It is a common programming pattern for the result of an invocation of map to be used immediately as an argument to filter. For instance, if we had a list ls of pairs of integers and wanted to draw up a list of their cdrs, but only the negative ones, we could write

However, implementing this pattern as shown, with explicit calls to filter and map, can be rather inefficient. The map procedure has to build up the entire list of cdrs even if only a few of them are negative, and filter has to build up its result list all over again. The whole process would be faster if filter and map were combined into a single procedure that could build up the result list just once, by deciding whether to include each of the results of the mapped procedure as soon as it is generated.

Define a filtermap procedure that implements this more efficient strategy. It should receive a unary predicate, a single-valued procedure, and one or more lists, with the arity of the procedure matching the number of lists. It should apply the procedure to corresponding elements of the lists, just as map does, but should then apply the unary predicate to each result of that application, returning a list of those that satisfy the predicate.