compacting native types with a type specification in context

This issue comes from https://github.com/digitalbazaar/jsonld.js/issues/466
I have the same issue when trying to round-trip from a framed JSON-LD to RDF and from the produced RDF to a framed JSON-LD.

{
  "@context": {
    "td": "http://example.org/",
    "xsd": "http://www.w3.org/2001/XMLSchema#",
    "title": {
      "@id": "td:title",
      "@type": "xsd:string"
    },
    "@language": "en"
  },
  "@id": "urn:something",
  "title": "the title"
}

The xsd:string typing in RDF is omitted as it is considered the default type which is fine.

<urn:something> <http://example.org/title> "the title" .

playground toRDF

When transforming the RDF data to JSON-LD again, we get

[
  {
    "@id": "urn:something",
    "http://example.org/title": [
      {
        "@value": "the title"
      }
    ]
  }
]

And when trying to compact or frame back the data with the same context, we get

{
  "@context": {
    "td": "http://example.org/",
    "xsd": "http://www.w3.org/2001/XMLSchema#",
    "title": {
      "@id": "td:title",
      "@type": "xsd:string"
    },
    "@language": "en"
  },
  "@id": "urn:something",
  "td:title": {
    "@value": "the title"
  }
}

playground framing with original context

It seems that the presence of "@type":"xsd:string" prevents the "title" term to be matched and framed.

The same compaction issues appears with the other native types playground xsd:boolean

Start by reproducing the toRDF and framing examples in the linked playgrounds, then read the linked jsonld.js issue 466 for related context. Trace how compaction and framing handle native values against a term with an @type specification. Done means the title and boolean examples round-trip and match their context-defined terms without losing the expected native values.