i have the next problem,
"return the numbers of natural numbers of an array"
ex. naturales(R,[6,-7,-4,3,2,8]).
R = 4
when a negative numbers appears return false and break my recursivity
naturales(R,[Head|Tail]):-naturales(R1,Tail), Head >= 0, R is R1+1.
naturales(0,[]).
Here is a very short solution :
naturales(In, Out) :-
aggregate(count,X^(member(X, In), X >= 0), Out).
If your predicate really needs to have only 2 arguments, one being the result, R, and the other one the given list, [H|T], you can do something like this. Note that the first predicate calls the second "naturales" with 3 arguments and then, that one starts the recursive process. The C is only a counter where you can add the number of positive elements and then copy that value to the result, in the last line of code. The first line just its just to make sure the empty list returns 0 positive elements. There is probably better ways to do this, this one is probably the most intuitive.
naturales(X, []):- X = 0.
naturales(R, [H|T]):- naturales(R, [H|T], 0).
naturales(R, [H|T], C):- (H > 0, C1 is C + 1, naturales(R1, T, C1), R = R1) ; naturales(R1, T, C), R = R1.
naturales(X, [], X).
A common prolog idiom is the use of a helper predicate with an accumulator (extra) variable. Try something like this:
natural_numbers( Xs, N ) :- natural_numbers( Xs, 0, N ).
natural_numbers( [] , N , N ) .
natural_numbers( [X|Xs] , T , N ) :-
( X > 0 -> T1 is T+1 ; T1 = T ) ,
natural_numbers( Xs, T1, N ).
As others pointed out, the recursive call cannot complete when there are negative numbers. So, you can just patch your program in this way
naturales(R,[Head|Tail]):-naturales(R1,Tail), (Head >= 0, R is R1+1 ; R=R1).
naturales(0,[]).
Now, nearly every Prolog out there (except mine :) implements (->)/2, also know as 'if-then-else'. So, the patch could also be written like
naturales(R,[Head|Tail]):-naturales(R1,Tail), (Head >= 0 -> R is R1+1 ; R=R1).
naturales(0,[]).
Given that naturales/2 is anyway not tail recursive (see #NicholasCarey answer for that), I think it has no practical relevance for you.
Related
I'm trying to iterate through a given list and put all the positive numbers into Y and all negatives into Z. My code works until I go to add a second element to either Y or Z. If I run the code like so "divide([1,-2],Y,Z)" the code executes with no errors its only if I were to enter "divide([1,-2,3],Y,Z)" it will fail when trying to add 3 to Y.
divide([],[Y],[Z]):- write(Y), write(Z).
divide([H|T],[Y],[Z]):- split(H,Y,Z), divide(T,Y,Z).
split(H,Y,Z):- (H>0 -> append([H],[],Y); append([H],[],Z)).
SWI-Prolog library(apply) offers partition/4, a builtin for your problem, but since I think that for learning you're better to correct your own code here is my advise. Keep it simpler: the base case, i.e. when you are given an empty list, would be just this simple clause:
divide([],[],[]).
Then you must handle a non empty list. If the value is positive, put it in the second list. Otherwise, put it in the third list. You see, we need two more clauses, I will show partially the second one:
divide([V|Vs],[V|Ps],Ns) :-
V>=0,
...
As you see, the head parameters act as both destructuring as well as constructing the relevant values. Put a recursive call instead of the three dots, and write the third clause to handle the case V<0.
I've attempted to use descriptive variables names: Vs stands for values, Ps for positives, Ns for negatives.
I see the other answer and I am confuse. I have been learning by copying others who know better than me my whole life. Maybe this is why I ended up as a teaching assistant intern, instead of a real job.
Here is what I get when I follow the instructions and try to learn by imitating:
list_pos_neg([], [], []).
list_pos_neg([H|T], P, N) :-
( H >= 0
-> P = [H|P0],
list_pos_neg(T, P0, N)
; N = [H|N0],
list_pos_neg(T, P, N0)
).
