Why does my clojure.core.logic nonmember function return two values?

Question

I'm trying to implement the opposite of membero in clojure.core.logic, but it's returning two values instead of one. Otherwise, it works fine (returns nothing when the value is in the list, and something when it is not).

(defne nonmembero
  "A relation where l is a collection, such that l does not contain x"
  [x l]
  ([_ ()])
  ([_ [head]]
     (!= x head))
  ([_ [head . tail]]
     (!= x head)
     (nonmembero x tail)))

Example runs:

user> (run* [x] (nonmembero 1 [2 3 4 5]))
(_0 _0)
user> (run* [x] (nonmembero 1 [2 3 1 4 5]))
()

Answer 1

You don't need the second pattern i.e the [_ [head]. This is causing a new branch in search space of core.logic engine and hence leads to the 2 output. The last pattern i.e [head . tail] is enough to handle the case where you have only one element in the list. Now your solution becomes:

(defne nonmembero
  "A relation where l is a collection, such that l does not contain x"
  [x l]
  ([_ ()])
  ([_ [head . tail]]
     (!= x head)
     (nonmembero x tail)))