at least one processor for executing the steps of:

mapping a base column x to an existing index on a column y that is correlated with column x through a piecewise monotonic function F(x);

rewriting an index construction statement to force the existing index on column y to track a piecewise monotonic property by assigning identical values of F(x) to different periods to different ranges to create an annotated index;

rewriting range queries over the annotated index on F(x) by modifying a derived predicate,

constructing said existing index;

wherein said constructing said existing index comprises:

recognizing said piecewise monotonic function and a periodicity of said piecewise monotonic function; and

building an index over the monotonic function,

wherein said recognizing said piecewise monotonic function is accomplished from explicit user input, recognizing semantically that a function is known to be a piecewise monotonic function and verifying a relationship between values of the base column x and an a derived column, and

wherein during said building an index over the monotonic function if a derived column is known to be a monotonic function by observation, at each of a plurality of updates a relationship should be verified.