9.7 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, S, apply the map function, m(x). We can use the universal quantifier: ∀_x∈Sm(x).

• Filter: This, also, means for all items in the source, S, pass those for which the filter function, f(x), is true. Here, also, we can use the universal quantifier: ∀_x∈Sx if f(x).

• 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 ∑ _x∈Sx and ∏ _x∈Sx.

Contrast these universal functions with the cases where we are only interested in locating a single item. We often describe these cases as...