% A for statement for(Identifier, Initial, Increment, Final)
% use like this: for(i,1,2,10),i(I)|..

for(Label,F):-for(Label,1,1,F).
for(Label,I,F):-for(Label,I,1,F).
for(Label,I,S,F):- V=I,V=<F, 
	 (Garbage=..[Label,_],  Garbage,abolish(Label); true),
         Count=..[Label,V], asserta(Count).
for(Label,I,S,F):-Count=..[Label,V], retract(Count,_), V+S=<F, 
         Next is V+S, Count2=..[Label,Next], asserta(Count2).
for(Label,I,S,F):-abolish(Label), fail.

isqrt(N,Sqrt):-for(i,N), i(I), I*I>N,!, Sqrt is I-1, abolish(i).
pyth(N):-for(i,N),i(I), I1 is I+1, for(j,I),j(J), for(k,I1,N),k(K), 
	K*K=:=I*I+J*J, print([I,J,K]).
sample(N):-for(i,N),i(I), for(j,I),j(J), for(k,J),k(K),print([I,J,K]).
lagrange(N):-isqrt(N,L),
	I1 is N - L*L, for(i,0,1,I1),i(I),prin(I),prin(' '),
	J1 is I1 - I*I, for(j,I,1,J1),j(J),prin(J),prin(' '),
	K1 is J1 - J*J, for(k,J,1,K1),k(K),prin(K),prin(' '),
	N=:=I*I+J*J+K*K+L*L,print,print([I,J,K,L]).