MapAt and generic Functions on Associations and Datasets

These are distinct but related questions about mapping functions to Associations and Datasets. Given:

assoc = <| a -> 1, b -> 2, c -> 3|>


And

data =
Dataset@{<| a -> 1, b -> 2, c -> 3|> , <|a -> 4, b -> 5, c -> 6|>}


Re MapAt:

MapAt[Framed, Key[b]][assoc]


Although Dataset is not explicitly mentioned in the doc page for MapAt, it's supposed to apply to generic expressions. However:

MapAt[Framed, Key[b]][data]


Next, consider mapping over a named Key with this syntax:

data[All, {Key[b] -> Framed}] // Normal


Why don't the following variations work on Dataset?

data[All, Key[b] -> Framed] // Normal


data[All, Key[b] -> Framed[#] &] // Normal


Finally, back to Association:

assoc[Key[b] -> Framed] // Normal


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That MapAt[Framed, Key[b]][data] doesn't work is a bug, which I'll fix (thanks!).

On the other hand, data[All, Key[b] -> Framed] is not a supported syntax for doing applying a function to a specific part. You have to have the enclosing list.

As for data[All, Key[b] -> Framed[#] &], the second query element there is a pure function. Pure functions get applied to the corresponding part of the Dataset, so the behavior you see is absolutely correct (and of course, useless).

In assoc[Key[b] -> Framed], you're doing a key-lookup on an association via function application. In particular you're looking up the key Key[b] -> Framed, which doesn't exist in the association. Hence you get Missing.

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Re "the second query element there is a pure function", how can generic functions with multiple arguments be passed, eg StringDrop[#,-1]&? - Of course can pass a predefined curried version but that's lame. – alancalvitti Jul 12 '14 at 13:52
@alancalvitti I think you are having a precedence problem. Is this what you want? data[All, {Key[b] -> (Framed[#] &)}] // Normal – Rojo Jul 12 '14 at 23:40
@alancalvitti I don't understand. StringDrop[#,-1]& is a pure function with a single argument. – Taliesin Beynon Jul 13 '14 at 0:25
@Rojo, thank you, that works. This precedence constraint isn't obvious to me, yet doesn't seem to be documented. – alancalvitti Jul 14 '14 at 18:37
@TaliesinBeynon, I mean that unlike Framed, which is a single argument function and can be passed as both Framed and Framed[#]&, how would you pass 2 argumen functions like StringDrop? However, Rojo simply parenthesized the pure function (of any # of arguments). Why isn't that documented? – alancalvitti Jul 14 '14 at 18:41