Editing Lambda calculus (section)

=== Notation ===
To keep the notation of lambda expressions uncluttered, the following conventions are usually applied:
* Outermost parentheses are dropped: ''M'' ''N'' instead of (''M'' ''N'').
* Applications are assumed to be left associative: ''M'' ''N'' ''P'' may be written instead of ((''M'' ''N'') ''P'').<ref name="lambda-bound">{{cite web|url=http://www.lambda-bound.com/book/lambdacalc/node27.html|title=Example for Rules of Associativity|publisher=Lambda-bound.com|access-date=2012-06-18}}</ref>
* When all variables are single-letter, the space in applications may be omitted: ''MNP'' instead of ''M'' ''N'' ''P''.<ref>{{cite web |title=The Basic Grammar of Lambda Expressions |url=https://softoption.us/node/33 |website=SoftOption |quote=Some other systems use juxtaposition to mean application, so 'ab' means 'a@b'. This is fine except that it requires that variables have length one so that we know that 'ab' is two variables juxtaposed not one variable of length 2. But we want to labels like 'firstVariable' to mean a single variable, so we cannot use this juxtaposition convention.}}</ref>
* The body of an abstraction extends [[Regular expression#Lazy matching|as far right as possible]]: λ''x''.''M N'' means λ''x''.(''M N'') and not (λ''x''.''M'') ''N''.
* A sequence of abstractions is contracted: λ''x''.λ''y''.λ''z''.''N'' is abbreviated as λ''xyz''.''N''.<ref name="Selinger">{{Citation|first1=Peter|last1=Selinger|title=Lecture Notes on the Lambda Calculus|year=2008|page=9|publisher=Department of Mathematics and Statistics, University of Ottawa|url=http://www.mathstat.dal.ca/~selinger/papers/lambdanotes.pdf|bibcode=2008arXiv0804.3434S|volume=0804|arxiv=0804.3434|issue=class: cs.LO}}</ref><ref name="lambda-bound" />