Fuzziness support for `bool_prefix`-type `multi_match` queries

[haversnail]

Is your feature request related to a problem? Please describe. Yes, see this open issue from Elasticsearch. TL;DR, querying search_as_you_type fields with the recommended multi_match bool_prefix query does not take into account any "fuzziness" value.

Steps to reproduce:

PUT /my_index

{
  "mappings": {
    "properties": {
      "field": {
        "my_field": "search_as_you_type"
      }
    }
  }
}

PUT /my_index/_doc/1

{
  "my_field": "license"
}

GET /my_index/_search

{
  "query": {
    "multi_match": {
      "query": "lisence", // misspelled word
      "type": "bool_prefix",
      "fuzziness": 1,
      "fields": [
        "my_field",
        "my_field._2gram",
        "my_field._3gram"
      ]
    }
  }
}

Currently, the steps above yield the following result:

{
  // ...
  "hits": {
    "total": {
      "value": 0,
      "relation": "eq"
    },
    "max_score": null,
    "hits": []
  }
}

Describe the solution you'd like It would be beneficial and intuitive to have fuzziness applied to the final search term, so that results are still returned as they would be for other common datatypes/query types with a fuzziness property specified.

Describe alternatives you've considered

• Adding a space to the end of the query value
  • While this works for complete word queries, this results in edge n-grams no longer being included in the search results. For example, lic would no longer return the document with the term license as it would normally.
• Including a suggestion block to the query
  • Although this solution "works," this requires an additional lookup with the suggested/proper term, as well as time/effort spent on the client side redesigning a workflow around this.

[epiphanatic]

This issue has been known about for about 3 years - Elastic search, I hope you guys realize that this exact issue is your competitors greatest strength

[dblock]

@epiphanatic care to contribute, maybe start by adding (failing) YAML REST tests that express the behavior you're looking for?