Is the failure of the 2nd Transpose here a known bug?

Dataset[{{0, 10}, {2, 11}, {3, 12}}][
 Transpose /* Map[MinMax] /* Transpose] // Normal 
Failure[Transpose, {"MessageTemplate" :> Transpose::nmtx, 
  "MessageParameters" -> {{__}, Transpose}}]

Similarly for

Dataset[{{0, 10}, {2, 11}, {3, 12}}][
 Query[Transpose /* Map[MinMax]] /* Transpose]

For both of these, without the Normal, the error msg is: "The first two levels of {__} cannot be transposed".

Yet the seeming equivalent query, albeit with an intermediate Dataset, works:

Dataset[{{0, 10}, {2, 11}, {3, 12}}][Transpose /* Map[MinMax] ][
  Transpose]// Normal

And without Dataset, this works also:

{{0, 10}, {2, 11}, {3, 12}} // Transpose // Map[MinMax] // Transpose

{{0, 10}, {3, 12}}


2 Answers 2


The problem is due to two factors:

  1. The type system cannot infer the data type that results from a call to MinMax.
  2. A type-checked application of the Transpose query operator will fail when applied to an argument with an unknown type (i.e. from MinMax).

I think that point #1 could be considered a bug, although the fact of the matter is that a great many operators are not (yet) known to the type system. Given these omissions, it might be reasonable to expect the Transpose operator to be more forgiving.

Analysis (current as of version 11.0.1)

When an operation succeeds outside of a Dataset but fails within, the cause is usually a type-inferencing failure. That is indeed the case here.

traceTypes will reveal the failure:

traceTypes[Dataset[{{0, 10}, {2, 11}, {3, 12}}]][Transpose /* Map[MinMax] /* Transpose]

traceTypes screenshot

We can see that the type machinery cannot infer the resultant type of applying MinMax to a list of integers:

TypeApply[MinMax, {Vector[Atom[Integer], 3]}]
(* UnknownType *)

Furthermore, a type-checked application of AssociationTranspose (the query-form of Transpose) will not accept a vector of unknown type:

TypeApply[AssociationTranspose, {Vector[UnknownType, 2]}]
(* FailureType[{Transpose, "nmtx"}, <|"Arguments" -> {__}|>] *)

This last failure is the source of the message we see.


As noted in the question, a work-around is to perform the final Transpose in a second query:

Dataset[{{0, 10}, {2, 11}, {3, 12}}][Transpose /* Map[MinMax]][Transpose]

double-query dataset screenshot

When the final query result is wrapped back into a dataset, type deduction takes place which is more reliable than type inferencing. By splitting our query in two, we allow such type deduction to take place so that the final Transpose operator can be applied to a known type:

Dataset[{{0, 10}, {2, 11}, {3, 12}}][Transpose /* Map[MinMax]] // GetType
(* Vector[Vector[Atom[Integer], 2], 2] *)

TypeApply[AssociationTranspose, {Vector[Vector[Atom[Integer], 2], 2]}]
(* Vector[Vector[Atom[Integer], 2], 2] *)
  • $\begingroup$ How come this is not an issue outside of Dataset? Is the type inference complexity worth it to basically give hints for formatting (and often the results are inconsistent anyway)? $\endgroup$ Feb 7, 2017 at 20:51
  • $\begingroup$ The type system is only invoked within Dataset. In v10.1, I noted that type information is used mainly for visualization and "sanity checking". The situation seems largely unchanged in v11.0.1. It would be nice if we could turn off the type-inferencing (and the sometimes flaky sanity checking) but retain the type-deduction (for visualization). It will be interesting to see what happens to the type system after the next-generation compiler is released. $\endgroup$
    – WReach
    Feb 7, 2017 at 22:24

If we change the last Transpose into a f,it will return a uncalculate structure

Dataset[{{0, 10}, {2, 11}, {3, 12}}][Transpose /* Map[MinMax] /* f]

f[{{0, 3}, {10, 12}}]

But the Transpose doesn't work here,so I tend to consider it as a bug about Dataset operate

And the following operation is right in current rule

Dataset[{{0, 10}, {2, 11}, {3, 12}}][Transpose /* Map[MinMax], All]



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