module lists.

type id       list A -> list A -> o.
type memb     A -> list A -> o.
type append   list A -> list A -> list A -> o.

id nil nil.
id (X::L) (X::K) :- id L K.

memb X (X::L).
memb X (Y::L) :- memb X L.

append nil K K.
append (X::L) K (X::M) :- append L K M.

type    memb_and_rest     A -> list A -> list A -> o.

memb_and_rest X (X::L) L.
memb_and_rest X (Y::K) (Y::L) :- memb_and_rest X K L.