partial function

The key idea is to consider a command as a partial function on some domain of states.

Say that 26 cannot be divided by 11; division becomes a partial function.

A heap is a partial function mapping memory addresses to values.

Having done so, then I must also accept that there is at least partial function of the optic nerves.

Note, however, that currying, while similar, is not the same operation as partial function application.

"The sensors reported at least partial function in several systems," Dax replied.

The set of all partial functions on a set, ordered by restriction.

A tuple is a partial function from attribute names to atomic values.

Finally, a partial function can be used by itself, and the result of calling it is equivalent to doing a match over it.

With the definition of a function as an ordered triple this would always be considered a partial function.

A general Turing machine will compute a partial function.

Partial functions are also used in the exception-handling portion of a statement:

Hence f is only a partial function from the real line to the real line.

A uniquely defined relation is a partial function.

Type families are a feature of some type systems that allow partial functions between types to be defined by pattern matching.

If a partial function is both upper and lower semicomputable it is called computable.

Partial functions and subsorting are also supported.

Currying and partial function application are often conflated.

Note that the result of partial function application in this case is a function that takes two arguments.

The use of the prefix "total" is to suggest that it is a special case of a partial function.

(Note that the single parameter of the partial function is never explicitly declared or named.)

For example, programs (or program phrases) might be represented by partial functions or by games between the environment and the system.

A partial function is defined for some natural numbers but not all-the specification of "some" has to come "up front".

There are two distinct meanings in current mathematical usage for the notion of the domain of a partial function.

In computer science a partial function corresponds to a subroutine that raises an exception or loops forever.