Properties may be tracked as interval computations are performed.
This was done in section 
, where the domain was tracked.
The framework introduced
to track domains will be generalized to track various properties.
denotes the property of interest.
is a function of the
m-ary function g being checked, the point
at which the function g is being checked at,
and the results of checking the property for g's
arguments.
For a property to fit into this framework,
the results of checking a property directly
must be equivalent to checking a property
recursively. Property is
recursively weakly checkable if
is recursively strongly checkable if
is the union of all the arguments of the 
functions.
Each can be considered a function of .
If is a function of 
then consider the above to be 
, defined as:
and 
are m-ary functions.
The value 
can be unambiguously built up
recursively, using the syntactic definition of g,
since each leaf node is a 0-ary function. For all discussed
properties, 
if g is a non-empty
0-ary function.
This can be verified by careful scrutiny
of the formal definitions.
| Jeff Tupper | March 1996 |