# Exploring Haskell: Types & Classes

Code examples are adapted from Introduction to Functional Programming course.

Access to GHCi is available on repl.it to test out these snippets online.

## Types #

Evaluating an expression `e`.

``e :: t -- This reads as e has type t, also used for type casting``

Every valid expression has a type, which is calculated using type inference.

To get a type in GHCi use `:t` which is an abbreviation for `:type` command.

``not False -- True:t not False -- not False :: Bool``

### Basic Types #

Some basic types that are common in other programming languages:

• `Bool` - logical values
• `Char` - single character
• `String` - strings of characters
• `Int` - fixed-precision integers
• `Integer` - arbitrary-precision integers
• `Float` - floating-point numbers
``:t True -- Bool - logical values:t 'H' -- Char - single character:t "Hi" -- [Char] - strings of characters:t 1 -- Num p => p2^64 :: Int -- is out of the Int range (Overflow):t 2^65 -- Num p => p2^65 :: Integer -- 36893488147419103232:t 1.5 -- Fractional p => p``

### List Types #

Lists in Haskell are polymorphic and can only contain a sequence of values with the same type.

``:t [False, True, False] -- [False, True, False] :: [Bool]:t ['a', 'b', 'c', 'd'] -- ['a', 'b', 'c', 'd'] :: [Char]:t [['a'], ['b', 'c']] -- [['a'], ['b', 'c']] -- :: [[Char]]``

### Tuple Types #

Tuples can contain sequence of values with different types

``:t (False, True) -- (False, True) :: (Bool, Bool):t (False,'a',True) -- (False, 'a', True) :: (Bool, Char, Bool):t ('a', (False, 'b')) -- ('a', (False, 'b')) :: (Char, (Bool, Char)):t (True, ['a', 'b']) -- (True, ['a', 'b']) -- :: (Bool, [Char])``

## Functions #

A function is a mapping from values of one type to values of another type:

``import Data.Char (isDigit) -- Necessary for isDigit to work:t isDigit -- isDigit :: Char -> Bool:t not -- not :: Bool -> Bool-- Example functionsadd (x, y) = x + y -- add :: Num a => (a, a) -> azeroto n = [0..n] -- zeroto :: (Num a, Enum a) => a -> [a]``

### Curried Functions #

When a function returns as a result an another function it is called a curried function.

``add' x y = x + y -- add' :: Num a => a -> a -> a``

Both `add` and `add'` produce the same result, where `add` takes all arguments at the same time, and `add'` can consume one at a time.

``-- Parenthesis in Haskell are right associative and are omitted for brevity.mult x y z = x * y * z -- mult :: Num a => a -> (a -> (a -> a))``

#### Why is Currying Useful? #

Currying makes functions more flexible and allows partial application.

Creating a function that increments by one:

``addOne = add' 1addOne 2 -- 3``

### Conventions for Currying #

To avoid excess parentheses when using curried functions there are two conventions:

1. The `->` in type definition associates to the right.

``Int -> Int -> Int -> Int -- Int -> (Int -> (Int -> Int))``
2. Function application is associated to the left.

``mult x y z -- ((mult x) y) z``

Unless explicitly required, all functions in Haskell are defined in the curried form.

## Polymorphic Functions #

A function can be called polymorphic when its type contains one or more type variables

``-- length takes a 'collection' of type 'a' and returns an 'Int':type length -- length :: Foldable t => t a -> Intlength [False, True] -- 2length [1, 2, 3, 4] -- 4-- More Examples:t fst -- fst :: (a, b) -> a:t head -- head :: [a] -> a:t take -- take :: Int -> [a] -> [a]:t zip -- zip :: [a] -> [b] -> [(a, b)]:t id -- id :: a -> a``

A polymorphic function is called overloaded if its type contains one or more class constraints.

``-- sum takes a list with numeric type 'a', and returns a value of type 'a'.:t sum -- sum :: (Foldable t, Num a) => t a -> asum [1, 2, 3] -- 6sum [1.1, 2.2, 3.3] - 6.6sum ['a', 'b', 'c'] -- error``

## Classes #

Haskell has a number of type classes:

• `Num` - Numeric types
• `Eq` - Equality types
• `Ord` - Ordered types
``:t (+) -- (+) :: Num a => a -> a -> a:t (==) -- (==) :: Eq a => a -> a -> Bool:t (<) -- (<) :: Ord a => a -> a -> Bool``

And that's it for now.