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A type for the construction of terms

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Algebraic data types are typically supported by functional programming languages. For instance, Language:Haskell, Language:Scala, and Language:SML support algebraic data types. Illustrations are given here for Language:Haskell.

A data type for shapes can be defined as follows:

data Shape = Circle Float
           | Rectangle Float Float

The data contructor Circle serves for the representation of circles; the one and only constructor component serves for the radius. The data constructor Rectangle serves for the representation of rectangles; the two constructor components serve for width and height.

Constructors can be used as functions to construct terms:

myCircle :: Shape
myCircle = Circle 42

myRectangle :: Shape
myRectangle = Rectangle 77 88

In fact, constructors are functions with the types of the constructor components as argument types and the type of algebraic data type as the result type:

> :t Circle
Circle :: Float -> Shape
> :t Rectangle 
Rectangle :: Float -> Float -> Shape

Pattern matching can be applied to terms of algebraic data types:

-- Test whether the shape is a circle
isCircle (Circle _) = True
isCircle (Rectangle _ _) = False

See Contribution:haskellData for a simple implementation of the @system which makes systematic use of algebraic data types]].

All predefined, compound types of Haskell are essentially algebraic data types. For instance, Haskell's Booleans could be defined by an algebraic data type with two data constructors as follows:

data Bool = True | False

Haskell's lists could be defined by an algebraic data type with two construtors as follows:

data List a = Nil | Cons a (List a)

The constructors Nil and Cons are meant to correspond to the empty list and ":" of Haskell's built-in lists. The Nil constructor has no constructor component, whereas the Cons constructor has two constructor components.

See also Maybe types for yet another illustration of algebraic data types.

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