Haskell

Features

A purely functional PL (referential transparency, deterministic behaviour)
Lazy (Calculates & executes when forced)
Statically typed
Type inference

GHCI

:t - typeof variable
:l - load file
:m + Data.List Data.Map Data.Set - load module

Simple operations

-- Arithmetic
2 + 15
50 * 100
5 * (-3) -- Parentheses needed
 
-- Booleans
not (True && False || False)
5 == 5
2 /= 5

Operators are just infix functions.

Functions

-- Defn
doubleMe x = x + x -- No brackets, space separated
 
-- Function application
doubleMe 5
 
-- Pre-infix functions
div 92 10
92 `div` 10

Order of definition does not matter.
We use ' at the end of functions to denote a strict version of the function.
Functions can't begin with uppercase letters

Conditionals

double x = if x > 100
			then x
			else x * 2

if conditional is an expression.

Lists

-- Defn
numbers = [1, 2, 3, 4, 5]
a = [1]
b = [2]
 
-- Concatenation
a ++ b
 
-- Cons
2 : a
'a' : " hello"  -- a hello
[1, 2, 3] == 1 : 2 : 3 : []
 
-- Indexing
"Hello" !! 2  -- l
 
-- Basic functions
head [1, 2, 3]  -- 1
tail [1, 2, 3]  -- [2, 3]
last [1, 2, 3]  -- 3
init [1, 2, 3]  -- [1, 2]
length [1, 2, 3]  -- 3
null []  -- True
reverse [1, 2, 3]  -- [3, 2, 1]
take 5 [1, 2]  -- [1, 2]
drop 5 [1, 2]  -- []
cycle [1, 2, 3]  -- Infinite list [1, 2, 3, 1, 2 ...]
repeat 5  -- [5, 5, 5, ...]
sum, product, maximum, minimum, elem
 
-- Ranges (Enumerated sequences)
a = [1..20]  -- Inclusive
a = [2,4..8] -- Step value of 2
b = [20..1]
 
-- List comprehension [expr|list,predicate]
double = [x*2 | x <- [1..10], x*2 >= 12, x > 1]
bb xs = [ if x < 10 then "BOOM" else "BANG" | x <- xs, odd x ]
a = [ x*y | x <- [2,5,10], y <- [8,10,11]]
length' xs = sum [1 | _ <- xs]

Homogenous data structure
Strings are a list of chars

Tuples

-- Defn
a = [(1, 2), (2, 3)]
b = [(1, "a"), (2, "b")]
rightTriangles = [ (a,b,c) | c <- [1..10], b <- [1..c], a <- [1..b], a^2 + b^2 == c^2]
 
-- Functions (pair only)
fst (2, 3)  -- 2
snd (2, 3)  -- 3
zip [1, 2] [3, 4]  -- [(1, 3), (2, 4)]

Type depends on components and number of values
Heterogeneous
No singleton tuples
Tuples of varying sizes cannot be compared

Types

-- Basic types (:: is read as - has type of)
'a' :: Char
True :: Bool
"a" :: [Char]
(True, 'a') :: (Bool, Char)
 
-- Functions
-- removeNonUppercase :: [Char] -> [Char]  
removeNonUppercase :: String -> String  
removeNonUppercase st = [ c | c <- st, c `elem` ['A'..'Z']]
 
addThree :: Int -> Int -> Int -> Int  
addThree x y z = x + y + z
 
-- Type variables
head :: [a] -> a

Types
- Int
- Integer - unbounded integer, can be very large
- Float
- Double
- Bool
- Char
Type variables
- Generic types usually represented by lowercase alphabets
- Functions that have type variables are called polymorphic functions

