Editing Expression (mathematics) (section)

===Lambda calculus===
{{Main|Lambda calculus}}

Formal languages allow [[Formal system|formalizing]] the concept of well-formed expressions.

In the 1930s, a new type of expression, the [[Lambda calculus#Definition|lambda expression]], was introduced by [[Alonzo Church]] and [[Stephen Kleene]] for formalizing [[function (mathematics)|function]]s and their evaluation.<ref>{{cite journal|first=Alonzo|last=Church|author-link=Alonzo Church|title=A set of postulates for the foundation of logic|journal=Annals of Mathematics|series=Series 2|volume=33|issue=2|pages=346–366|year=1932|doi=10.2307/1968337|jstor=1968337}}</ref>{{efn|For a full history, see Cardone and Hindley's "History of Lambda-calculus and Combinatory Logic" (2006).}} The lambda operators (lambda abstraction and function application) form the basis for lambda calculus, a formal system used in [[mathematical logic]] and [[programming language theory]].

The equivalence of two lambda expressions is [[decision problem|undecidable]] (but see [[unification (computer science)]]). This is also the case for the expressions representing real numbers, which are built from the integers by using the arithmetical operations, the logarithm and the exponential ([[Richardson's theorem]]).