Introduction to Functional Programming

Sébastien BESNIER

initialModel =
    { count = 0 }


type Msg
    = Increment
    | Decrement


update msg model =
    case msg of
        Increment ->
            { model | count = model.count + 1 }

        Decrement ->
            { model | count = model.count - 1 }


view model =
    div [style "font-size" "200%"]
        [ button [ onClick Increment ] [ text "+1" ]
        , div [ style "color" "red" ] [ text <| String.fromInt model.count ]
        , button [ onClick Decrement ] [ text "-1" ]
        ]

https://ellie-app.com/fDyHsFVJCska1

Challenge: Reset to 0

No mutation! Only values and pure functions

 

 

No mutation! Only values and pure functions

 

Do you know impure functions?

See Elm architecture:

https://youtu.be/kEitFAY7Gc8?t=1476

eight = 5 + 3

Affectation

Try it online

https://guide.elm-lang.org/core_language.html

eight = round 8.3

Function call

add a b = a + b

Function definition

add a b = a + b

-- call that function:
eight = add 7 1

Function definition

Challenge

Compute length of \(\texttt{"hello world"}\) and add 5 to it using the \(\texttt{add}\) function (in 1 expresion!)

String.length "abc" -- returns 3
eight = add 7 1

add a b = a + b

Order of declarations does not matter

add : Int -> Int -> Int
add a b = a + b

Types


String.length : ???

What is the type of String.length ?


String.length : String -> Int

What is the type of String.length ?


add3 a b c = a + b + c

What is the type of add3?

add3:
    Int
    -> Int
    -> Int
    -> Int
add3 a b c = a + b + c

Good practice:
add type anotation!

String.append "hello " "world" 
-- returns "hello world"

What is the type of String.append ?

String.append "hello " "world" 
-- returns "hello world"






String.append : String -> String -> String

What is the type of String.append ?

t = add 5 String.append "hey" "hoy"


f a b = 
   String.length (String.append a b)

g a b =
    add (String.append a a) b  
    
h a b =
    add (String.append a b) b

What is the type of the following expressions?


user = 
    { name = "Seb"
    , score = 42
    , city = "Paris"
    }

Records

user : User
user = 
    { name = "Seb"
    , score = 42
    , city = "Paris"
    }

Records

type alias User =
    { name : String
    , score : Int
    , city : String
    }

Records


newUser =
    { user | score = 43 }


newUserBis =
    { user | score = user.score + 1 }

Record updates

newUser : User
newUser =
    { user | score = 43 }

newUserBis : User
newUserBis =
    { user | score = user.score + 1 }

Record updates

rewardUser : User -> User
-- increase the score by one

Record updates

rewardUser : User -> User
rewardUser user =
    { user | score = user.score + 1 }

Record updates

Challenge: add type definition for the model in the counter example

https://ellie-app.com/fDyHsFVJCska1

Custom types

Records to store multiple data
(name, score, city....)

Custom types

Records to store multiple data
(name, score, city....)

What about data following various patterns ?

Modeling a shape

      Point                          Circle Float           Rectangle Float Float

Radius

Length

Width

What is the type of a shape?

Reminder: counter

type Msg
    = Increment
    | Decrement

First variant

 Second variant

Modeling a shape

      Point                          Circle Float           Rectangle Float Float

Radius

Length

Width

Modeling a shape

      Point                          Circle Float           Rectangle Float Float

Modeling a shape

type Shape =
    Point | Circle Float | Rectangle Float Float

Use a custom type

myRect = Rectangle 10 20

bigCircle = Circle 420000

describe : ???
describe shape =
  case shape of
    Point ->
      "A lonely point"
    Circle radius ->
      "A circle of radius " 
         ++ String.fromFloat radius
    Rectangle width height ->
      "A rectangle of area "
         ++ String.fromFloat (width*height)

Use a custom type

myRect = Rectangle 10 20

bigCircle = Circle 420000

describe : Shape -> String
describe shape =
  case shape of
    Point ->
      "A lonely point"
    Circle radius ->
      "A circle of radius " 
         ++ String.fromFloat radius
    Rectangle width height ->
      "A rectangle of area "
         ++ String.fromFloat (width*height)

Boolean

Defined by the language

-- Defined by Elm
type Bool = True | False

-- our code:
myBool = True

res = 
 case myBool of
    True -> 42
    False -> 18

Boolean

Defined by the language

-- Defined by Elm
type Bool = True | False

-- our code:
myBool = True

res =
 case myBool of
    True -> 42
    False -> 18
    

res =
  if myBool then
    42
  else
    18

Preferred way:

if(condition) {
   myVar = 42;
} else {
   myVar = 18;
}
myVar = condition ? 42 : 18;

VS

Conditionals

in imperative language (Java, C, Python...)

 

Conditionals

in imperative language (Java, C, Python...)

