Week 9 #

Infix Operators #

Any curried function that takes 2 parameters can be converted, and vice versa

x = 3 + 2 -- infix
x = (+) 3 2 -- function

y = elem 3 [1,2,3]
y = 3 `elem` [1,2,3] -- infix

Type Synonyms #

Giving existing types an alias or new name

type NewType = OldType

Useful for readability (String instead of [Char])

User Defined Data Types #

General Syntax:

data NewType = Constructor1 Type1 | ... | ConstructorN TypeN

|: represents union of the constructor and types

export Type NewType = Type1 | ... | TypeN

TypeI: previously defined types
ConstructorI: creates a value of NewType type
Type can be omitted if the constructor does not need any argument (constants)

Enumerated Types #

data NumberType = Odd | Even
--- only constants

--- pattern matching on constructors
mod2 :: Num a => NumberType -> a
mod2 Odd = 1
mod2 Even = 2

Variant/Union Types #

data Text = Letter Char | Word [Char]
--- either a single Letter or multiple letters (word)

textLen :: Text -> Int
textLen (Letter _) = 1
textLen (Word w) = length w

Mutually Recursive Types #

--- parametric polymorphism here
data Tree a = Leaf a | Node a (Tree a) (Tree a)
--- Tree is a type constructor
--- Node is a curried value constructor

countNodes:: Tree a -> Int
countNodes (Leaf _) = 1
countNodes (Node _ left right) = countNodes left + countNodes right + 1
--- the structure of the function is the same as the data type
--- i.e the recursive pattern is the same on both