Typeclasses & More types

-- Typeclass defn
(==) :: (Eq a) => a -> a -> Bool  -- Eq or equality typeclass
 
-- Typeclass examples
(==) :: (Eq a) => a -> a -> Bool  -- Equality, members implement == & /=
(>) :: (Ord a) => a -> a -> Bool  -- Ordering, members implement >,<,>=,<=
show :: (Show a) => a -> String  -- Shown as strings
read :: (Read a) => String -> a  -- Opposite of Show, reads a string and returns a type which is a member of Read
Enum  -- Members are sequentially ordered types
Bounded  -- Have upper and lower bound
Num  -- Numeric typeclass, members act like numbers (take in ints and floats)
fromIntegral :: (Num b, Integral a) => a -> b  -- Num but only integral numbers
Floating  -- double & float
 
-- Algebraic data types (ADT)
data Bool = False | True  -- Defining a new type
 
data Shape = Circle Float | Rectangle Float Float deriving (Show)  -- makes part of Show typeclass
surface :: Shape -> Float  
surface (Circle r) = pi * r ^ 2  
surface (Rectangle x1 y1) = (abs $ x1 - y1) * (abs $ y1 - x1)
 
-- Records
data Person = Person { firstName :: String  
                     , lastName :: String  
                     , age :: Int  
                     } deriving (Show)
Person {firstName="", lastName="", age=5}
 
-- Type parameters
data Maybe a = Nothing | Just a
data (Ord k) => Map k v  -- Bad practice
 
-- Deriving typeclasses
data Person = Person { firstName :: String  
                     , lastName :: String  
                     , age :: Int  
                     } deriving (Eq)  -- All fields of type must be constrained by Eq
data Day = Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday   
           deriving (Eq, Ord, Show, Read, Bounded, Enum)  -- Enum applied for successor & predecessor and Bounded for max, min bounds
 
-- Type synonyms
type String = [Char]  -- type alias, not a new type
type AssocList k v = [(k,v)]  -- Parameterized
type IntMap = Map Int  -- Partially applied (v)

Sort of interface that defines behaviour. If a type is a part of a typeclass, that means that it supports and implements the behaviour the typeclass describes.
=> is a class constraint. The type of values must be a member of the typeclass
Creating types
- We use the data keyword to create types.
- data A = B
- Here, A is the type name and B is called a value constructor. Both are capital
- Value constructors can have fields which can contain values
- These fields are actually params to the value constructors which are functions
- We can pattern match value constructors but not use them as types.
- It's common to use the same name as the type if there's only one value constructor
Records
- Creates functions that can lookup fields in the type
- Order does not matter
Type parameters
- Type constructors take types as parameters to produce new types. (Generics)
- Type constructors can contain class constraints but this is not good practice as you will have to include the constraint in functions anyways.
Derived types
- Ex: When we derive the Eq instance for a type and then try to compare two values of that type with == or /=, Haskell will see if the value constructors match and then check data inside too

Pattern matching

-- Fn body pattern matching
lucky :: (Integral a) => a -> String  
lucky 7 = "LUCKY NUMBER SEVEN!"  
lucky x = "Sorry, you're out of luck, pal!"
 
factorial :: (Integral a) => a -> a  
factorial 0 = 1  
factorial n = n * factorial (n - 1)
 
addVectors :: (Num a) => (a, a) -> (a, a) -> (a, a)  -- Tuple patterns
addVectors (x1, y1) (x2, y2) = (x1 + x2, y1 + y2)
 
head' :: [a] -> a  -- List patterns using cons
head' [] = error "Can't call head on an empty list, dummy!"  
head' (x:_) = x
 
length' :: (Num b) => [a] -> b  
length' [] = 0  
length' (_:xs) = 1 + length' xs
 
capital :: String -> String  
capital "" = "Empty string, whoops!"  
capital all@(x:xs) = all ++ " " ++ xs ++ " " ++ [x]  -- for hello - hello ello h
 
-- Guards
bmiTell :: (RealFloat a) => a -> String  
bmiTell bmi  
    | bmi <= 18.5 = "You're underweight"  
    | bmi <= 25.0 = "You're normal."  
    | bmi <= 30.0 = "You're fat"  
    | otherwise   = "You're whale"
 
