# BasicOperatorFunctions1 A¶

- A: SetCategory

This package exports functions to set some commonly used properties of operators, including properties which contain functions.

- constantOperator: A -> BasicOperator
`constantOperator(a)`

returns a nullary operator op such that`op()`

always evaluate to`a`

.

- constantOpIfCan: BasicOperator -> Union(A, failed)
`constantOpIfCan(op)`

returns`a`

if`op`

is the constant nullary operator always returning`a`

, “failed” otherwise.

- derivative: (BasicOperator, A -> A) -> BasicOperator
`derivative(op, foo)`

attaches foo as the “%diff” property of`op`

. If`op`

has an “%diff” property`f`

, then applying a derivation`D`

to`op`

(a) returns`f(a) * D(a)`

. Argument`op`

must be unary.

- derivative: (BasicOperator, List List A -> A) -> BasicOperator
`derivative(op, [foo1, ..., foon])`

attaches [`foo1`

, …, foon] as the “%diff” property of`op`

. If`op`

has an “%diff” property`[f1, ..., fn]`

then applying a derivation`D`

to`op(a1, ..., an)`

returns`f1(a1, ..., an) * D(a1) + ... + fn(a1, ..., an) * D(an)`

.

- derivative: BasicOperator -> Union(List List A -> A, failed)
`derivative(op)`

returns the value of the “%diff” property of`op`

if it has one, and “failed” otherwise.

- evaluate: (BasicOperator, A -> A) -> BasicOperator
`evaluate(op, foo)`

attaches foo as the “%eval” property of`op`

. If`op`

has an “%eval” property`f`

, then applying`op`

to a returns the result of`f(a)`

. Argument`op`

must be unary.

- evaluate: (BasicOperator, List A -> A) -> BasicOperator
`evaluate(op, foo)`

attaches foo as the “%eval” property of`op`

. If`op`

has an “%eval” property`f`

, then applying`op`

to`(a1, ..., an)`

returns the result of`f(a1, ..., an)`

.

- evaluate: (BasicOperator, List A) -> Union(A, failed)
`evaluate(op, [a1,...,an])`

checks if`op`

has an “%eval” property`f`

. If it has, then`f(a1, ..., an)`

is returned, and “failed” otherwise.

- evaluate: BasicOperator -> Union(List A -> A, failed)
`evaluate(op)`

returns the value of the “%eval” property of`op`

if it has one, and “failed” otherwise.