Related
New to prolog and trying to implement the following function that takes 3 lists:
True if lists are the same length
True if elements of third list is sum of the two lists
Example: fn([1,2,3],[4,5,6],[5,7,9]) returns true. Note that the sum is element-wise addition.
This is what I have so far:
fn([],[],[]).
fn([_|T1], [_|T2], [_|T3]) :-
fn(T1,T2,T3), % check they are same length
fn(T1,T2,N1), % check that T3=T1+T2
N1 is T1+T2,
N1 = T3.
From what I understand, the error is due to the base case (it has empty lists which causes error with evaluation of addition?)
Thanks for any help and explanations!
In addition to #GuyCoder's answer, I would point out that it is worthwhile to consider using one of the maplist predicates from library(apply) when modifying all elements of lists. You can use a predicate to describe the relation between three numbers...
:- use_module(library(apply)). % for maplist/4
num_num_sum(X,Y,S) :-
S is X+Y.
... and subsequently use maplist/4 to apply it to entire lists:
fn(X,Y,Z) :-
maplist(num_num_sum,X,Y,Z).
This predicate yields the desired results if the first two lists are fully instantiated:
?- fn([1,2,3],[4,5,6],X).
X = [5,7,9]
However, due to the use of is/2 you get instantiation errors if the first two lists contain variables:
?- fn([1,A,3],[4,5,6],[5,7,9]).
ERROR at clause 1 of user:num_num_sum/3 !!
INSTANTIATION ERROR- X is _+B: expected bound value
?- fn([1,2,3],[4,5,A],[5,7,9]).
ERROR at clause 1 of user:num_num_sum/3 !!
INSTANTIATION ERROR- X is A+B: expected bound value
If you only want to use the predicate for lists of integers, you can use CLP(FD) to make it more versatile:
:- use_module(library(apply)).
:- use_module(library(clpfd)). % <- use CLP(FD)
int_int_sum(X,Y,S) :-
S #= X+Y. % use CLP(FD) constraint #=/2 instead of is/2
fnCLP(X,Y,Z) :-
maplist(int_int_sum,X,Y,Z).
With this definition the previously problematic queries work as well:
?- fnCLP([1,A,3],[4,5,6],[5,7,9]).
A = 2
?- fnCLP([1,2,3],[4,5,A],[5,7,9]).
A = 6
Even the most general query yields results with this version:
?- fnCLP(X,Y,Z).
X = Y = Z = [] ? ;
X = [_A],
Y = [_B],
Z = [_C],
_A+_B#=_C ? ;
X = [_A,_B],
Y = [_C,_D],
Z = [_E,_F],
_A+_C#=_E,
_B+_D#=_F ? ;
.
.
.
Since the numbers in the above answers are not uniquely determined, you get residual goals instead of actual numbers. In order to get actual numbers in the answers, you have to restrict the range of two of the lists and label them subsequently (see documentation for details), e.g. to generate lists containing the numbers 3,4,5 in the first list and 6,7,8 in the second list, you can query:
label the lists
restrict the domain | |
v v v v
?- fnCLP(X,Y,Z), X ins 3..5, Y ins 6..8, label(X), label(Y).
X = Y = Z = [] ? ;
X = [3],
Y = [6],
Z = [9] ? ;
X = [3],
Y = [7],
Z = [10] ? ;
.
.
.
X = [3,4],
Y = [6,7],
Z = [9,11] ? ;
X = [3,4],
Y = [6,8],
Z = [9,12] ? ;
.
.
.
On an additional note: there are also clp libraries for booleans (CLP(B)), rationals and reals (CLP(Q,R)) that you might find interesting.
From what I understand, the error is due to the base case.
I don't see it that way.
The first problem I see is that you are trying to process list which leads to thinking about using DCGs, but since you are new I will avoid that route.