I usually try to avoid the cut and use -> ; instead. But in this case, I think it is clearer this way:
div_pos_neg([], [], []).
div_pos_neg([H|T], [H|P], N) :- H >= 0, !, div_pos_neg(T, P, N).
div_pos_neg([H|T], P, [H|N]) :- H < 0, div_pos_neg(T, P, N).
Note that the condition is still necessary in the last clause so that calls like div_post_neg([1,2], [], [1, 2]) return the right answer (failure!).
That seems ... complicated. How about just
partition( [] , [] , [] ) .
partition( [X|Xs] , [X|Ns] , Ps ) :- X < 0 , partition(Xs,Ns,Ps) .
partition( [X|Xs] , Ns , [X|Ps] ) :- X >= 0 , partition(Xs,Ns,Ps) .
I am new to prolog, I wish to get a function:
drop(N, X, Y) that prints list Y which is the list X with its Nth element removed. If X does not have an Nth element then the predicate should fail.
Example:
1)drop(2,[1,2,3,4,5,6],Y) should give Y=[1,3,4,5,6].
2)drop(8,[1,2,3,4,5,6],Y) should fail.
I tried to get a function that appends an element of X to Y if it is not an Nth element and skips the element if it is an Nth element. Please see the following code:
drop(N,X,Y) :- integer(N),N>0,drop(X,1,N,Y).
drop([], _ , _ , [] ) .
drop( [X1|X] , P , N , [X1|Y] ) :- N=\=P , P1 is P+1 , drop(X,P1,N,Y) .
drop( [_|X] , P , N ,Y) :- N =:= P , P1 is P+1 , drop(X,P1,N,Y) .
The problem arises if N is greater than the length of the list, my code will print the entire list, but the function is supposed to fail in this case. I am not able to find a way to compare N with the length of the list since every function in prolog returns a binary value(according to my knowledge).
Any help will be much appreciated!
You are quite close. There are two things that you should change here:
once we have reached the correct index, we should no longer recurse on drop but just return the rest of the list; and
you should remove the drop([], _, _, []) line, since given we dropped an element, we will no longer recurse (see previous point).
Note that we can each time decrement the value for N and thus prevent using two variables. Like:
drop(N, X, Y) :-
integer(N),
drop_(N, X, Y).
drop_(1, [_|T], T).
drop_(N, [X|T], [X|T2]) :-
N > 1,
N1 is N-1,
drop_(N1, T, T2).
countdown(0, Y).
countdown(X, Y):-
append(Y, X, Y),
Y is Y-1,
countdown(X, Y).
So for this program i am trying to make a countdown program which will take Y a number and count down from say 3 to 0 while adding each number to a list so countdown(3, Y). should produce the result Y=[3,2,1]. I can't seem the end the recursion when i run this and i was wondering if anyone could help me?
I cant seem to get this code to work any help? I seem to be getting out of global stack so I dont understand how to end the recursion.
Your original code
countdown( 0 , Y ) .
countdown( X , Y ) :-
append(Y, X, Y),
Y is Y-1,
countdown(X, Y).
has some problems:
countdown(0,Y). doesn't unify Y with anything.
Y is Y-1 is trying to unify Y with the value of Y-1. In Prolog, variables, once bound to a value, cease to be variable: they become that with which they were unified. So if Y was a numeric value, Y is Y-1 would fail. If Y were a variable, depending on your Prolog implementation, it would either fail or throw an error.
You're never working with lists. You are expecting append(Y,X,Y) to magically produce a list.
A common Prolog idiom is to build lists as you recurse along. The tail of the list is passed along on each recursion and the list itself is incomplete. A complete list is one in which the last item is the atom [], denoting the empty list. While building a list this way, the last item is always a variable and the list won't be complete until the recursion succeeds. So, the simple solution is just to build the list as you recurse down:
countdown( 0 , [] ) . % The special case.
countdown( N , [N|Ns] ) :- % The general case: to count down from N...
N > 0 , % - N must be greater than 0.
N1 is N-1 , % - decrement N
countdown(N1,Ns) % - recurse down, with the original N prepended to the [incomplete] result list.
. % Easy!
