-- Shakespeare, The Tempest
Act II, Scene I, Line 207
Zip can be thought of as the more generic form of Map. Think of Zip as applying a function against each member of the collections given to it, thus mapping more than one collection to another collection. It is a lot easier to see than to explain in words.
I believe Zip2 would get the following definition:
zip2 :: (α → β → γ) → ([α] → [β] → [γ])
zip2 f = fold (λx y xs ys → f x y : xs ys) [ ]
This would be if we limit Zip to being used on 2 collections (this is mine definition, Dr. Graham Hutton has nothing to do with this definition, blame me if it is wrong).
Folding a Zip we'll need a collection to seed with then we just apply the given function against each member from each collection concatenating it with the seed, just as we did with Map.
Next we'll look at a simple example adding the members of two collections together.
First Memoize has nothing and X has 1 while Y has 10 giving the result of 11.
Next Memoize has 11 and X has 2 while Y has 20 giving the result of 11, 22.
Lets see some code examples.
With Clojure we do not have to worry about the number of collection we'll give our Zip function since we can use destructing to say and everything else. We can then apply map to create a vector containing all the elements next to each other, we'll see this is common in the other languages since the implementation of reduce is only design to work with a single collection. From here it is just like Map except that we need to use apply since are members are a collection themselves.
With C# we have to specify the number of collection we are going to Zip, in this case we'll do two. We need to Zip the members from the two collections together into a Tuple (which is a bit of cheating but I can find no other way to do it with LINQ). From there it is just like Map. With this implementation we do have a limitation in that the two collections must be the same size, since to get around that would be a bit of work and we rather have a readable implementation than perfect code.
There you have it showing once again that all you need is Zip.