
  • To calculate how many possible values the new type has, we count and sum all the possible values, therefore "sum type"
  • Each option must start with an uppercase letter
data KnownColor -- the new type's name
  = Red         -- One possible value
  | Blue
  | Green

redColor :: KnownColor
redColor = Red

Defining Types - Product Types

  • We can also use data to define compound data of existing types
  • Similar to structs in other languages
  • To calculate how many possible values the new type has, we count and multiply the amount of possible values for each type. Therefore "product type"
data RGB
  = MkRGB Int Int Int
{-
      ^    ^   ^   ^
      |    |   |   |
      |    |   |   +- This is the blue component
      |    |   |
      |    |   +----- This is the green component
      |    |
      |    +--------- This is the red component
      |
      +------------- This is called the value constructor, or "tag"
-}

magenta :: RGB
magenta = MkRGB 255 0 255

Defining types - Sum and Product Types

  • We can mix sum and product types in one type
  • This is often called an algebraic data type, or ADT
  • Value constructors (like Red, Blue, Green or RGB) create a value of the type
  • If they represent a product (like RGB), value constructors can be used as regular functions to build values of the type
  • This also means they can be partially applied
data Color
  = Red
  | Blue
  | Green
  | RGB Int Int Int

blue :: Color
blue = Blue

magenta :: Color
magenta = RGB 255 0 255

Defining types - Records

  • Records allow us to name the fields in a product type
  • There is more to records, but we won't talk too much about it here
data RGB = MkRGB
  { rgbRed   :: Int
  , rgbGreen :: Int
  , rgbBlue  :: Int
  }


red :: RGB
red = MkRGB
  { rgbRed   = 255
  , rgbGreen = 0
  , rgbBlue  = 0
  }

The Type of Functions

  • We use -> to denote the type of a function from one type to another type
increment :: Int -> Int
increment n = n + 1

sum3 :: Int -> Int -> Int -> Int
sum3 x y z = x + y + z

supplyGreenAndBlue :: Int -> Int -> Color
supplyGreenAndBlue = RGB 100

The Type of Functions

  • -> is right associative, The function definitions from the previous slide will be parsed like this:
increment :: Int -> Int
increment n = n + 1

sum3 :: (Int -> (Int -> (Int -> Int)))
sum3 x y z = x + y + z

supplyGreenAndBlue :: (Int -> (Int -> Color))
supplyGreenAndBlue = RGB 100
  • This is why partial function application works.

Parametric Polymorphism in Type Signatures

  • Also known as "generics" in other languages
  • Names that starts with an upper case letter in types are concrete types
  • Names that starts with a lower case letter in types are type variables
  • Just as a variable represent some value of a given type, a type variable represents some type
  • A type variable represents one type across the type signature (and function definition) in the same way a variable represent a value throughout the scope it's defined in

Parametric Polymorphism in Type Signatures

-- I only take concrete `Int` values
identityInt :: Int -> Int
identityInt x = x

five :: Int
five = identityInt 5

-- `a` represents any one type
identity :: a -> a
identity x = x

seven :: Int
seven = identity 7

true :: Bool
true = identity True

const :: a -> b -> a
const x y = x

Parametric Polymorphism in Type Signatures

-- will fail because nothing in the type signature suggests that
-- `a` and `b` necessarily represent the same type
identity1 :: a -> b
identity1 x = x

-- will fail because we don't know if `a` is `Int`
identity2 :: a -> Int
identity2 x = x

-- will fail because we don't know if `a` is `Int`
identity3 :: Int -> a
identity3 x = x

One More Thing About Functions

  • In Haskell functions are first class values
  • They can be put in variables, passed and returned from functions, etc
  • This is a function that takes two functions and a value, applies the second function to the value and then applies the first function to the result
  • AKA function composition
compose :: (b -> c) -> (a -> b) -> a -> c
compose f g x = f (g x)

f . g = compose f g

One More Thing About Functions

  • Remember, -> in type signatures is right associative
  • Doesn't it look like we take two functions and return a third from the type signature?
compose :: ((b -> c) -> ((a -> b) -> (a -> c)))
compose f g x = f (g x)

Definitions - Global type inference

As we saw earlier, Haskell is globally type inferred. We can remove almost all type signatures and Haskell will choose the most general type signature for us.


Recursive Types and Data Structures

  • A recursive data type is a data definition that refers to itself
  • This lets us define even more interesting data structures such as linked lists and trees
data IntList
  = EndOfIntList
  | ValAndNext Int IntList

-- the list [1,2,3]
list123 :: IntList
list123 = ValAndNext 1 (ValAndNext 2 (ValAndNext 3 EndOfList))

Recursive Types and Data Structures

  • A recursive data type is a data definition that refers to itself
  • This lets us define even more interesting data structures such as linked lists and trees
data IntTree
  = Leaf
  | Node
      IntTree      -- Left subtree
      Int          -- Node value
      IntTree      -- Right subtree

--     2
--    / \
--   1   3
--  /
-- 1
tree1123 :: IntTree
tree1123 =
  Node
    (Node (Node Leaf 1 Leaf) 1 Leaf)
    2
    (Node Leaf 3 Leaf)

Defining Types - Type variables

  • We can use type variables when defining types
  • We can define generic structures
  • This way we don't have to restrict our structure to a specific type such as Int or Bool like in the previous slide
-- a value of type a or nothing
data Maybe a
  = Just a
  | Nothing

-- a value of type a or a value of type b
data Either a b
  = Left a
  | Right b

-- A linked list of `a`s

-- Note: there's also a built in syntax in Haskell for linked lists

data List a          -- [a]    -- special syntax for a linked list of a generic type `a`
  = Nil              -- []     -- special syntax for the empty list
  | Cons a (List a)  -- x : xs -- special operator for constructing a list

Case Expression (Pattern Matching)

  • Allows us to write control flows on data types
  • Matches from top to bottom
case <expr> of
  <pattern1> -> <result1>
  <pattern2> -> <result2>
  ...
  <patternN> -> <resultN>

Case Expression (Pattern Matching)

  • Allows us to write control flows on data types
  • Matches from top to bottom
myIf :: Bool -> a -> a -> a
myIf test trueBranch falseBranch =
  case test of
    True  -> trueBranch
    False -> falseBranch

Case Expression (Pattern Matching)

  • Allows us to write control flows on data types
  • Matches from top to bottom
factorial :: Int -> Int
factorial num =
  case num of
    0 -> 1
    n -> n * factorial (n - 1)

Case Expression (Pattern Matching)

  • Allows us to write control flows on data types
  • Matches from top to bottom
  • The pattern _ means match anything
colorName :: Color -> String
colorName color =
  case color of
    Red -> "red"
    Green -> "green"
    Blue -> "blue"
    RGB 255 0 255 -> "magenta"
    RGB _ 255 _ -> "well it has a lot of green in it"
    _ -> "i don't know this color"

Do notation

  • Do notation is special syntax for writing IO actions in a way that looks imperative
  • <- is used to bind the result of an IO action to a variable when using do notation
  • let is used to bind an expression to a name
main :: IO ()
main = do
  putStrLn "Hello!"
  putStrLn "What is your name?"
  result <- getLine
  putStrLn ("Nice to meet you, " ++ result)
  putStrLn "Here is the result of 1+1: "
  let calculation = factorial 100 -- note that when using do notation we don't need to use `in`
  putStrLn (show (factorial 100))
  putStrLn "Bye!"

Example


Want to learn more?