Haskell

Part 3

Recap

:t <something>

:i <something>

GHC.IO

Defining stuff

let count = 1
let add x y = x + y

let v = 2 :: Int
let h = 3 :: Float

Calling functions

add 1 2

let add10 = add 10

Basic Types

'c', False,"123", 1, [1,2,3], (1,True)

Lists 

Can only be of single type

(++), (:), (!!)

head, tail, last, init

length, reverse, drop, take

sum, product, minimum, maximum, elem

Ranges

[1..20], ['a'..'z'], ['V'..'Z']

[1,2..20]

cycle, repeat, replicate,

List comprehensions

[x*2 | x <- [1..10], x*2 >= 12] 
[ x*y | x <- [2,5,10], y <- [8,10,11]]  
[x*2 | x <- [1..10]] 

Tuples

fst, snd, zip

In Haskell

Everything has a type

(+1) :: Int -> Int
(+) :: Int -> Int -> Int

Typeclasses

Things that defines behaviour

Not like classes

Think of them as interfaces
instead.

Example

:t (==)

== is actually a function.

So is +, -, /, * and almost all operators. 

The Eq Typeclass

for types that support equality testing.

Almost all of the standard types

(==) :: (Eq a) => a -> a -> Bool  

Everything before => is called a class constraint 

The (==) function takes ​two values of the same type and returns a Bool.

The type of the two types must be a member of the the Eq typeclass,

The elem function

has the type

elem :: (Eq a) => a -> [a] -> Bool

because it uses the (==) function over a list to check whether it contains the value we are looking for 

Example

data Day = Mon | Tue | Wed | Thu | Fri | Sat | Sun 
                                        deriving (Eq)
Mon == Fri
Fri /= Wed

The Ord Typeclass

for types that have ordering

(<) :: (Ord a) => a -> a -> Bool  
:t (<)

Example

data Day = Mon | Tue | Wed | Thu | Fri | Sat | Sun 
                                        deriving (Eq, Ord)
Mon > Fri
Fri > Wed

The Enum Typeclass

for types  that are sequentially ordered 

allows you to use them in list ranges

Example

data Day = Mon | Tue | Wed | Thu | Fri | Sat | Sun 
                                        deriving (Enum)
[Mon..Fri]
succ Fri
pred Fri

The Show Typeclass

Example

data Day = Mon | Tue | Wed | Thu | Fri | Sat | Sun 
                                        deriving (Show)
show Fri

The Read Typeclass

Example

data Day = Mon | Tue | Wed | Thu | Fri | Sat | Sun 
                                        deriving (Read)
read "Fri"

The Num Typeclass

for types that act like numbers

Type of a number

13 :: (Num t) => t  
:t 13

Whole numbers can act like 

any type that's a member of Num

:t 13 :: Int
:t 13 :: Float
:t 13 :: Double
:t (+)
(+) :: (Num a) => a -> a -> a  

So you can add numbers like so:

(1 :: Double) + (3 :: Int)

Functor

is just another typeclass

What behaviour does it define?

Context

A value can be wrapped in a context

The Maybe type

data Maybe a = Nothing | Just a
2             -- a normal value
Just 2      -- a type of context wrapping a value
Nothing -- an empty type of context
Nothing :: Maybe a
Just :: a -> Maybe a

When a value is wrapped in a context (eg a list, or maybe)

You can't apply a normal function to it.

fmap

fmap knows how to apply a function to a value in a context

> fmap (+3) (Just 2)
Just 5
> fmap (+3) Nothing
Nothing
class Functor f where
    fmap :: (a -> b) -> f a -> f b

To make datatype f a functor

You'll need to implement this function for your data type 

Pattern Matching

isOne :: Int -> Bool
isOne 1 = True
isOne _ = False
pow :: Int -> Int -> Int
pow _ 0 = 1
pow a b = a^b
instance Functor Maybe where  
    fmap function (Just x) = Just (function x)  
    fmap function Nothing = Nothing  
fmap (+3) (Just 2)
fmap (+3) Nothing

Another Example

fmap (+3) [2,4,6]
instance Functor [] where
    fmap = map

That's all for this week

Questions?

That's all folks

Applicatives

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