Editing Partial function (section)

=== Bottom element ===

In [[denotational semantics]] a partial function is considered as returning the [[bottom element]] when it is undefined.

In [[computer science]] a partial function corresponds to a subroutine that raises an exception or loops forever. The [[IEEE floating point]] standard defines a [[not-a-number]] value which is returned when a floating point operation is undefined and exceptions are suppressed, e.g. when the square root of a negative number is requested.

In a [[programming language]] where function parameters are [[statically typed]], a function may be defined as a partial function because the language's [[type system]] cannot express the exact domain of the function, so the programmer instead gives it the smallest domain which is expressible as a type and contains the domain of definition of the function.