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----------------------------------------------------
-- 1. Primitive Datatypes and Operators
----------------------------------------------------

-- You have numbers
3 -- 3

-- Math is what you would expect
1 + 1 -- 2
8 - 1 -- 7
10 * 2 -- 20
35 / 5 -- 7.0

-- Division is not integer division by default
35 / 4 -- 8.75

-- integer division
35 `div` 4 -- 8

-- Boolean values are primitives
True
False

-- Boolean operations
not True -- False
not False -- True
True && False -- False
True || False -- True
1 == 1 -- True
1 /= 1 -- False
1 < 10 -- True

-- In the above examples, `not` is a function that takes one value.
-- Haskell doesn't need parentheses for function calls...all the arguments
-- are just listed after the function. So the general pattern is:
-- func arg1 arg2 arg3...
-- See the section on functions for information on how to write your own.

-- Strings and characters
"This is a string."
'a' -- character
'You cant use single quotes for strings.' -- error!

-- Strings can be concatenated
"Hello " ++ "world!" -- "Hello world!"

-- A string is a list of characters
['H', 'e', 'l', 'l', 'o'] -- "Hello"

-- Lists can be indexed with the `!!` operator followed by an index
-- but this is an O(n) operation because lists are linked lists
"This is a string" !! 0 -- 'T'


----------------------------------------------------
-- 2. Lists and Tuples
----------------------------------------------------

-- Every element in a list must have the same type.
-- These two lists are equal:
[1, 2, 3, 4, 5]
[1..5]

-- Ranges are versatile.
['A'..'F'] -- "ABCDEF"

-- You can create a step in a range.
[0,2..10] -- [0, 2, 4, 6, 8, 10]
[5..1] -- [] (Haskell defaults to incrementing)
[5,4..1] -- [5, 4, 3, 2, 1]

-- indexing into a list
[1..10] !! 3 -- 4 (zero-based indexing)

-- You can also have infinite lists in Haskell!
[1..] -- a list of all the natural numbers

-- Infinite lists work because Haskell has "lazy evaluation". This means
-- that Haskell only evaluates things when it needs to. So you can ask for
-- the 1000th element of your list and Haskell will give it to you:

[1..] !! 999 -- 1000

-- And now Haskell has evaluated elements 1 - 1000 of this list...but the
-- rest of the elements of this "infinite" list don't exist yet! Haskell won't
-- actually evaluate them until it needs to.

-- joining two lists
[1..5] ++ [6..10]

-- adding to the head of a list
0:[1..5] -- [0, 1, 2, 3, 4, 5]

-- more list operations
head [1..5] -- 1
tail [1..5] -- [2, 3, 4, 5]
init [1..5] -- [1, 2, 3, 4]
last [1..5] -- 5

-- list comprehensions
[x*2 | x <- [1..5]] -- [2, 4, 6, 8, 10]

-- with a conditional
[x*2 | x <- [1..5], x*2 > 4] -- [6, 8, 10]

-- Every element in a tuple can be a different type, but a tuple has a
-- fixed length.
-- A tuple:
("haskell", 1)

-- accessing elements of a pair (i.e. a tuple of length 2)
fst ("haskell", 1) -- "haskell"
snd ("haskell", 1) -- 1

-- pair element accessing does not work on n-tuples (i.e. triple, quadruple, etc)
snd ("snd", "can't touch this", "da na na na") -- error! see function below

----------------------------------------------------
-- 3. Functions
----------------------------------------------------
-- A simple function that takes two variables
add a b = a + b

-- Note that if you are using ghci (the Haskell interpreter)
-- You'll need to use `let`, i.e.
-- let add a b = a + b

-- Using the function
add 1 2 -- 3

-- You can also put the function name between the two arguments
-- with backticks:
1 `add` 2 -- 3

-- You can also define functions that have no letters! This lets
-- you define your own operators! Here's an operator that does
-- integer division
(//) a b = a `div` b
35 // 4 -- 8

-- Guards: an easy way to do branching in functions
fib x
  | x < 2 = 1
  | otherwise = fib (x - 1) + fib (x - 2)

-- Pattern matching is similar. Here we have given three different
-- equations that define fib. Haskell will automatically use the first
-- equation whose left hand side pattern matches the value.
fib 1 = 1
fib 2 = 2
fib x = fib (x - 1) + fib (x - 2)

