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Existential type

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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]

See also the concept of Smart constructor.

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 keyword
    is used for their notation.
  • Essential Haskell Compiler overview
  • Examples