Editing Denotational semantics (section)

===Denotations of data types===
Many programming languages allow users to define [[recursive data type]]s. For example, the type of lists of numbers can be specified by
<syntaxhighlight lang=sml>datatype list = Cons of nat * list | Empty</syntaxhighlight>
This section deals only with functional data structures that cannot change.  Conventional imperative programming languages would typically allow the elements of such a recursive list to be changed.

For another example: the type of denotations of the [[untyped lambda calculus]] is
<syntaxhighlight lang=sml>datatype D = D of (D → D)</syntaxhighlight>
The problem of ''solving domain equations'' is concerned with finding domains that model these kinds of datatypes. One approach, roughly speaking, is to consider the collection of all domains as a domain itself, and then solve the recursive definition there.

[[Polymorphism (computer science)|Polymorphic data types]] are data types that are defined with a parameter. For example, the type of α {{code|list}}s is defined by
<syntaxhighlight lang=sml>datatype α list = Cons of α * α list | Empty</syntaxhighlight>
Lists of natural numbers, then, are of type {{code|nat list}}, while lists of strings are of {{code|string list}}.

Some researchers have developed domain theoretic models of polymorphism. Other researchers have also modeled [[parametric polymorphism]] within constructive set theories.

A recent research area has involved denotational semantics for object and class based programming languages.<ref>{{cite journal |first1=Bernhard |last1=Reus |first2=Thomas |last2=Streicher |title=Semantics and logic of object calculi |journal=Theor. Comput. Sci. |volume=316|issue=1 |pages=191–213 |year=2004 |doi=10.1016/j.tcs.2004.01.030 |doi-access=free }}</ref>