Editing Kleene's recursion theorem (section)

{{Short description|Theorem in computability theory}}
{{distinguish|text=[[Kleene's theorem]] for regular languages}}
{{Use shortened footnotes|date=May 2021}}  
In [[computability theory]],  '''Kleene's recursion theorems''' are a pair of fundamental results about the application of [[computable function]]s to their own descriptions.    The theorems were first proved by [[Stephen Cole Kleene|Stephen Kleene]] in 1938{{r|Kleene1938}} and appear in his 1952 book ''Introduction to Metamathematics''.{{sfn|Kleene|1952}} A related theorem, which constructs fixed points of a computable function, is known as '''Rogers's theorem''' and is due to [[Hartley Rogers, Jr.]]{{sfn|Rogers|1967}}

The recursion theorems can be applied to construct [[fixed point (mathematics)|fixed points]] of certain operations on [[computable function]]s, to generate [[quine (computing)|quines]], and to construct functions defined via [[recursive definition]]s.