Improve ConstraintHandling of SkolemTypes

[EugeneFlesselle]

By retaining instantiated type vars in LevelAvoidMap when possible.

Fixes #19955

Consider pos/i19955a as an example.
We try to adapt the given_IsInt_U for skolems of the form (?2 : Int) and (?7 : ?8.Out) where ?8 is an unknown value of type given_IsWrapOfInt_R[Int, Wrap[Int]], but only the former succeeds, even though ?8.Out is trivially within the bounds of U.

The typing trace from the two implicit search results includes:

[log typer] ==> typedImplicit(Cand(given_IsInt_U L4), IsInt[(?2 : Int)], <empty>, <399..399>)?
[log typer]   ==> isSubType(IsInt[U], IsInt[(?2 : Int)])?
[log typer]     ==> isSameType((?2 : Int), U)?
[log typer]       ==> isSubType((?2 : Int), U)?
[log typer]       <== isSubType((?2 : Int), U) = true
[log typer]       ==> isSubType(U, (?2 : Int))?
[log typer]       <== isSubType(U, (?2 : Int)) = true
[log typer]     <== isSameType((?2 : Int), U) = true
[log typer]   <== isSubType(IsInt[U], IsInt[(?2 : Int)]) = true
[log typer] <== typedImplicit(Cand(given_IsInt_U L4), IsInt[(?2 : Int)], <empty>, <399..399>) = SearchSuccess: (given_IsInt_U : [U <: Int]: IsInt[U]) via given_IsInt_U[(?2 : Int)]
[log typer] ==> typedImplicit(Cand(given_IsInt_U L4), IsInt[(?7 : ?8.Out)], <empty>, <423..423>)?
[log typer]   ==> isSubType(IsInt[U], IsInt[(?7 : ?8.Out)])?
[log typer]     ==> isSameType((?7 : ?8.Out), U)?
[log typer]       ==> isSubType((?7 : ?8.Out), U)?
[log typer]       <== isSubType((?7 : ?8.Out), U) = true
[log typer]       ==> isSubType(Int, (?7 : ?8.Out))?
[log typer]       <== isSubType(Int, (?7 : ?8.Out)) = false
[log typer]     <== isSameType((?7 : ?8.Out), U) = false
[log typer]   <== isSubType(IsInt[U], IsInt[(?7 : ?8.Out)]) = false
[log typer] <== typedImplicit(Cand(given_IsInt_U L4), IsInt[(?7 : ?8.Out)], <empty>, <423..423>) = Search Failure: given_IsInt_U[U]

The difference in the failing case from the passing case is that the type variable U has been instantiated to Int by the first direction of isSameType before attempting the second direction.

If we look closer at the ConstraintHandling:

[log typer]         ==> addConstraint(U, (?2 : Int), true)?
[log typer]           ==> legalBound(U, (?2 : Int), false)?
[log typer]             ==> ApproximatingTypeMap#derivedSkolemType((?2 : Int), Int)?
[log typer]             <== ApproximatingTypeMap#derivedSkolemType((?2 : Int), Int) = (?2 : Int)
[log typer]           <== legalBound(U, (?2 : Int), false) = (?2 : Int)
[log typer]           ==> isSubType((?2 : Int), Int)?
[log typer]           <== isSubType((?2 : Int), Int) = true
[log typer]         <== addConstraint(U, (?2 : Int), true) = true
[log typer]         ==> addConstraint(U, (?7 : ?8.Out), true)?
[log typer]           ==> legalBound(U, (?7 : ?8.Out), false)?
[log typer]             ==> ApproximatingTypeMap#derivedSkolemType((?8 : given_IsWrapOfInt_R[Int, Wrap[Int]]), given_IsWrapOfInt_R[Int, Wrap[Int]])?
[log typer]             <== ApproximatingTypeMap#derivedSkolemType((?8 : given_IsWrapOfInt_R[Int, Wrap[Int]]), given_IsWrapOfInt_R[Int, Wrap[Int]]) = given_IsWrapOfInt_R[Int, Wrap[Int]]
[log typer]             ==> ApproximatingTypeMap#derivedSkolemType((?7 : ?8.Out), Int)?
[log typer]             <== ApproximatingTypeMap#derivedSkolemType((?7 : ?8.Out), Int) = Int
[log typer]           <== legalBound(U, (?7 : ?8.Out), false) = Int
[log typer]         <== addConstraint(U, (?7 : ?8.Out), true) = true

we can see that the issue lies in the approximation in the LevelAvoidMap used to obtain the legalBound.

Modifying ApproximatingTypeMap#derivedSkolemType from if info eq tp.info then tp to if info frozen_=:= tp.info then tp.derivedSkolem(info), allows each direction of the subtyping checks in isSameType to obtain the more precise skolem as legal bound. But it does not solve the issue, since they obtain distinct skolems even if they equivalently-shaped, the constraints are still unsatisfiable.

We can instead try to make info eq tp.info be true. It was not the case in the above example because given_IsWrapOfInt_R[Int, Wrap[Int]] contained a type variable R := Wrap[Int] which was substituted by the map.

We can modify TypeMap to keep type variables rather than replace them by their instance when possible, i.e. when the instance is itself not transformed by the map. This solves the issue but breaks other places which assumed the stripping of type vars in TypeMaps. That problem is avoided by doing the changes in LevelAvoidMap only.

[smarter]

This solves the issue but breaks other places which assumed the stripping of type vars in TypeMaps

Can we do it on all ApproximatingTypeMap?

[EugeneFlesselle]

Can we do it on all ApproximatingTypeMap?

Doing so doesn't seem to break any thing.