Haskell

Functional Programming

is scary

Unfamiliar

Functor

Mappable 

Catamorphism

Collapsible
Foldable

Monad

Flatmappable

Chainable

AndThenable

Computation builder

( I'll come back to this one )

Monoid

Aggregatable

Currying

Currying?

Applicatives

Applicatives?

Object Oriented

Programming

is scary

very much so.

Inheritance
Covariance

Polymorphism

SOLID
SRP,OCP,LSP
DIP

Functional Programming

Ideas

Maths
is your
Friend

Mathematical assertions are

Precise

 


 

Mathematical assertions are usually

Generalized

( You can often apply them to many different instances )
 

Mathematical reasoning is/can be

Proved


 

Functions are pure 

Given the same inputs, always will return same output

( Referential transparency ) 

 

Types
are not
Classes

What are types?

Int is a type

String is a type
User is a type 

 

Functions 

are types

Int -> Int
(+3)

Functions
are 
Things

You can:

Return functions from functions

Pass functions as parameters

Writing functions in different ways

add :: Int -> Int -> Int
add x y = x + y
add :: Int -> Int -> Int
add = (\x y -> x + y)
add :: Int -> (Int -> Int)
add x = (\y -> x + y)
three = 1 + 2
three = (+) 2 1
add1 = (+) 2

Missing a parameter?

Composition
Everywhere!

show :: Int -> String
length :: String -> Int
digitCount :: Int -> Int
digitCount :: Int -> Int
digitCount value = length (show value)
digitCount :: Int -> Int
digitCount value = length . show value
digitCount :: Int -> Int
digitCount = length . show

. is a function!

show is (a -> b) (Int -> String)
length is (b -> c) (String -> Int)
the number you pass in is a 

(.) :: (b -> c) -> (a -> b) -> a -> c

Functions
all the
Way Down

Types

are your
Friends

Use types to represent

Constraints

data Suit = Club | Diamond | Spades | Diamond
data Rank = Two 
          | Three 
          | Four 
          | Five 
          | Six 
          | Seven 
          | Eight 
          | Nine 
          | Ten 
          | Jack 
          | Queen 
          | King 
          | Ace
data Card = Card Suit Rank
type Deck = [Card]

Use types to indicate

Errors

parseInt :: String -> Int
parseInt :: String -> Maybe Int

  • No nulls

  • No exceptions

Make illegal states

Unrepresentable

data Status = Verified | Unverified

Use types for 

State Machines

data ShoppingCart = Empty | Active [Item] | Paid [Item]

Beautiful clean

internal model

Dirty unclean outside world

The Great Gate

Monoids, Functors,  Applicatives and Monads

Are all different algebras

They are ideas about computation

Not just specific to Haskell

Functions of type

a -> b

 

Transform values of type a to values of type b 

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

( Increments a number by 1 )

( Returns the string representation of a number )

But what if a value is in some kind of container?

eg a maybe

Maybe

data Maybe a = Nothing | Just a
2      -- a value
Just 2 -- a value with context.

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

But how does fmap do this wizardry?

Functor is a typeclass

A typeclass is a sort of interface that defines some behavior.

If a type is part of a typeclass,

that means it implements the behaviour the typeclass describes 

class Functor f where
    fmap :: (a -> b) -> f a -> f b

To make data type f a functor

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

The map function

map :: (a -> b) -> [a] -> [b]
map :: (Int -> String) -> [Int] -> [String]
map show [1, 2, 3, 4] 
["1", "2", "3", "4"]
map (+1) [1, 2, 3, 4]
[2, 3, 4, 5]

If something is a functor

then there exists a function called fmap that will lift transformations from

a -> b

to

 f a -> f b

Examples

fmap specialized to lists has the type:

(a -> b) -> ([a] -> [b])

fmap specialized to Maybe has the type:

(a -> b) -> (Maybe a -> Maybe b)

We can also have containers with functions in them

Subtitle

Values

2

2 (+1) = 3

Context

Just 1 

data Maybe a = Nothing | Just a
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