-- where & let-in bindings
foo :: Int -> Int
foo bar = a + b
	where 
		a = bar * 5
		b = bar + 2
 
foo :: Int -> Int
foo bar =
	let 
		a = bar * 5
		b = bar + 2
	in a + b
[let square x = x * x; y = 5 in (square 5, square 3, square y)]
 
calcBmis :: (RealFloat a) => [(a, a)] -> [a]  
-- in not required due to predefined name visibility
calcBmis xs = [bmi | (w, h) <- xs, let bmi = w / h ^ 2, bmi >= 25.0]
 
-- case expressions
head' :: [a] -> a  
head' xs = case xs of [] -> error "No head for empty lists!"  
                      (x:_) -> x

Pattern matching consists of specifying patterns to which some data should conform and then checking to see if it does and deconstructing the data according to those patterns
Haskell does not check for exhaustivity of patterns and hence, matches can fail
_ is used to ignore a pattern
Patterns (@) are a handy way of breaking something up according to a pattern and binding it to names whilst still keeping a reference to the whole thing.
Guards are boolean exprs and are indicated by pipes that follow a function's name and params
Bindings
- Names defined in where are only visible to that function
- Can use pattern matching in where name declarations
- let-in is more constrained than where but lets you bind variables anywhere unlike where.
- let-in is an expression but where is a syntactic construct
Function pattern matching is syntactic sugar for case exprs

Recursion

maximum' :: (Ord a) => [a] -> a  
maximum' [] = error "maximum of empty list"  
maximum' [x] = x  
-- maximum' (x:xs)   
--    | x > maxTail = x  
--    | otherwise = maxTail  
--    where maxTail = maximum' xs
maximum' (x:xs) = max x (maximum' xs)

Recursion is a way of defining functions in which the function is applied inside its own definition. Due to the lack of loops in Haskell, we use recursion.
Define a terminating edge/base case and work your way through to find the general case.

Higher order functions

-- Currying
max 4 5
(max 4) 5
 
compareWithHundred x = compare 100 x
compareWithHundred = compare 100
 
divideByTen = (/10)  -- Infix curry (does x / 10)
 
-- Higher order fns
applyTwice :: (a -> a) -> a -> a  
applyTwice f x = f (f x)
 
zipWith' :: (a -> b -> c) -> [a] -> [b] -> [c]  
zipWith' _ [] _ = []  
zipWith' _ _ [] = []  
zipWith' f (x:xs) (y:ys) = f x y : zipWith' f xs ys
 
map :: (a -> b) -> [a] -> [b]  
map _ [] = []  
map f (x:xs) = f x : map f xs
 
filter :: (a -> Bool) -> [a] -> [a]  
filter _ [] = []  
filter p (x:xs)   
    | p x       = x : filter p xs  
    | otherwise = filter p xs
 
takeWhile (<10000) [1..]  -- Takes nums while predicate is true
 
-- Lambdas
zipWith (\a b -> (a * 30 + 3) / b) [5,4,3,2,1] [1,2,3,4,5]
map (\(a,b) -> a + b) [(1,2),(3,5),(6,3),(2,6),(2,5)]  -- With pattern matching
 
-- Folds
sum' :: (Num a) => [a] -> a  
-- sum' xs = foldl (\acc x -> acc + x) 0 xs
sum' = foldl (+) 0
 
elem' :: (Eq a) => a -> [a] -> Bool  
elem' y ys = foldl (\acc x -> if x == y then True else acc) False ys
 
map' :: (a -> b) -> [a] -> [b]  
map' f xs = foldr (\x acc -> f x : acc) [] xs  -- Left fold requires ++ which is costly
 
-- Function application
($) :: (a -> b) -> a -> b  
f $ x = f x
 
map ($ 3) [(4+), (10*), (^2), sqrt]
 
-- Function composition
(.) :: (b -> c) -> (a -> b) -> a -> c  
f . g = \x -> f (g x)
 
map (negate . abs) [5,-3,-6,7,-3,2,-19,24]
map (negate . sum . tail) [[1..5],[3..6],[1..7]]
(sum . replicate 5 . max 6.7) 8.9  -- Multiple param composition
fn = ceiling . negate . tan . cos . max 50  -- Point free style

