Dataset type system fail with composite keys and Infinity

Question

In 11.1, a Dataset consisting of an Association with composite keys with an Infinity causes failure in keying-in:

as = {{-\[Infinity], 0}, {0, 1}, {1, 2}, {3, \[Infinity]}} -> 
   Table[<|"a" -> RandomReal[]|>, {4}] // AssociationThread 

This works:

as // Key[{0, 1}]

<|"a" -> 0.701279|>

But not in Dataset:

Dataset[as][ Key[{0, 1}]]

Failure[[WarningSign] Message: Key Key[{0, 1}] is not one of {1, 2, 3, 4}.Tag: Dataset]

Yet pre-filtering out at least one Key containing an Infinity works, eg 1st infinity out:

Dataset[as // Query[(;; 3)]][ Key[{0, 1}]]

<|"a" -> 0.701279|> (* when Normal'd *)

Similarly:

Dataset[as // Query[(2 ;;)]][ Key[{0, 1}]]

<|"a" -> 0.701279|>

Yet filtering out as a Dataset query again fails:

Dataset[as][2 ;;][Key[{0, 1}]]

Failure[[WarningSign] Message: Key Key[{0, 1}] is not one of {}. Tag: Dataset]

Further showing the kludge nature of Dataset's type system, if the keys are Quantities:

asq = ({{-\[Infinity], 0}, {0, 1}, {1, 2}, {3, \[Infinity]}} // 
     Map[Quantity[#, "Days"] &]) -> 
   Table[<|"a" -> RandomReal[]|>, {4}] // AssociationThread 

<|{-[Infinity]days,0days}-><|a->0.777112|>,{0days,1day}-><|a->0.715397|>,{1day,2days}-><|a->0.5147|>,{3days,[Infinity]days}-><|a->0.635806|>|>

It works:

Dataset[asq][Key[{Quantity[0, "Days"], Quantity[1, "Days"]}]]

<|"a" -> 0.715397|>

Anyone have similar experiences with composite keys failing?

Answer 1

As noted in a comment by @chuy, this problem is not directly related to the use of Infinity. The problem is essentially the same as that reported in (140541): there is a type-inferencing failure when attempting to type-check a part reference. See that question for more discussion on this point.

Analysis (current as of version 11.1.0)

We can reproduce the problem like this:

Dataset[<|{"a", 0} -> 1, {"b", 0} -> 2|>][Key[{"a", 0}]]
(* Failure - Key[{a, 0}] is not one of {1, 2}. *)

As usual, the operation works if we bypass the type system:

<|{"a", 0} -> 1, {"b", 0} -> 2|> // Query[Key[{"a", 0"}]]
(* 1 *)

We can pinpoint the type inferencing failure:

Needs["Dataset`"]
Needs["TypeSystem`"]

Dataset[<|{"a", 0} -> 1, {"b", 0} -> 2|>] // GetType
(* Assoc[Vector[AnyType, 2], Atom[Integer], 2] *)

Query[Key[{"a", 0}]] // Normal
(* GeneralUtilities`Slice[Key[{"a", 0}]] *)

TypeApply[
  GeneralUtilities`Slice[Key[{"a",0}]]
, {Assoc[Vector[AnyType,2],Atom[Integer],2]}
]
(* FailureType[{Part, "Mismatch"}
   , <|"Type" -> Assoc[Vector[AnyType, 2], Atom[Integer], 2], "Part" -> Key[{"a", 0}]|>]
*)

If we look at relevant parts of the trace, we can see that the ultimate failure lies in the internal function SmallConformsQ:

The expression SmallConformsQ[{x, 0}, Vector[AnyType, 2]] generates a suspicious trace:

The test Length[2] == {x, 0}] in the last expression is nonsensical and surely the result of a bug.