append([],Ys,Ys).
append([X|Xs],Ys,[X|Zs]):-
	append(Xs,Ys,Zs).
	

list([]).
list([H|T]):-list(T).

plist([]).
plist([H|T]):-
	p(H),
	plist(T).
	
p(1).
p(2).


% fib(N,F) <- F is the N-th Fibonacci number
% inefficient doubly-recursive version
fib(1,1).
fib(2,1).
fib(N,F):-
	N>2,N1 is N-1,N2 is N-2,
	fib(N1,F1),fib(N2,F2),
	F is F1+F2.


% We can get a more efficient version 
% by solving a more general problem!

% fibn(N,F) <- F is the N-th Fibonacci number
% efficient tail-recursive version
fibn(N,F):-
	fibn(N,1,1,F).
	
% fibn(N,Na,Nb,F) <- F is the N-th Fibonacci number
%                   in the sequence starting with Na, Nb
fibn(1,Na,_,Na).
fibn(2,_,Nb,Nb).
fibn(N,Na,Nb,F):-
	N>2, N1 is N-1,
	Nc is Na+Nb,
	fibn(N1,Nb,Nc,F).