# Existential type

From HaskellWiki

## Contents

## Dynamic dispatch mechanism of OOP

**Existential types** in conjunction with type classes can be used to emulate the dynamic dispatch mechanism of object oriented programming languages. To illustrate this concept I show how a classic example from object oriented programming can be encoded in Haskell.

```
class Shape_ a where
perimeter :: a -> Double
area :: a -> Double
data Shape = forall a. Shape_ a => Shape a
type Radius = Double
type Side = Double
data Circle = Circle Radius
data Rectangle = Rectangle Side Side
data Square = Square Side
instance Shape_ Circle where
perimeter (Circle r) = 2 * pi * r
area (Circle r) = pi * r * r
instance Shape_ Rectangle where
perimeter (Rectangle x y) = 2*(x + y)
area (Rectangle x y) = x * y
instance Shape_ Square where
perimeter (Square s) = 4*s
area (Square s) = s*s
instance Shape_ Shape where
perimeter (Shape shape) = perimeter shape
area (Shape shape) = area shape
--
-- Smart constructor
--
circle :: Radius -> Shape
circle r = Shape (Circle r)
rectangle :: Side -> Side -> Shape
rectangle x y = Shape (Rectangle x y)
square :: Side -> Shape
square s = Shape (Square s)
shapes :: [Shape]
shapes = [circle 2.4, rectangle 3.1 4.4, square 2.1]
```

(You may see other Smart constructors for other purposes).

## Generalised algebraic datatype

The type of the `parse`

function for this GADT is a good example to illustrate the concept of existential type.

## Examples from the Essential Haskell Compiler project

See the documentation on EHC, each paper at the *Version 4* part:

- Chapter 8 (EH4) of Atze Dijksta's Essential Haskell PhD thesis (most recent version). A detailed explanation. It explains also that existential types can be expressed in Haskell, but their use is restricted to data declarations, and the notation (using keyword
`forall`

) may be confusing. In Essential Haskell, existential types can occur not only in data declarations, and a separate keyword`exists`

is used for their notation. - Essential Haskell Compiler overview
- Examples

## Trac

Existential Quantification is a detailed material on the topic. It has link also to the smaller Existential Quantifier page.