I have been looking for a predicate to split a list L into three pieces:

• Front (a list)
• Element at Index N (0-based)
• Back (a list) such that:

  append([Front,[Element],Back],L).

  Here is one. It is still not predicatly enough and unable to compute Index or List from the other parameters.

  % split_list(+List, +Index, Element, Front, Back)
  
  split_list([L|Lr], N, El, [L|Front], Back) :-
     N>0,!,
     Nm is N-1,
     split_list(Lr,Nm,El,Front,Back).
  
  split_list([L|Lr], 0, L, [], Lr).

  (From https://stackoverflow.com/questions/61028457/an-easier-way-to-split-a-list-at-the-n-th-place-in-prolog/ )