n. 1. a condition that imposes a constraint on the possible values of a variable, on the domain of definition of an expression, or on the range of arguments of a function. 2. a function defined on a subset of the domain of a given function and taking the same values as the given function for those arguments. The restriction f_E(x) of the function f(x) to the set E is the set of pairs (x, y) such that y = f(x) and x is a member of E; the restriction itself is sometimes written f |E. Compare extension.