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A '''supercombinator''' is a [[mathematical]] [[mathematical expression|expression]] which is [[Free variables and bound variables|fully-bound]] and [[self-contained]]. It may either be a [[constant]] or a [[combinator]] where all the [[subexpressions]] are supercombinators.
 
In mathematical terms, a [[lambda expression]] ''S'' is a supercombinator of [[arity]] ''n'' if it has no free variables and is of the form &lambda;x<sub>1</sub>.&lambda;x<sub>2</sub>...&lambda;x<sub>n</sub>.''E'' (with ''n''&nbsp;≥&nbsp;0, so that lambdas are not required) such that ''E'' itself is not a [[lambda abstraction]] and any lambda abstraction in ''E'' is again a supercombinator.
It may be defined, in mathematical terms, as the following:
 
:A supercombinator, ''S'' of arity ''n'' is a [[lambda]] expression of the form
:&lambda;x<sub>1</sub>.&lambda;x<sub>2</sub>...&lambda;x<sub>n</sub>.''E''
:where ''E'' is not a lambda abstraction, such that:
:# ''S'' has no free variables.
:# any lambda abstraction in ''E'' is a supercombinator.
:# ''n'' ≥ 0, so that lambdas are not required.
 
==References==