Functions that can take functions as parameters and return functions as return values are called higher order functions.
Every fn in Haskell takes only one parameter. The functions that accept more are curried.
max :: (Ord a) => a -> a -> a can be read as max :: (Ord a) => a -> (a -> a) which explains why type declarations are separated by arrows.
Infix functions can be partially applied by using sections - surrounding it with parentheses
- (-5) is an exception is just negative 5
Function types need a mandatory parentheses because -> is naturally right associative
Lambdas are anonymous functions usually to pass them to a higher order function. They are expressions. Lambdas are normally surrounded by parentheses unless we mean for them to extend all the way to the right.
A fold takes a binary function, a starting value (the accumulator) and a list to fold up. The resultant acc is returned. foldl starts from the left and foldr from the right.
scanl & scanr are similar but report intermediate values in a list instead of the acc.
Function application or $ has the lowest precedence and right associative.

Modules

-- Imports
import Data.List
 
numUniques :: (Eq a) => [a] -> Int  
numUniques = length . nub  -- nub exists in Data.List and gets unique elements
 
import Data.List (nub, sort)
import Data.List hiding (nub)
import qualified Data.Map as M  -- Qualified imports (M.foo)
 
-- Data.List
intersperse '.' "MONKEY"  -- "M.O.N.K.E.Y"
intercalate [0,0,0] [[1,2,3],[4,5,6],[7,8,9]]  -- [1,2,3,0,0,0,4,5,6,0,0,0,7,8,9]
transpose [[1,2,3],[4,5,6],[7,8,9]]
concat [[3,4,5],[2,3,4],[2,1,1]]  -- [3,4,5,2,3,4,2,1,1]
and $ map (==4) [4,4,4,3,4]  -- False
or $ map (==4) [2,3,4,5,6,1]  -- True
any (==4) [2,3,5,6,1,4]
any (==4) [2,3,5,6,1,4]
iterate (*2) 1  -- Infinite multiples
group [1,1,2,2,2,2,3,3,2,2,2,5,6,7]  -- [[1,1],[2,2,2,2],[3,3],[2,2,2],[5],[6],[7]]
find (>4) [1,2,3,4,5,6]  -- Just 5
lines "first line\nsecond line"  -- ["first line","second line"]
[1..10] \\ [2,5,9]  -- [1,3,4,6,7,8,10] (List difference)
groupBy ((==) `on` (> 0)) values  -- Group by equality on condition - greater than zero
 
-- Maps / Association lists
phoneBook =   
    [("betty","555-2938")  
    ,("bonnie","452-2928")  
    ,("patsy","493-2928")  
    ]
 
findKey :: (Eq k) => k -> [(k,v)] -> Maybe v  
findKey key = foldr (\(k,v) acc -> if key == k then Just v else acc) Nothing
 
Map.null $ Map.fromList [(2,3),(5,5)]
Map.insert 5 600 . Map.insert 4 200 . Map.insert 3 100 $ Map.empty
 
-- Creating modules
module Geometry  
( Point(..)  -- Exported all constructors of a datatype
, Shape(Circle)
, sphereVolume  -- Exported functions
, sphereArea
) where

A Haskell module is a collection of related functions, types and typeclasses.
A Haskell program is a collection of modules where the main module loads up the other modules and then uses the functions defined in them.
The Prelude module is imported by default.
import has to be at the top of the file, before any fn definition
foldl' and foldl1' are stricter versions of their respective lazy versions. When using lazy folds on really big lists, you might often get a stack overflow error. The culprit for that is because the accumulator value isn't actually updated as the folding happens. It makes a promise that it will compute its value when asked to actually produce the result (also called a thunk).
Maps need keys to be orderable as they are internally represented by trees.
All elements of a set are unique and ordered.
Creating modules
- The module name is the file name. Ex: Foo
- If a module is present in a folder, it's a submodule. Ex: Foo/Bar implies Foo.Bar

Racket