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 λx<sub>1</sub>.λx<sub>2</sub>...λx<sub>n</sub>.''E'' (with ''n'' ≥ 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