Supercombinator
Encyclopedia
A supercombinator is a mathematical expression which is 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 λx1.λx2...λxn.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.
Free variables and bound variables
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation that specifies places in an expression where substitution may take place...
and self-contained. It may either be a constant or a combinator where all the subexpressions are supercombinators.
In mathematical terms, a lambda expression
Lambda expression
Lambda expression may refer to:*Anonymous function*Lambda calculus#Definition...
S is a supercombinator of arity
Arity
In logic, mathematics, and computer science, the arity of a function or operation is the number of arguments or operands that the function takes. The arity of a relation is the dimension of the domain in the corresponding Cartesian product...
n if it has no free variables and is of the form λx1.λx2...λxn.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.