You might note that this will succeed for countdown(0,L), producing L = []. You could fix it by changing up the rules a we bit. The special (terminating) case is a little different and the general case enforces a lower bound of N > 1 instead of N > 0.
countdown( 1 , [1] ) .
countdown( N , [N|Ns] ) :-
N > 1 ,
N1 is N-1 ,
countdown(N1,Ns)
.
If you really wanted to use append/3, you could. It introduces another common Prolog idiom: the concept of a helper predicate that carries state and does all the work. It is common for the helper predicate to have the same name as the "public" predicate, with a higher arity. Something like this:
countdown(N,L) :- % to count down from N to 1...
N > 0 , % - N must first be greater than 0,
countdown(N,[],L) % - then, we just invoke the helper with its accumulator seeded as the empty list
. % Easy!
Here, countdown/2 is our "public predicate. It calls countdown/3 to do the work. The additional argument carries the required state. That helper will look like something like this:
countdown( 0 , L , L ) . % once the countdown is complete, unify the accumulator with the result list
countdown( N , T , L ) . % otherwise...
N > 0 , % - if N is greater than 0
N1 is N-1 , % - decrement N
append(T,[N],T1) , % - append N to the accumulator (note that append/3 requires lists)
countdown(N1,T1,L) % - and recurse down.
. %
You might notice that using append/3 like this means that it iterates over the accumulator on each invocation, thus giving you O(N2) performance rather than the desired O(N) performance.
One way to avoid this is to just build the list in reverse order and reverse that at the very end. This requires just a single extra pass over the list, meaning you get O(2N) performance rather than O(N2) performance. That gives you this helper:
countdown( 0 , T , L ) :- % once the countdown is complete,
reverse(T,L) % reverse the accumulator and unify it with the result list
. %
countdown( N , T , L ) :- % otherwise...
N > 0 , % - if N is greater than 0
N1 is N-1 , % - decrement N
append(T,[N],T1) , % - append N to the accumulator (note that append/3 requires lists)
countdown(N1,T1,L) % - and recurse down.
. %
There are several errors in your code:
first clause does not unify Y.
second clause uses append with first and third argument Y, which would only succeed if X=[].
in that clause you are trying to unify Y with another value which will always fail.
Y should be a list (according to your comment) in the head but you are using it to unify an integer.
You might do it this way:
countdown(X, L):-
findall(Y, between(1, X, Y), R),
reverse(R, L).
between/3 will give you every number from 1 to X (backtracking). Therefore findall/3 can collect all the numbers. This will give you ascending order so we reverse/2 it to get the descending order.
If you want to code yourself recursively:
countdown(X, [X|Z]):-
X > 1,
Y is X-1,
countdown(Y, Z).
countdown(1, [1]).
Base case (clause 2) states that number 1 yields a list with item 1.
Recursive clause (first clause) states that if X is greater than 1 then the output list should contain X appended with the result from the recursive call.
Working on a predicate, rotate(L,M,N), where L is a new list formed by rotating M to the right N times.
My approach was to just append the tail of M to its head N times.
rotate(L, M, N) :-
( N > 0,
rotate2(L, M, N)
; L = M
).
rotate2(L, [H|T], Ct) :-
append(T, [H], L),
Ct2 is Ct - 1,
rotate2(L, T, Ct2).
Currently, my code returns L equal to the original M, no matter what N is set to.
Seems like when I'm recursing, the tail isn't properly moved to the head.
You can use append to split lists, and length to create lists:
% rotate(+List, +N, -RotatedList)
% True when RotatedList is List rotated N positions to the right
rotate(List, N, RotatedList) :-
length(Back, N), % create a list of variables of length N
append(Front, Back, List), % split L
append(Back, Front, RotatedList).
Note: this only works for N <= length(L). You can use arithmetic to fix that.
Edit for clarity
This predicate is defined for List and N arguments that are not variables when the predicate is called. I inadvertently reordered the arguments from your original question, because in Prolog, the convention is that strictly input arguments should come before output arguments. So, List and N and input arguments, RotatedList is an output argument. So these are correct queries:
?- rotate([a,b,c], 2, R).
