Editing Subtyping (section)

== Origins ==
The notion of subtyping in programming languages dates back to the 1960s; it was introduced in [[Simula]] derivatives. The first formal treatments of subtyping were given by [[John C. Reynolds]] in 1980 who used [[category theory]] to formalize [[implicit conversion]]s, and [[Luca Cardelli]] (1985).<ref>Pierce, ch. 15 notes</ref>

The concept of subtyping has gained visibility (and synonymy with polymorphism in some circles) with the mainstream adoption of object-oriented programming. In this context, the principle of safe substitution is often called the [[Liskov substitution principle]], after [[Barbara Liskov]] who popularized it in a [[keynote]] address at a conference on object-oriented programming in 1987. Because it must consider mutable objects, the ideal notion of subtyping defined by Liskov and [[Jeannette Wing]], called [[behavioral subtyping]] is considerably stronger than what can be implemented in a [[type checker]]. (See {{section link||Function types}} below for details.)