 

myVar = condition ? 42 : 18;

VS

INSTRUCTION:

changes the state

EXPRESSION:

compute a new value

if(condition) {
   myVar = 42;
} else {
   myVar = 18;
}

Implement highlight on hover

 

https://ellie-app.com/fF4BSNrDVK4a1

 

1st step: define Model & Msg and implement update

A bit of maths

  • Custom types are "sum" types
  • Records are "product" types
  • (Functions are "exponent" types)

That's all you need!

[] -- empty list
[1, 2, 6] : List number
["Hello", "world"] : List String

Lists

[] -- empty list
[1, 2, 6] : List number
["Hello", "world"] : List String
["Hello", 42] -- impossible!

Lists are homogeneous




ages : List Int
ages = [ 18, 14, 35, 10, 51 ]

agesInFiveYears : List Int
agesInFiveYears =
    -- add five to each element

No for-loops!

addFive : Int -> Int
addFive x = 5 + x

ages : List Int
ages = [ 18, 14, 35, 10, 51 ]

agesInFiveYears : List Int
agesInFiveYears =
    List.map addFive ages

No for-loops!

List.map :
    (a -> b)
    -> List a
    -> List b



agesInFiveYears =
    List.map addFive ages

Map signature

ages : List Int
ages = [ 18, 14, 35, 10, 51 ]

-- transform into : 
-- [ "18 ans", "14 ans", ... ]

-- Hint:
-- String.fromInt : Int -> Str

Map challenge

ages : List Int
ages = [ 18, 14, 35, 10, 51 ]

displayAge : Int -> String
displayAge age =
    String.fromInt age ++ " ans"

agesDisplayed =
    List.map displayAge ages

Map challenge

{-| Compute the total number of chars in the 
list of strings given in argument. Example:
    
    totalLength ["hey!", "I am", "Hungry!!"]
    
returns 16
-}
totalLength : List String -> Int
totalLength strings = ...


-- HINT: List.sum : List Int -> Int

Map challenge 2

{-| Compute the total number of chars in the 
list of strings given in argument. Example:
    
    totalLength ["hey!", "I am", "Hungry!!"]
    
returns 16
-}
totalLength : List String -> Int
totalLength strings =
  List.sum (List.map String.length strings)

Map challenge 2

Implement a Nim game

 

https://ellie-app.com/fF4PS3bjTb7a1

 

Rules:

  • 10 lucifers     at the beginning
  • 2 players
  • at his turn, the player can take 1,2 or 3 matches
  • the player taking the last lucifer lost

Talks

By groups of ~2, about 5-10 mins.

  1. Trees (the data structure): examples, how to implement it in elm, some basic algorithms (e.g. computing depth) -> Lionel, Teddy, Ilyane
  2. Modules: how do they work in elm? How do we use them to enforce some properties (give concrete examples)? Keyword: Opaque Type
    -> Hugo, Jacky
  3. List.foldr/List.foldl: explain how it works, give some examples (maybe compare some "for loop" implementation with foldX one?). How to write "map" from it?
    -> Léo, Luis
  4. Lists: How could we define the List type ourself? How to implement length/map/filter with this implementation? (to simplify, we could just define "List of Ints")
    -> Rémy, Nacer
  5. Maybe/Result: how do we handle errors in Elm? Give the definition of those types. Give examples with "map" (and if you feel it, "andThen")
    -> Maxime, Gaspard

Retro

https://easyretro.io/publicboard/sDkw7EXZGvdmZaqHz5u2Bmkyvk62/d7b3112e-2cac-47d4-928d-b24117c13d88

-- True if the 1st arg is in the second arg
member : a -> List a -> Bool

-- True if any element of the list is True
any : List Bool -> Bool

-- True if all elements of the list is True
all : List Bool -> Bool

-- rewrite member using map and any

isAscending : List Int -> Bool

Exercises on list

implement those functions using recursion and List.foldl (except for the last: use only recursion)

import Dict exposing (Dict)

d1 = Dict.empty

d2 = Dict.insert "Seb" 42 d1

age = case Dict.get "Seb" d2 of
  Just a -> "Seb is " ++ String.fromInt a
  Nothing -> "I don't know Seb"

d3 = 
  Dict.fromList [("Seb", 42), ("George", 45)]

Dictionary

associate a key to a value

Dictionary

associate a key to a value

 

 

See the docs:

https://package.elm-lang.org/packages/elm/core/latest/Dict

 

Keys have to be comparable:

String, Int, Float, List and Tuples of comparable are comparable

Challenge:

People list!

https://github.com/sebsheep/intro-to-fp/tree/main/contact-list

 

Follow the TODOs!

Parsing

Parsing

type alias Affectation =
    { varName : String
    , value : Int
    }
    
fromString :
    String
    -> Affectation


fromString "foo = 3" 
--{varName="foo",value=3}

Challenges:

String type documentation

 

https://package.elm-lang.org/packages/elm/core/latest/String

Introduction to Functional Programming

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