When processing list you typically process the head of the list then pass the tail back to the predicate using recursion.
e.g. for length of list you would have
ln([],N,N).
ln([_|T],N0,N) :-
N1 is N0+1,
ln(T,N1,N).
ln(L,N) :-
ln(L,0,N).
The predicate ln/2 is used to set up the initial count of 0 and the predicate ln/3 does the work using recursion. Notice how the head of the list is taken off the front of the list and the tail of the list is passed recursively onto the predicate again. When the list is empty the predicate ln([],N,N). unifies, in this case think copies, the intermediate count from the second position into the third position, which it what is passed back with ln/2.
Now back to your problem.
The base case is fine
fn([],[],[]).
There are three list and for each one look at the list as [H|T]
fn([H1|T1],[H2|T2],[H3|T3])
and the call to do the recursion on the tail is
fn(T1,T2,T3)
all that is left is to process the heads which is
H3 is H1 + H2
putting it all together gives us
fn([],[],[]).
fn([H1|T1], [H2|T2], [H3|T3]) :-
H3 is H1 + H2,
fn(T1,T2,T3).
and a quick few checks.
?- fn([],[],[]).
true.
?- fn([1],[1],[2]).
true.
?- fn([1,2],[3,4],[4,6]).
true.
?- fn([1,2],[3,4,5],[4,6,5]).
false.
With regards to the two conditions. When I look at exercises problems for logic programming they sometimes give a condition like True if lists are the same length or some other condition that returns true. I tend to ignore those at first and concentrate on getting the other part done first, in this case elements of third list is sum of the two lists then I check to see if the other conditions are correct. For most simple classroom exercises they are. I sometimes think teacher try to give out these extra conditions to confuse the student, but in reality the are there just to clarify how the code should work.
So I'm making a predicate called removeN(List1, N, List2). It should basically function like this:
removeN([o, o, o, o], 3, List2).
List2 = [o].
The first argument is a list with a number of the same members ([o, o, o] or [x, x, x]). The second argument is the number of members you wanna remove, and the third argument is the list with the removed members.
How should I go about this, I was thinking about using length of some sort.
Thanks in advance.
Another approach would be to use append/3 and length/2:
remove_n(List, N, ShorterList) :-
length(Prefix, N),
append(Prefix, ShorterList, List).
Think about what the predicate should describe. It's a relation between a list, a number and a list that is either equal to the first or is missing the specified number of the first elements. Let's pick a descriptive name for it, say list_n_removed/3. Since you want a number of identical elements to be removed, let's keep the head of the list for comparison reasons, so list_n_removed/3 is just the calling predicate and another predicate with and additional argument, let's call it list_n_removed_head/4, describes the actual relation:
list_n_removed([X|Xs],N,R) :-
list_n_removed_head([X|Xs],N,R,X).
The predicate list_n_removed_head/4 has to deal with two distinct cases: either N=0, then the first and the third argument are the same list or N>0, then the head of the first list has to be equal to the reference element (4th argument) and the relation has to hold for the tail as well:
list_n_removed_head(L,0,L,_X).
list_n_removed_head([X|Xs],N,R,X) :-
N>0,
N0 is N-1,
list_n_removed_head(Xs,N0,R,X).
Now let's see how it works. Your example query yields the desired result:
?- list_n_removed([o,o,o,o],3,R).
R = [o] ;
false.
If the first three elements are not equal the predicate fails:
?- list_n_removed([o,b,o,o],3,R).
false.
If the length of the list equals N the result is the empty list:
?- list_n_removed([o,o,o],3,R).
R = [].
If the length of the list is smaller than N the predicate fails:
?- list_n_removed([o,o],3,R).
false.
If N=0 the two lists are identical:
?- list_n_removed([o,o,o,o],0,R).
R = [o, o, o, o] ;
false.
If N<0 the predicate fails:
?- list_n_removed([o,o,o,o],-1,R).
false.
The predicate can be used in the other direction as well:
?- list_n_removed(L,0,[o]).
L = [o] ;
false.
