**Linearity and distribution:**

A function is additive or multiplicative if the use of addition or multiplication in the function can be distributed out into separate calls. A function is outative if constants can be distributed out, and a function is an oddfun if its sign can be distributed out. Finally, a function is linear if it is both additive and outative.

**Input properties:**

The operator properties commutative, symmetric, antisymmetric, evenfun, nary, lassociative, and rassociative describe the input properties of a function.