Editing Standard ML (section)

===Algebraic datatypes===
Standard ML provides strong support for [[algebraic datatype]]s (ADT). A [[data type]] can be thought of as a [[disjoint union]] of tuples (or a "sum of products"). They are easy to define and easy to use, largely because of [[pattern matching]], and most Standard ML implementations' [[Partial function|pattern-exhaustiveness]] checking and pattern redundancy checking.

In [[object-oriented programming]] languages, a disjoint union can be expressed as [[Class (computer programming)|class]] hierarchies. However, in contrast to [[Class hierarchy|class hierarchies]], ADTs are [[Closed-world assumption|closed]]. Thus, the extensibility of ADTs is orthogonal to the extensibility of class hierarchies. Class hierarchies can be extended with new subclasses which implement the same interface, while the functions of ADTs can be extended for the fixed set of constructors. See [[expression problem]].

A datatype is defined with the keyword {{code|lang=sml|datatype}}, as in:

<syntaxhighlight lang="sml">
datatype shape
    = Circle   of loc * real      (* center and radius *)
    | Square   of loc * real      (* upper-left corner and side length; axis-aligned *)
    | Triangle of loc * loc * loc (* corners *)
</syntaxhighlight>

Note that a type synonym cannot be recursive; datatypes are necessary to define recursive constructors. (This is not at issue in this example.)