-- Pattern matching on tuples
sndOfTriple (_, y, _) = y -- use a wild card (_) to bypass naming unused value

-- Pattern matching on lists. Here `x` is the first element
-- in the list, and `xs` is the rest of the list. We can write
-- our own map function:
myMap func [] = []
myMap func (x:xs) = func x:(myMap func xs)

-- Anonymous functions are created with a backslash followed by
-- all the arguments.
myMap (\x -> x + 2) [1..5] -- [3, 4, 5, 6, 7]

-- using fold (called `inject` in some languages) with an anonymous
-- function. foldl1 means fold left, and use the first value in the
-- list as the initial value for the accumulator.
foldl1 (\acc x -> acc + x) [1..5] -- 15

----------------------------------------------------
-- 4. More functions
----------------------------------------------------

-- partial application: if you don't pass in all the arguments to a function,
-- it gets "partially applied". That means it returns a function that takes the
-- rest of the arguments.

add a b = a + b
foo = add 10 -- foo is now a function that takes a number and adds 10 to it
foo 5 -- 15

-- Another way to write the same thing
foo = (10+)
foo 5 -- 15

-- function composition
-- the operator `.` chains functions together.
-- For example, here foo is a function that takes a value. It adds 10 to it,
-- multiplies the result of that by 4, and then returns the final value.
foo = (4*) . (10+)

-- 4*(10+5) = 60
foo 5 -- 60

-- fixing precedence
-- Haskell has an operator called `$`. This operator applies a function
-- to a given parameter. In contrast to standard function application, which
-- has highest possible priority of 10 and is left-associative, the `$` operator
-- has priority of 0 and is right-associative. Such a low priority means that
-- the expression on its right is applied as a parameter to the function on its left.

-- before
even (fib 7) -- false

-- equivalently
even $ fib 7 -- false

-- composing functions
even . fib $ 7 -- false


----------------------------------------------------
-- 5. Type signatures
----------------------------------------------------

-- Haskell has a very strong type system, and every valid expression has a type.

-- Some basic types:
5 :: Integer
"hello" :: String
True :: Bool

-- Functions have types too.
-- `not` takes a boolean and returns a boolean:
-- not :: Bool -> Bool

-- Here's a function that takes two arguments:
-- add :: Integer -> Integer -> Integer

-- When you define a value, it's good practice to write its type above it:
double :: Integer -> Integer
double x = x * 2

----------------------------------------------------
-- 6. Control Flow and If Expressions
----------------------------------------------------

-- if-expressions
haskell = if 1 == 1 then "awesome" else "awful" -- haskell = "awesome"

-- if-expressions can be on multiple lines too, indentation is important
haskell = if 1 == 1
            then "awesome"
            else "awful"

-- case expressions: Here's how you could parse command line arguments
case args of
  "help" -> printHelp
  "start" -> startProgram
  _ -> putStrLn "bad args"

-- Haskell doesn't have loops; it uses recursion instead.
-- map applies a function over every element in a list

map (*2) [1..5] -- [2, 4, 6, 8, 10]

-- you can make a for function using map
for list func = map func list

-- and then use it
for [0..5] $ \i -> show i

-- we could've written that like this too:
for [0..5] show

-- filter keeps only the elements in a list that satisfy a condition
filter even [1..10] -- [2, 4, 8, 10]

-- You can use foldl or foldr to reduce a list
-- foldl <fn> <initial value> <list>
foldl (\x y -> 2*x + y) 4 [1,2,3] -- 43

-- This is the same as
(2 * (2 * (2 * 4 + 1) + 2) + 3)

-- foldl is left-handed, foldr is right-handed
foldr (\x y -> 2*x + y) 4 [1,2,3] -- 16

-- This is now the same as
(2 * 1 + (2 * 2 + (2 * 3 + 4)))

----------------------------------------------------
-- 7. Data Types
----------------------------------------------------

-- A data type is declared with a 'type constructor' on the left
-- and one or more 'data constructors' on the right, separated by
-- the pipe | symbol. This is a sum/union type. Each data constructor
-- is a (possibly nullary) function that creates an object of the type
-- named by the type constructor.

-- This is essentially an enum

data Color = Red | Blue | Green

-- Now you can use it in a function:

say :: Color -> String
say Red   = "You are Red!"
say Blue  = "You are Blue!"
say Green = "You are Green!"

