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
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|