Predicate function exists()

Using the exists(expression) one can check for a property or path in a graph database. Looking at the example from the docs. You can use exists on properties as in exists(n.surname) and also on path. But from the example in the docs

SELECT * FROM cypher('graph_name', $$
 MATCH (n)
 WHERE exists(n)-[]-(name: 'Willem Defoe')
 RETURN n.full_name
$$) as (full_name agtype);

I’d expect the query to be

SELECT * FROM cypher('graph_name', $$
 MATCH (n)
 WHERE exists((n)-[]-(name: 'Willem Defoe')) 
 RETURN n.full_name 
$$) as (full_name agtype);

Since the syntax is exists(path). Also since the expression name: ‘Willem Defoe’ is a property I’d also expect that to be in curly braces thus the final query looks like this

SELECT * FROM cypher('graph_name', $$
 MATCH (n)
 WHERE exists((n)-[]-({name: 'Willem Defoe'})) 
 RETURN n.full_name 
$$) as (full_name agtype);

Or am I missing something?

Yes, you are right. The query given in the documentation has a syntax error and the correct query as stated would be:

SELECT * FROM cypher('graph_name', $$
 MATCH (n)
 WHERE exists((n)-[]-({name: 'Willem Defoe'})) 
 RETURN n.full_name 
$$) as (full_name agtype);

You can raise an issue here on GitHub.

The correction that you have suggested is how it should be written. If you run the first query, it will produce an error that says:

ERROR:  syntax error at or near ")"
LINE 3:  WHERE exists(n)-[]-(name: 'Willem Defoe')
                       ^

Similarly, the second query produces an error that says:

ERROR:  syntax error at or near "'Willem Defoe'"
LINE 3:  WHERE exists((n)-[]-(name: 'Willem Defoe'))
                                    ^

Only the third query successfully parses and produces a proper output.

You are absolutely correct, the documentation surely has syntax error and the query you suggested should be the correct one.

You are right. EXISTS clause take argument property which is a vertex or a path so, in this example it should be like this

WHERE exists((n)-[]-({name: 'Willem Defoe'}))