Come il concetto di funzione viene introtto nel Bell & Machover (uno dei manuali standard di logica, North-Holland, 1977).

A function (map, mapping) is a class F of ordered pairs such that, whenever (x,y)∈F and (x,z)∈F we have y=z.
The domain of F is the class {x: for some y, (x,y)∈F} and the image of F is the class {y: for some x, (x,y)∈F}.