successor-arithmetics

Can someone explain to me why this prolog query works the way it does. The definition is: add(0,Y,Y). add(succ(X),Y,succ(Z)):- add(X,Y,Z). Given this: ?- add(succ(succ(succ(0))), succ(succ(0)), R). Heres the trace of the query: Call: (6) add(succ(succ(succ(0))), succ(succ(0)), R) Call: (7) add(succ(succ(0)), succ(succ(0)), _G648) Call: (8) add(succ(0), succ(succ(0)), _G650) Call: (9) add(0, succ(succ(0)), _G652) Exit: (9) add(0, succ(succ(0)), succ(succ(0))) Exit: (8) add(succ(0), succ(succ(0)), succ(succ(succ(0)))) Exit: (7) add(succ(succ(0)), succ(succ(0)), succ(succ(succ(succ(0))))) Exit:

I have been trying to learn Prolog, and am totally stumped on what the predicate s() does. I see it used often and there is so little resources on the internet about Prolog that I cannot find an answer. Ex. /* sum(Is,S) is true if S is the sum of the list of integers Is. */ sum([],0). sum([0|Is],S):-sum(Is,S). sum([s(I)|Is], s(Z) ):-sum([I|Is],Z). s/1 does not do anything in itself, and it's not really a predicate. They are just terms, a representation of the successor of their argument. So, s(0) is used to represent the successor of 0 (i.e. 1 ), s(s(0)) is used to represent the successor of s

Let's consider that n=s(s(...s(0)...)) (simply n= s^n(0)). How could write a program calculating the division of two integers? I mean s^(n//m) (thats the definition of the division) . Any ideas? For example, if we had the question: ?-divide(s(s(s(s(0)))),s(0),D). i have written the following code: nat(0). nat(s(X)) :- nat(X). divide(0,_,D) :- D is 0. divide(s(X),s(Y),D) :- divide(X,Y,D). Your predicate divide/3 assumes wrongly that the following equation holds when x and y are numbers: (x-1)/(y-1) = x/y A counter-example is: (16-1)/(4-1) = 5 is different from 16/4 = 4 It seems you are trying

I'm doing a very simple exercise in Prolog and there's something I don't understand in the trace. The program is a "greater than" ( > ) on integers represented as successors: greater_than(succ(_), 0). greater_than(succ(A), succ(B)) :- greater_than(A, B). My problem: I don't understand why the request greater_than(succ(succ(succ(0))),succ(0)) generates a redo in the following trace: [trace] ?- greater_than(succ(succ(succ(0))),succ(0)). Call: (6) greater_than(succ(succ(succ(0))), succ(0)) ? creep Call: (7) greater_than(succ(succ(0)), 0) ? creep Exit: (7) greater_than(succ(succ(0)), 0) ? creep

Let's consider the following Prolog program (from "The Art of Prolog"): natural_number(0). natural_number(s(X)) :- natural_number(X). plus(X, 0, X) :- natural_number(X). plus(X, s(Y), s(Z)) :- plus(X, Y, Z). and the query: ?- plus(s(s(s(0))), s(0), Z). Both SICStus and SWI produce the expected Z = s(s(s(s(0)))) answer, but query the user for the next answer (a correct no / false answer). However, I cannot understand why there is an open branch in the SLD tree after the only goal is found. I tried debugging both under SICStus and under SWI, but I am not really able to interpret the result yet.

I'm trying to write reversible relations in "pure" Prolog (no is , cut, or similar stuff. Yes it's homework), and I must admit I don't have a clue how. I don't see any process to create such a thing. We are given "unpure" but reversible arithmetic relations (add,mult,equal,less,...) which we must use to create those relations. Right now I'm trying to understand how to create reversible functions by creating the relation tree(List,Tree) which is true if List is the list of the leaves of the binary tree Tree . To achieve such a thing I'm trying to create the tree_size(Tree,N) relation which is

I have the next procedure for natural number is SWI-prolog: natural_number(0). natural_number(s(X)) :- natural_number(X). Now I want to do a recursive call, that stop when we arrive to 0. My natural number is represented by - s(0)=0, s(s(0))=1, s(s(s(0)))=2, etc So I define: recommend(A, B, natural_number(0)) :- dosomeFINITEfunction (a,b). recommend(a,b,mynumber):- dosomeFINITEfunction(a,b), recommend (a,b, natural_number(mynumber)). and call with: 3,5,s(0). But it gives me the error: out of local stack . What is the problem? Thank you. natural_number(s(0), 0). natural_number(s(s(X)), N) :-