Algebraic Types

A language to share data representation

Modeling a shape

Point Circle Radius Rectangle Width Height

OOP Solution

Shape

Abstract class

drawAt(x,y)

OOP Solution

Point

drawAt(x,y) { ...}

Shape

Abstract class

drawAt(x,y)

Circle

Attribute: radius

drawAt(x,y) { ...}

Rectangle

Attributes:

width, height

drawAt(x,y) { ...}

OOP Solution

Classes
Abstract classes
Inheritance
Method
(this/self)

Modeling a shape

Point Circle Radius Rectangle Width Height

Modeling a shape

Point Circle Radius Rectangle Width Height

Modeling a shape

type Shape =
    Point | Circle Radius | Rectangle Width Height

Modeling a shape

type Shape =
    Point | Circle Radius | Rectangle Width Height

type alias Radius = Float
type alias Width = Float
type alias Height = Float

Modeling a shape

type Shape =
    Point | Circle Radius | Rectangle Width Height

type alias Radius = Float
type alias Width = Float
type alias Height = Float

Equivalent:

type Shape =
    Point | Circle Float | Rectangle Float Float

Modeling a shape

type Shape =
    Point | Circle Radius | Rectangle Width Height

type alias Radius = Float
type alias Width = Float
type alias Height = Float

Equivalent:

type Shape =
    Point | Circle Float | Rectangle Float Float

Algebraic Data Type !

Use an ADT

myRect = Rectangle 10 20

bigCircle = Circle 420000

drawAt (x, y) shape =
    case shape of
        Point ->
            ...
        Circle radius ->
            ...
        Rectangle width height ->
            ...

myDrawing1 = drawAt (5, 7) (Circle 10)
myDrawing2 = drawAt (10, 5) myRect

Advanced shape

R. I. P.

Bob

Advanced shape

tombstone =

        (Rectangle 50 50)

Advanced shape

tombstone =
    Union
        (Rectangle 50 50)
        (Circle 25)

Advanced shape

shift

tombstone =
    Union
        (Rectangle 50 50)
        (Circle 25)
        (0, 25)
        -- the circle is 
        -- shifted by 25
        -- vertically

Advanced shape

shift

type Shape
    = Point 
    | Circle Radius
    | Rectangle Width Height 
    | Union Shape Shape Shift

type alias Shift = 
    (Float, Float)

Advanced shape

And more:

intersection
symmetric difference
rotation
...

Translation

Todo list

Appeler Bob

Lire H2G2

Tester Elm

New

3 elements

Translation

Todo list

3 elements

New

Title

Appeler Bob

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Tester Elm

Translation

Todo list

3 elements

New

NumberOfElements 3

Title

Appeler Bob

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Tester Elm

Translation

Todo list

3 elements

New

New

Title

Appeler Bob

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Tester Elm

NumberOfElements 3

Translation

Todo list

3 elements

New

Title

New

type StaticText 
    = Title
    | NumberOfElements Int
    | New

Appeler Bob

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NumberOfElements 3

renderEnglish text =
    case text of
        Title ->
            "Todo list"

        NumberOfElements n ->
            toString n ++ " elements"

        New ->
            "New"

renderEnglish text =
    case text of
        Title ->
            "Todo list"

        NumberOfElements n ->
            case n of
                0 ->
                    "You have nothing to do!"

                1 ->
                    "One more thing to do!"

                _ -> --default case
                    toString n ++ " elements"

        New ->
            "New"

renderFrench text =
    case text of
        Title ->
            "À faire !"

        NumberOfElements n ->
            case n of
                0 ->
                    "Tu n'as rien à faire !"

                1 ->
                    "Une seule chose à faire !"

                _ -> --default case
                    toString n ++ " élements"

        New ->
            "Nouveau"

Translation

À faire !

Nouveau

3 élements

Appeler Bob

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Tester Elm

Can I use?

(non-exhaustive)

FULL SUPPORT

ML-family

Haskell, Elm, PureScript, ReasonML, OCaml, ...

Rust

Scala

PARTIAL SUPPORT

TypeScript

Define ADTs: Ok Pattern matching:

... hack it yourself!

EMULATION

All languages!

(not recommended)

DEMAND EXPRESSIVENESS FROM YOUR LANGUAGE!