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Schema

To set up a lambda mutation, first you need to define it on your GraphQL schema by using the @lambda directive.
add, update, and delete are reserved prefixes and they can’t be used to define Lambda mutations.
For example, to define a lambda mutation for Author that creates a new author with a default reputation of 3.0 given just the name: 
type Author {
  id: ID!
  name: String! @search(by: [hash, trigram])
  dob: DateTime
  reputation: Float
}

type Mutation {
  newAuthor(name: String!): ID! @lambda
}

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Resolver

Once the schema is ready, you can define your JavaScript mutation function and add it as resolver in your JS source code. To add the resolver you can use either the addGraphQLResolvers or addMultiParentGraphQLResolvers methods.
A Lambda Mutation resolver can use a combination of parents, args, dql, or graphql inside the function.
This example uses graphql for the resolver function. You can find additional resolver examples using dql in the Lambda queries article, and using parent in the Lambda fields article.
For example, to define the JavaScript newAuthor() lambda function and add it as resolver: 
async function newAuthor({ args, graphql }) {
  // lets give every new author a reputation of 3 by default
  const results = await graphql(
    `
      mutation ($name: String!) {
        addAuthor(input: [{ name: $name, reputation: 3.0 }]) {
          author {
            id
            reputation
          }
        }
      }
    `,
    { name: args.name },
  )
  return results.data.addAuthor.author[0].id
}

self.addGraphQLResolvers({
  "Mutation.newAuthor": newAuthor,
})
Alternatively, you can use dql.mutate to achieve the same results: 
async function newAuthor({ args, dql, graphql }) {
  // lets give every new author a reputation of 3 by default
  const res = await dql.mutate(`{
        set {
            _:newAuth <Author.name> "${args.name}" .
            _:newAuth <Author.reputation> "3.0" .
            _:newAuth <dgraph.type> "Author" .
        }
    }`)
  return res.data.uids.newAuth
}

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Example

Finally, if you execute this lambda mutation a new author Ken Addams with reputation=3.0 should be added to the database: 
mutation {
  newAuthor(name: "Ken Addams")
}
Afterwards, if you query the GraphQL database for Ken Addams, you would see: 
{
  "getAuthor": {
    "name": "Ken Addams",
    "reputation": 3.0
  }
}