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A simple interval arithmetic which handles
partial functions gracefully is
:
This is not an utter abuse of notation, as
for any : every member
of may be described as a member of .
Furthermore, any non-trivial warrants the full descriptive power of .
A trivial may be simulated by appropriately constructing
models.
Consider the square root operator, denoted here as g.
It is a unary partial function, undefined for negative arguments.
Consider using : is
undefined if j contains only negative numbers. Consider the
following examples:
This illustrates one approach implementations may take when
confronted with partial functions.
Another approach is shown in the next section.
Another pair of examples follow:
Next: 2.12 Property Tracking
Up: 2.11 Interval Function Domains
Previous: 2.11.4 Conjunctions