IDLE currently completes global names, attributes after ., and filename segments after / or \ within a string.  In the later two cases, a box will pop up automatically after a user selected time after typing . or /\ and nothing thereafter.  The filename segments are not quoted in the list box.

These completions work within subscripts.
d[a<tab or wait> pops up global name completion box
d['/<tab or wait> pops up filename completion box

Raymond proposes that IDLE complete 'dictionary [string] keys'.  To properly code and test, we need a more complete specification.  For instance, "a string key box should open after an opening quote that follows '[' that follows a dict expression".  Any opening quote should work, just as for filename completion.

This is similar "a calltip opens after a '(' that follows a callable expresssion".  For calltips, the expression cannot contain a function call, because calls can take an indeterminant amount of time.  If "expression.find('(') != -1", the calltip is aborted and the same should be true here.  Also, calltips.get_entity(expression) should be reused to get the dict object.  (test_calltips should but does not test that 'f()(' is ignored and get_entity not called.  The same should be true for "f()['".)

Nice (?) but not necessary: delayed auto-popup after typing "d[<open quote>".  This seems that it would be more difficult than the current auto popups.  And see the following.

This proposal conflicts with filename completion for subscripts.  When one is accessing an existing value, one would want key completion.  If one is assigning a value to a new filename key, one would want filename completion.  The simplest solution I can think of is to not auto pop up key completion but to require <tab> before typing (/\) and waiting.

Lastly, should the string keys be quoted in the box?
| long key  |
| short key |
or
|'long key' |
|'short key'|
?

Selecting key objects by their representation is tempting, but it is conceptually different from completing names.  Objects may have one canonical representation, but many possible representations.  So clicking on a list  (which currently does not work) or using movement keys is more sensible than typing chars that have to match one of many possibilities.  String keys would have to be quoted.

So I would only consider this as a separate issue, depending on a fix for clicks.  It should only be accessed by <tab> immediately after '[', and I might want to disable selection by character matching.

Even then, I would be dubious.  I grepped idlelib for "\w\[".  A majority of subscripts are names, handled by current name completion or not (if the names are local, which they often are).  The rest are either list indexes and slices involving literal ints or string keys, which this proposal would handle for accessible dicts.  I am pretty sure there are no keys other than names and strings.

But the sparsity of use cases is my problem even with this proposal. Calltips are useful because there are many globally accessible callables, including builtins and imports.  But other than class __dicts__, there are few globally accessible dicts, except perhaps in toy beginner code.  Raymond, have I missed something?

The idlelib grep had 763 hits and I believe more that half are for dicts.  But they may all be locals or self attributes.  I would love to be able, for instance, to type "local_dict['<tab>" and fill in 'background', but that will not work.