-- Note that the type constructor is used in the type signature
-- and the data constructors are used in the body of the function
-- Data constructors are primarily pattern-matched against

-- This next one is a traditional container type holding two fields
-- In a type declaration, data constructors take types as parameters
-- Data constructors can have the same name as type constructors
-- This is common where the type only has a single data constructor

data Point = Point Float Float

-- This can be used in a function like:

distance :: Point -> Point -> Float
distance (Point x y) (Point x' y') = sqrt $ dx + dy
    where dx = (x - x') ** 2
          dy = (y - y') ** 2
          
-- Types can have multiple data constructors with arguments, too

data Name = Mononym String
          | FirstLastName String String
          | FullName String String String

-- To make things clearer we can use record syntax

data Point2D = CartesianPoint2D { x :: Float, y :: Float } 
             | PolarPoint2D { r :: Float, theta :: Float }

myPoint = CartesianPoint2D { x = 7.0, y = 10.0 }

-- Using record syntax automatically creates accessor functions
-- (the name of the field)

xOfMyPoint = x myPoint

-- xOfMyPoint is equal to 7.0

-- Record syntax also allows a simple form of update

myPoint' = myPoint { x = 9.0 }

-- myPoint' is CartesianPoint2D { x = 9.0, y = 10.0 }

-- Even if a type is defined with record syntax, it can be declared like
-- a simple data constructor. This is fine:

myPoint'2 = CartesianPoint2D 3.3 4.0

-- It's also useful to pattern match data constructors in `case` expressions

distanceFromOrigin x = 
    case x of (CartesianPoint2D x y) -> sqrt $ x ** 2 + y ** 2
              (PolarPoint2D r _) -> r

-- Your data types can have type parameters too:

data Maybe a = Nothing | Just a

-- These are all of type Maybe
Just "hello"    -- of type `Maybe String`
Just 1          -- of type `Maybe Int`
Nothing         -- of type `Maybe a` for any `a`

-- For convenience we can also create type synonyms with the 'type' keyword

type String = [Char]

-- Unlike `data` types, type synonyms need no constructor, and can be used 
-- anywhere a synonymous data type could be used. Say we have the 
-- following type synonyms and items with the following type signatures

type Weight = Float
type Height = Float
type Point = (Float, Float)
getMyHeightAndWeight :: Person -> (Height, Weight)
findCenter :: Circle -> Point
somePerson :: Person
someCircle :: Circle
distance :: Point -> Point -> Float

-- The following would compile and run without issue, 
-- even though it does not make sense semantically,
-- because the type synonyms reduce to the same base types

distance (getMyHeightAndWeight somePerson) (findCenter someCircle)

----------------------------------------------------
-- 8. Typeclasses
----------------------------------------------------

-- Typeclasses are one way Haskell does polymorphism
-- They are similar to interfaces in other languages
-- A typeclass defines a set of functions that must 
-- work on any type that is in that typeclass.

-- The Eq typeclass is for types whose instances can 
-- be tested for equality with one another.

class Eq a where  
    (==) :: a -> a -> Bool  
    (/=) :: a -> a -> Bool  
    x == y = not (x /= y)  
    x /= y = not (x == y)
    
-- This defines a typeclass that requires two functions, (==) and (/=)
-- It also declares that one function can be declared in terms of another
-- So it is enough that *either* the (==) function or the (/=) is defined
-- And the other will be 'filled in' based on the typeclass definition

-- To make a type a member of a type class, the instance keyword is used

instance Eq TrafficLight where  
    Red == Red = True  
    Green == Green = True  
    Yellow == Yellow = True  
    _ == _ = False 
    
-- Now we can use (==) and (/=) with TrafficLight objects

canProceedThrough :: TrafficLight -> Bool
canProceedThrough t = t /= Red

-- You can NOT create an instance definition for a type synonym

-- Functions can be written to take typeclasses with type parameters, 
-- rather than types, assuming that the function only relies on 
-- features of the typeclass

isEqual :: (Eq a) => a -> a -> Bool
isEqual x y = x == y

-- Note that x and y MUST be the same type, as they are both defined
-- as being of type parameter 'a'.
-- A typeclass does not state that different types in the typeclass can 
-- be mixed together.
-- So `isEqual Red 2` is invalid, even though 2 is an Int which is an 
-- instance of Eq, and Red is a TrafficLight which is also an instance of Eq

