information:extraction, information:filtering
Function expressions

To give an example from mathematics, consider an expression which defines a function

where t is an expression. t may contain some, all or none of the x, …, x and it may contain other variables. In this case we say that function definition binds the variables x, …, x.

In this manner, function definition expressions of the kind shown above can be thought of as the variable binding operator, analogous to the lambda expressions of lambda calculus. Other binding operators, like the summation sign, can be thought of as higher-order functions applying to a function. So, for example, the expression

could be treated as a notation for

where ∑ S f {\displaystyle \sum _{S}{f}} is an operator with two parameters—a one-parameter function, and a set to evaluate that function over. The other operators listed above can be expressed in similar ways; for example, the universal quantifier ∀ x ∈ S P (x) {\displaystyle \forall x\in S\ P(x)} can be thought of as an operator that evaluates to the logical conjunction of the Boolean-valued function P applied over the (possibly infinite) set S.