Vectorization
Any list can be turned into a vector by using the . operator. A vector is just a list, but it prefers to apply operands to its elements instead of the list as a whole.
"abc","123" len
"abc","123". len
2
3 3
Automatic vectorization can occur to fit the type specification of an operator. For example, the type of + is Int Int -> Int and so if you give it a list for any of the arguments, their rank is too high and so it vectorizes said argument to bring it down. It is essentially performing a map.
1,2,3.+4 p
1,2,3+4 p
<5,6,7>
<5,6,7>
Note that the type is a vector not a list, even though 1,2,3 is a list, it was first vectorized. You can convert a vector back to a list using %. But usually this isn't needed because unvectorization is also automatically done if an arguments rank is too low.
1,2,3+4% len
1,2,3+4 len
3
3
If two vectors are present it pairs them off an performs the operation on each pair. It is essentially performing a zipWith
(1,2,3) + (2,4,6)
3 6 9
Longer lists are truncated to that of the smaller (this isn't the case for all vectorized languages, but useful in Atlas since we frequently use infinite lists).
(1,2) + (2,4,6)
3 6
Automatic vectorization can work on non scalar arguments as well.
"1 2 3","4 5" read p
<[1,2,3],[4,5]>
Read expects a string, but was given a list of strings so it vectorizes. Read returns a list of ints always, so that part is just normal operation.
It can even work on more complicated types like the type of append ([a] [a] -> [a]).
"abc","xyz" append "123" p
<"abc123","xyz123">
Automatic Vectorization can only lower rank, sometimes it needs to be raised. For example transpose works on 2D lists, but if you give it a 1D list it needs to become a 2D list first, by just making it a list with a single element (the original list). I call this promotion.
"123" \ p
["1","2","3"]
Automatic promotion and vectorization can both be done implicitly together. For example:
'a take (1,0) p
<"a","">
The (1,0) is vectorized and the 'a is promoted to a string.
Unvectorization is preferred to promotion. That is why the earlier example 1,2,3+4 len returned 3 instead of [1,1,1].
There is one exception to these rules which is for , and this is to enable intuitive list construction from data. This is how "abc","123","xyz" creates a list of strings. Without preferring promotion over vectorization of the first arg, , would need to be type a a -> [a] to get the first use to work and type [a] a -> [a] to get the second op to work as well. , just prefers to promote once rather than automatically vectorize the first arg, you can still vectorize that arg, you will just need to do so explicitly.