The signature should be something like:

enum class PathSemantics { kFieldPath, kOther };
Type expression::traversePath(Type, FieldPath, PathSemantics);

traversePath should implement the traversal semantics used in the evaluation of the Expression classes and return the Type of the result.

There's a few different ways in which a path can be traversed in a pipeline:

•  FieldPathExpression - the $a.b syntax
•  GetFieldExpression - the $getField expression
•  Document::getNestedField - method called in aggregation pipelines in places, not strictly within Expressions.
•  there might be more!

We are only implementing the $a.b case in this project, the rest falls implicitly under kOther and will not be implemented.

See the Design Appendix.

It shows some of the values that are produced from $a.b. The evaluation code is in evaluatePath and evaluateArrayPath in evaluate_bson.cpp and that is what we need to replicate in the Type system.

Our expression::traversePath(input, "a.b", PathSemantics::kFieldPath) should produce Types that contain the values produced by the evaluation function. 

Examples:

• {a: number}

  with path 'a' produces number

• {a: number}

  with path 'a.b' produces missing

• {a: {b: number}} with path 'a' produces {b: number}
• {a: {b: number}} with path 'a.b' produces number

• Unknown macro: {a}
  with path 'a.b' produces number|array

We should refactor the resolveFieldOrigin which might cover most/all of those and remove the function if not necessary.