# Existential type

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Revision as of 18:58, 2 May 2006 by EndreyMark (Talk | contribs)

## Contents |

## 1 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).

## 2 Generalised algebraic datatype

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

## 3 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 ) may be confusing. In Essential Haskell, existential types can occur not only in data declarations, and a separate keywordforallis used for their notation.exists
- Essential Haskell Compiler overview
- Examples

## 4 Trac

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