Over the years I've found that these transposition problems are a huge drag on programs, and once you recognize them you start seeing them all over the place. They make simple and obvious relational tasks into dozens of lines of nested data structure traversal and manipulation.
The notion of transposition comes from the array programming world, where a multi-dimensional array/tensor can be seen as a tree structure, whose levels may be easily reordered by transposition. I sometimes use numpy arrays for general-purpose programming; it can be very powerful with a well-chosen representation. Unfortunately array concepts basically require the data to be rectangular -- `x[i]` has the same shape as `x[j]` -- which can be hard to adapt to general problems.
My dream then is a general-purpose data structure that takes the best of both the relational and array-programming worlds: the freedom and flatness of relational tables, enriched with tacit ideas like broadcasting that make array programming so ergonomic.