-- Other common typeclasses are:
-- Ord for types that can be ordered, allowing you to use >, <=, etc.
-- Read for types that can be created from a string representation
-- Show for types that can be converted to a string for display
-- Num, Real, Integral, Fractional for types that can do math
-- Enum for types that can be stepped through
-- Bounded for types with a maximum and minimum

-- Haskell can automatically make types part of Eq, Ord, Read, Show, Enum, 
-- and Bounded with the `deriving` keyword at the end of the type declaration

data Point = Point Float Float deriving (Eq, Read, Show)
    
-- In this case it is NOT necessary to create an 'instance' definition

----------------------------------------------------
-- 9. Haskell IO
----------------------------------------------------

-- While IO can't be explained fully without explaining monads,
-- it is not hard to explain enough to get going.

-- When a Haskell program is executed, `main` is
-- called. It must return a value of type `IO a` for some type `a`. For example:

main :: IO ()
main = putStrLn $ "Hello, sky! " ++ (say Blue)
-- putStrLn has type String -> IO ()

-- It is easiest to do IO if you can implement your program as
-- a function from String to String. The function
--    interact :: (String -> String) -> IO ()
-- inputs some text, runs a function on it, and prints out the
-- output.

countLines :: String -> String
countLines = show . length . lines

main' = interact countLines

-- You can think of a value of type `IO ()` as representing a
-- sequence of actions for the computer to do, much like a
-- computer program written in an imperative language. We can use
-- the `do` notation to chain actions together. For example:

sayHello :: IO ()
sayHello = do
   putStrLn "What is your name?"
   name <- getLine -- this gets a line and gives it the name "name"
   putStrLn $ "Hello, " ++ name

-- Exercise: write your own version of `interact` that only reads
--           one line of input.

-- The code in `sayHello` will never be executed, however. The only
-- action that ever gets executed is the value of `main`.
-- To run `sayHello` comment out the above definition of `main`
-- and replace it with:
--   main = sayHello

-- Let's understand better how the function `getLine` we just
-- used works. Its type is:
--    getLine :: IO String
-- You can think of a value of type `IO a` as representing a
-- computer program that will generate a value of type `a`
-- when executed (in addition to anything else it does). We can
-- name and reuse this value using `<-`. We can also
-- make our own action of type `IO String`:

action :: IO String
action = do
   putStrLn "This is a line. Duh"
   input1 <- getLine
   input2 <- getLine
   -- The type of the `do` statement is that of its last line.
   -- `return` is not a keyword, but merely a function
   return (input1 ++ "\n" ++ input2) -- return :: String -> IO String

-- We can use this just like we used `getLine`:

main'' = do
    putStrLn "I will echo two lines!"
    result <- action
    putStrLn result
    putStrLn "This was all, folks!"

-- The type `IO` is an example of a "monad". The way Haskell uses a monad to
-- do IO allows it to be a purely functional language. Any function that
-- interacts with the outside world (i.e. does IO) gets marked as `IO` in its
-- type signature. This lets us reason about which functions are "pure" (don't
-- interact with the outside world or modify state) and which functions aren't.

-- This is a powerful feature, because it's easy to run pure functions
-- concurrently; so, concurrency in Haskell is very easy.


----------------------------------------------------
-- 10. The Haskell REPL
----------------------------------------------------

-- Start the repl by typing `ghci`.
-- Now you can type in Haskell code. Any new values
-- need to be created with `let`:

let foo = 5

-- You can see the type of any value or expression with `:t`:

> :t foo
foo :: Integer

-- Operators, such as `+`, `:` and `$`, are functions.
-- Their type can be inspected by putting the operator in parentheses:

> :t (:)
(:) :: a -> [a] -> [a]

-- You can get additional information on any `name` using `:i`:

> :i (+)
class Num a where
  (+) :: a -> a -> a
  ...
    -- Defined in ‘GHC.Num’
infixl 6 +

-- You can also run any action of type `IO ()`

> sayHello
What is your name?
Friend!
Hello, Friend!

qsort [] = []
qsort (p:xs) = qsort lesser ++ [p] ++ qsort greater
    where lesser  = filter (< p) xs
          greater = filter (>= p) xs