What does it mean for a table to be a flipped dictionary?

Short answer:

A table is a reference to a (column) dictionary.

---

The internal representation of a table is nearly identical to that of a dictionary. We can use the flip command to create a table from a dictionary:

q)t: ([] a: 1 2 3; b: 4 5 6; c: 7 8 9)
q)d: `a`b`c ! (1 2 3; 4 5 6; 7 8 9)
q)t ~ flip d
1b
q)

In fact, when a dictionary is flip‘ed, the underlying core data structure remains untouched. The table itself is a simple, small object that refers to the original dictionary. Using .Q.w, we can measure how much more memory a table takes than the corresponding dictionary:

q).Q.w[]`used         // memory usage baseline
112992j
q)x:`a`b`c!3 3#til 9  // create a small dictionary
q).Q.w[]`used
113424j
q)x:flip x
q).Q.w[]`used         // memory usage delta is
113456j               // just 32 more bytes
q)

No matter how large the underlying dictionary is, creating a table is fast and still takes only 32 bytes:

q)x:`a`b`c!3 100000#til 10
q).Q.w[]`used
1686192j
q)x:flip x
q).Q.w[]`used
1686224j          // 32 = 1686224 - 1686192
q)

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Now, Let’s examine how a keyed table is related to a dictionary. We start by creating a simple keyed table:

q)t: ([] a: 1 2 3; b: 4 5 6; c: 7 8 9)
q)keyedTable: `a`b xkey t
q)keyedTable
a b| c
---| -
1 4| 7
2 5| 8
3 6| 9
q)keys keyedTable
`a`b
q)

Since keyedTable is a table, one might expect it to have the same type as t but instead, q presents the following surprise:

q)type t
98h                  // type table as expected
q)type keyedTable
99h                  // *NOT* 98h
q)

Type 99h is the type number for dictionaries. If keyedTable really is a dictionary, we should be able to extract its key and value:

q)key keyedTable
a b
---
1 4
2 5
3 6
q)value keyedTable
c
-
7
8
9
q)

Indeed, keyedTable is a dictionary – one that holds unkeyed tables for both its key and its value:

q)type key keyedTable
98h
q)type value keyedTable
98h
q)

This suggests that we can create a keyed table by using the ! (dict) operator with two unkeyed tables:

q)(key keyedTable)!(value keyedTable)
a b| c
---| -
1 4| 7
2 5| 8
3 6| 9
q)

Lastly, joining the two flipped tables brings us back to the original dict.

q)(flip key keyedTable),(flip value keyedTable)
a| 1 2 3
b| 4 5 6
c| 7 8 9
q)

For more information, see Creating dictionaries and tables from C and , (join).