?- rotate([a,b,c], 1, [c,a,b]).
but this:
?- rotate(L, 2, [a,b,c]).
will go into infinite recursion after finding one answer.
When reading the SWI-Prolog documentation, look out for predicate arguments marked with a "?", as in length. They can be used as shown in this example.
We want to build a predicate that gets a list L and a number N and is true if N is the length of the longest sequence of list L.
For example:
?- ls([1,2,2,4,4,4,2,3,2],3).
true.
?- ls([1,2,3,2,3,2,1,7,8],3).
false.
For this I built -
head([X|S],X). % head of the list
ls([H|T],N) :- head(T,X),H=X, NN is N-1 , ls(T,NN) . % if the head equal to his following
ls(_,0) :- !. % get seq in length N
ls([H|T],N) :- head(T,X) , not(H=X) ,ls(T,N). % if the head doesn't equal to his following
The concept is simply - check if the head equal to his following , if so , continue with the tail and decrement the N .
I checked my code and it works well (ignore cases which N = 1) -
ls([1,2,2,4,4,4,2,3,2],3).
true ;
false .
But the true answer isn't finite and there is more answer after that , how could I make it to return finite answer ?
Prolog-wise, you have a few problems. One is that your predicate only works when both arguments are instantiated, which is disappointing to Prolog. Another is your style—head/2 doesn't really add anything over [H|T]. I also think this algorithm is fundamentally flawed. I don't think you can be sure that no sequence of longer length exists in the tail of the list without retaining an unchanged copy of the guessed length. In other words, the second thing #Zakum points out, I don't think there will be a simple solution for it.
This is how I would have approached the problem. First a helper predicate for getting the maximum of two values:
max(X, Y, X) :- X >= Y.
max(X, Y, Y) :- Y > X.
Now most of the work sequence_length/2 does is delegated to a loop, except for the base case of the empty list:
sequence_length([], 0).
sequence_length([X|Xs], Length) :-
once(sequence_length_loop(X, Xs, 1, Length)).
The call to once/1 ensures we only get one answer. This will prevent the predicate from usefully generating lists with sequences while also making the predicate deterministic, which is something you desired. (It has the same effect as a nicely placed cut).
Loop's base case: copy the accumulator to the output parameter:
sequence_length_loop(_, [], Length, Length).
Inductive case #1: we have another copy of the same value. Increment the accumulator and recur.
sequence_length_loop(X, [X|Xs], Acc, Length) :-
succ(Acc, Acc1),
sequence_length_loop(X, Xs, Acc1, Length).
Inductive case #2: we have a different value. Calculate the sequence length of the remainder of the list; if it is larger than our accumulator, use that; otherwise, use the accumulator.
sequence_length_loop(X, [Y|Xs], Acc, Length) :-
X \= Y,
sequence_length([Y|Xs], LengthRemaining),
max(Acc, LengthRemaining, Length).
This is how I would approach this problem. I don't know if it will be useful for you or not, but I hope you can glean something from it.
How about adding a break to the last rule?
head([X|S],X). % head of the list
ls([H|T],N) :- head(T,X),H=X, NN is N-1 , ls(T,NN) . % if the head equal to his following
ls(_,0) :- !. % get seq in length N
ls([H|T],N) :- head(T,X) , not(H=X) ,ls(T,N),!. % if the head doesn't equal to his following
Works for me, though I'm no Prolog expert.
//EDIT: btw. try
14 ?- ls([1,2,2,4,4,4,2,3,2],2).
true ;
false.
Looks false to me, there is no check whether N is the longest sequence. Or did I get the requirements wrong?
Your code is checking if there is in list at least a sequence of elements of specified length. You need more arguments to keep the state of the search while visiting the list:
ls([E|Es], L) :- ls(E, 1, Es, L).
ls(X, N, [Y|Ys], L) :-
( X = Y
-> M is N+1,
ls(X, M, Ys, L)
; ls(Y, 1, Ys, M),
( M > N -> L = M ; L = N )
).
ls(_, N, [], N).