Editing Lambda calculus (section)

=== Standard terms ===
Certain terms have commonly accepted names:<ref>{{cite web |last1=Ker |first1=Andrew D. |title=Lambda Calculus and Types |url=https://www.cs.ox.ac.uk/andrew.ker/docs/lambdacalculus-lecture-notes-ht2009.pdf#page=18|page=6 |access-date=14 January 2022}}</ref><ref>{{cite book |last1=Dezani-Ciancaglini |first1=Mariangiola |last2=Ghilezan |first2=Silvia |title=Rewriting and Typed Lambda Calculi |chapter=Preciseness of Subtyping on Intersection and Union Types |series=Lecture Notes in Computer Science |date=2014 |volume=8560 |page=196 |doi=10.1007/978-3-319-08918-8_14|hdl=2318/149874 |isbn=978-3-319-08917-1 |chapter-url=http://www.di.unito.it/~dezani/papers/dg14.pdf#page=3 |access-date=14 January 2022}}</ref><ref>{{cite journal |last1=Forster |first1=Yannick |last2=Smolka |first2=Gert |title=Call-by-Value Lambda Calculus as a Model of Computation in Coq |journal=Journal of Automated Reasoning |date=August 2019 |volume=63 |issue=2 |pages=393–413 |doi=10.1007/s10817-018-9484-2 |s2cid=53087112 |url=https://www.ps.uni-saarland.de/Publications/documents/ForsterSmolka_2018_Computability-JAR.pdf#page=4 |access-date=14 January 2022}}</ref>

: {{anchor|I}} {{Mono|1='''I''' := λ''x''.''x''}}
: {{anchor|S}} {{Mono|1='''S''' := λ''x''.λ''y''.λ''z''.''x'' ''z'' (''y'' ''z'')}}
: {{anchor|K}} {{Mono|1='''K''' := λ''x''.λ''y''.''x''}}
: {{anchor|B}} {{Mono|1='''B''' := λ''x''.λ''y''.λ''z''.''x'' (''y'' ''z'')}}
: {{anchor|C}} {{Mono|1='''C''' := λ''x''.λ''y''.λ''z''.''x'' ''z'' ''y''}}
: {{anchor|W}} {{Mono|1='''W''' := λ''x''.λ''y''.''x'' ''y'' ''y''}}
: {{anchor|omega}} {{Mono|1='''ω''' or '''Δ''' or '''U''' := λ''x''.''x'' ''x''}}
: {{anchor|Omega}} {{Mono|1='''Ω''' := '''ω ω'''}}

{{Mono|'''I'''}} is the identity function. {{Mono|'''SK'''}} and {{Mono|'''BCKW'''}} form complete [[combinator calculus]] systems that can express any lambda term - see 
[[#Abstraction elimination|the next section]]. {{Mono|'''Ω'''}} is {{Mono|'''UU'''}}, the smallest term that has no normal form. {{Mono|'''YI'''}} is another such term.
{{Mono|'''Y'''}} is standard and defined [[#Y|above]], and can also be defined as {{Mono|'''Y'''{{=}}'''BU(CBU)'''}}, so that {{Mono|'''Y'''g{{=}}g('''Y'''g)}}. {{Mono|TRUE}} and {{Mono|FALSE}} defined [[#Logic and predicates|above]] are commonly abbreviated as {{Mono|'''T'''}} and {{Mono|'''F'''}}.