On issue #176 there is a discussion about how to possibly map JSON Patch paths.

I've added some examples here for further discussion.

How to replace the title of a post:

PATCH /posts/1

# JSON Patch Document:
[
  { "op": "replace", "path": "/posts/1/title", "value": "New Title" }
]

# JSON API resource:
{
  "posts": [{
    "id": "1",
    "title": "Old Title"
  }]
}

# JSON Patch equivalent structure:
{
  "posts": {
    "1": {
      "id": "1",
      "title": "The title"
    }
  }
}

How to remove comment 5:

PATCH /posts/1
 
# JSON Patch Document: 
[
  { "op": "remove", "path": "/posts/1/comments/5" }
]
 
# JSON API resource:
{
  "posts": [{
    "id": "1",
    "links": {
      "comments": [ "1", "3", "5", "7" ]
    }
  }]
}
 
# JSON Patch equivalent structure:
{
  "posts": {
    "1": {
      "id": "1",
      "links": {
        "comments": {
          "1": "1",
          "3": "3",
          "5": "5",
          "7": "7"
        }
      }
    }
  }
}

How to replace author type with a new value of "human":

PATCH /posts/1
 
# JSON Patch Document: 
[
  { "op": "replace", "path": "/posts/1/author/type", "value": "human" }
]
 
# JSON API resource:
{
  "posts": [{
    "id": "1",
    "title": "Rails is Omakase",
    "links": {
      "author": {
        "href": "http://example.com/people/17",
        "id": "17",
        "type": "people"
      }
    }
  }]
}

# JSON Patch equivalent structure: 
{
  "posts": {
    "1": {
      "id": "1",
      "links": {
        "author": {
          "href": "http://example.com/people/17",
          "id": "17",
          "type": "people"
        }
      }
    }
  }
}

How to replace author type with id of 1 to "not-dog":

PATCH /posts/1
 
# JSON Patch Document: 
[
  { "op": "replace", "path": "/posts/1/authors/1", "value": "not-dog" }
]
 
# JSON API resource:
{
  "posts": [
    {
      "id": "1",
      "title": "One Type Purr Author",
      "links": {
        "authors": [
          {
            "href": "http://example.com/people/9",
            "id": "9",
            "type": "people"
          },
          {
            "href": "http://example.com/cats/1",
            "id": "1",
            "type": "cats"
          }
        ]
      }
    }
  ]
}
 
# JSON Patch equivalent structure:
{
  "posts": {
    "1": {
      "id": "1",
      "links": {
        "authors": {
          "9": {
            "href": "http://example.com/people/9",
            "id": "9",
            "type": "people"
          },
          "1": {
            "href": "http://example.com/cats/1",
            "id": "1",
            "type": "cats"
          }
        }
      }
    }
  }
}

How to remove multiple posts:

 
PATCH /posts
 
# JSON Patch Document: 
[
  { "op": "remove", "path": "/posts/1" },
  { "op": "remove", "path": "/posts/2" },
  { "op": "remove", "path": "/posts/3" },
  { "op": "remove", "path": "/posts/4" }
]
 
# JSON API resource:
{
  "posts": [
    {
      "id": "1",
      "title": "One Type Purr Author",
    },
    {
      "id": "2",
      "title": "One Type Purr Author",
    },
    {
      "id": "3",
      "title": "One Type Purr Author",
    },
    {
      "id": "4",
      "title": "One Type Purr Author",
    }
  ]
}
 
# JSON Patch equivalent structure:
{
  "posts": {
    "1": {
      "id": "1",
      "title": "One Type Purr Author",
    },
    "2": {
      "id": "2",
      "title": "One Type Purr Author",
    },
    "3": {
      "id": "3",
      "title": "One Type Purr Author",
    },
    "4": {
      "id": "4",
      "title": "One Type Purr Author",
    }
  }
}