Implementing "there exists" processing

The processing patterns we've been looking at can all be summarized with the universal quantifier, , meaning for all. It's been an implicit part of all of the processing definitions:

• Map: For all items in the source, , apply the map function, . We can change notation to have an explicit use of the universal quantifier: .
• Filter: For all items in the source, pass those for which the filter function is true. Here, also, we've used the universal quantifier to make this explicit: .
• Reduce: For all items in the source, use the given operator and base value to compute a summary. The universal quantification is implicit in the definition of operators like .

There are also cases where we are only interested in locating a single item. We often describe these cases as a search to show there exists at least one item where a condition is true. This can be called the existential quantifier, ,...