Definition 1 :-

mult(0, X, 0).
mult(s(X), Y, Z) :- mult(X, Y, Z1), add(Y, Z1, Z). 

add(0,X,X).
add(s(X),Y,s(Z)) :- add(X,Y,Z).

----


| ?- mult(X, Y, s(s(0))).
 
X = s(0)
Y = s(s(0)) ? ;
 
X = s(s(0))
Y = s(0) ? ;
 
Fatal Error: global stack overflow (size: 8193 Kb, environment variable used: GLOBALSZ)

	///////

Definition 2 :-

mult(0, X, 0).
mult(s(X), Y, Z) :- add(Y, Z1, Z), mult(X, Y, Z1).

add(0,X,X).
add(s(X),Y,s(Z)) :- add(X,Y,Z).	

----

| ?- mult(X, Y, s(s(0))).
 
Fatal Error: global stack overflow (size: 8193 Kb, environment variable used: GLOBALSZ)

 Permutation

Definition:-

/* erase(X, Y, Z) means
        Z is Y with one occurrence of X removed */
 
erase(X, [X|Y], Y).
erase(X, [Y|Z], [Y|Z1]) :- erase(X, Z, Z1).
 
/* perm(L1, L2) means
        L2 is a permutation of L1 */
 
perm([], []).
perm([A|R], X) :- perm(R, X1),
                erase(A, X, X1).

----

Note the effect of changing the order of arguments to the predicate.

| ?- perm([a,b,c], Ans).
 
Ans = [a,b,c] ? ;
 
Ans = [b,a,c] ? ;
 
Ans = [b,c,a] ? ;
 
Ans = [a,c,b] ? ;
 
Ans = [c,a,b] ? ;
 
Ans = [c,b,a] ? ;
 
no
| ?-
 program halts. 

| ?- perm(Ans, [a,b,c]).
 
Ans = [a,b,c] ? ;
 
Ans = [b,a,c] ? ;
 
Ans = [c,a,b] ? ;
 
Ans = [a,c,b] ? ;
 
Ans = [b,c,a] ? ;
 
Ans = [c,b,a] ? ;

 program does not halt!.. 

 Simple counter using built-in functions




Definition:-

ctr(0).
ctr(X) :- ctr(Y), X is Y + 1.

----

| ?- ctr(X).
 
X = 0 ? ;
 
X = 1 ? ;
 
X = 2 ? ;
 
X = 3 ? ;
 
X = 4 ?


 goes on forever.... 

 Insertion Sort 




Definition:-

/* To sort a list, sort its tail, then insert its head in the right position. */ 
isort([Head|Tail],Result) :- isort(Tail,SortedTail),
        insert(Head,SortedTail,Result).
isort([],[]).
 
/* To insert an item into the correct position in a sorted list: Put it at the beginning if it should precede the first element; otherwise go down the list until a position is found where this is the case. */
 
insert(X,[Y|Tail],[X,Y|Tail]) :- X =< Y.
insert(X,[Y|Tail],[Y|Z]) :- X > Y,
                        insert(X,Tail,Z).
insert(X,[],[X]).

----

Note the effect of changing the order of arguments to the predicate.


| ?- isort([1,3,2], Ans).
 
Ans = [1,2,3] ? ;
 
no
| ?- isort([1,3,2,0],Ans).
 
Ans = [0,1,2,3] ? ;
 
no
| ?- isort([1,3,2,0,1],Ans).
 
Ans = [0,1,1,2,3] ? ;
 
no
| ?- isort(Ans, [1,3,2]).
 
Fatal Error: local stack overflow (size: 4096 Kb, environment variable used: LOCALSZ)