% This is the general append function that defines a relationship between 3 lists, where
% list 3 is the product of sticking list 1 and list 2 together. As Prolog does not 'return'
% values, you can use append in any which way you like by specifying which of these 3 lists
% is unknown (or more than 1 unknown if you like), not just L3.

% Base case, an empty list + any list is just that list.
append([],L2,L2).
% General case. L1 is represented here as X (head) and L1t (tail)
% L2 is represented in full as L2.
% L3 is represented as X (same X as above, this is important) and L3t (tail).
% So this defines the relation where L1's tail + L2 is L3's tail, and L1's head = L3's head.
% Think about it, this makes sense:
%     L1 = [1, 2]
%     L2 = [3, 4]
%     L3 = [1, 2, 3, 4]
% L1 and L3 always have the same head. And what is the tail of L3? [2, 3, 4]
% It is the tail of L1 [2] appended with L2 [3, 4].
append([X|L1t],L2,[X|L3t]) :-
    append(L1t,L2,L3t).

% This one's for Ben. I haven't tested it so it may not be valid but the idea is there.
% Generate a list of zeroes. 'zeroes' defines a relationship between a number and a list
% which holds if that list is a list containing that number of zeroes. The base case is
% simple (and can be written in a multitude of ways, this being the shortest):
zeroes(1, [0]).
% That simply states that zeroes(1, [0]). is valid.

% Here is the general case for X zeroes in list L. We will define it as the appending
% of a zero to the list found by zeroes(X - 1, ?).
zeroes(X, L) :-
    X2 is X - 1,        % Here we can make a variable for the hell of it.
    zeroes(X2, L2),     % Find the list L2 that satisfies the condition of one less zero than required.
    append(L2, [0], L). % Here we state for the rule to be true/complete/succeed we need
                        % to find L (still unknown) such that appending [0] to L2 (known) gives it.
                        % It is not really a function call, it is a condition, they all are!
                        % The fact that we use verbs for rule names is confusing but done
                        % for brevity. Really it could be like listAandBmakeC(A, B, C); i.e.
                        % a rule like isAPerson(X) .. if that helps at all.

% Now as soon as you use 'is', the function becomes irreversible, I believe, so you can't do
% zeroes(HowMany, [0, 0, 0]).
% and get
% HowMany = 3.