recursion in prolog (on lists)

Question

can someone please help me just w/ the basics on performing recursive prolog functions..

append([],X,X). % base
append([X|Y],Z,[X|W]) :- append(Y,Z,W). %recursive

% base case
addup([], 0). % sum of the empty list of numbers is zero

% recursive case: if the base-case rule does not match, this one must:
addup([FirstNumber | RestOfList], Total) :-
    addup(RestOfList, TotalOfRest),   % add up the numbers in RestOfList
    Total is FirstNumber + TotalOfRest.

Can someone explain either in English or in C/C++/Java whatever.. how the steps. I actually would prefer to see something like append or reverse.. I'm mostly just manipulating lists of variables instead of integers.. (I've tried to work through append like 10 times.. ugh).

Answer 1

append(A, B, R) means that R is the result of appending A to B.

The base case

append([], X, X).

says that if A = [] and B = X then R = X = B: an empty list A appended to some other list B is equal to B.

The recursive case

append([X | Y], Z, [X | W]) :- append(Y, Z, W).

says that if A = [X | Y] is a non-empty list to append to B = Z, and if W is Y appended to Z, then R = [X | W].

Another way of saying it is: to append a non-empty list A to another list B, first append the tail of A to B and then add the head of A to the front of the list.