?- list_n_removed(L,3,[o]).
L = [_G275, _G275, _G275, o] ;
false.
However, if the second argument is variable:
?- list_n_removed([o,o,o,o],N,[o]).
ERROR: >/2: Arguments are not sufficiently instantiated
This can be avoided by using CLP(FD). Consider the following changes:
:- use_module(library(clpfd)). % <- new
list_n_removed([X|Xs],N,R) :-
list_n_removed_head([X|Xs],N,R,X).
list_n_removed_head(L,0,L,_X).
list_n_removed_head([X|Xs],N,R,X) :-
N #> 0, % <- change
N0 #= N-1, % <- change
list_n_removed_head(Xs,N0,R,X).
Now the above query delivers the expected result:
?- list_n_removed([o,o,o,o],N,[o]).
N = 3 ;
false.
As does the most general query:
?- list_n_removed(L,N,R).
L = R, R = [_G653|_G654],
N = 0 ;
L = [_G653|R],
N = 1 ;
L = [_G26, _G26|R],
N = 2 ;
L = [_G26, _G26, _G26|R],
N = 3 ;
.
.
.
The other queries above yield the same answers with the CLP(FD) version.
Alternative solution using foldl/4:
remove_step(N, _Item, Idx:Tail, IdxPlusOne:Tail) :-
Idx < N, succ(Idx, IdxPlusOne).
remove_step(N, Item, Idx:Tail, IdxPlusOne:NewTail) :-
Idx >= N, succ(Idx, IdxPlusOne),
Tail = [Item|NewTail].
remove_n(List1, N, List2) :-
foldl(remove_step(N), List1, 0:List2, _:[]).
The idea here is to go through the list while tracking index of current element. While element index is below specified number N we essentially do nothing. After index becomes equal to N, we start building output list by appending all remaining elements from source list.
Not effective, but you still might be interested in the solution, as it demonstrates usage of a very powerful foldl predicate, which can be used to solve wide range of list processing problems.
Counting down should work fine
removeN([],K,[]) :- K>=0.
removeN(X,0,X).
removeN([_|R],K,Y) :- K2 is K-1, removeN(R,K2,Y).
This works for me.
I think this is the easiest way to do this.
trim(L,N,L2). L is the list and N is number of elements.
trim(_,0,[]).
trim([H|T],N,[H|T1]):-N1 is N-1,trim(T,N1,T1).
I want to count the number of elements in a list which have a relation with the element following.
The predicate I have works by using an accumulator variable which it increments if the predicate related returns true.
The following example code is to check the number of times an element is greater than it's previous element.
So for example
count_list([1,2,3,2,1,3,2],Count).
should return 3.
The code almost works. It increments the accumulator variable correctly. However, the function returns false, when it tries to compare the final 2 at the end with the non-existent next term.
listofitems([],N,N).
%count number of items which are related to the previous
listofitems([A,B|T],Acc,N) :-
write(A),write(' '), write(B),
( related(A,B) -> Acc1 is Acc+1 ; Acc1 = Acc ),
write(Acc1),write('\n'),
listofitems([B|T],Acc1,N).
count_list(L,N):-
listofitems(L,0,N).
%define the relationship to be counted
related(A,B):-
B>A.
Does anyone have any suggestions as to how to create an elegant terminating condition so I can return the accumulated value?
Does anyone have any suggestions as to how to create an elegant terminating condition so I can return the accumulated value?
The problem you have is that your query fails. Try first to minimize the query as much as possible. Certainly, you expect it to work for:
?- listofitems([], Count).
Count = 0.
Yet, it already fails for:
?- listofitems([1], Count).
false.
So let's try to dig into the reason for that.
And since your program is pure (apart from those writes), it is possible to diagnose this a little better by considering a generalization of your program. I prefer to look at such generalizations as I do not want to read too much (eye strain and such):
:- op(950, fy, *).
*_.
listofitems([], N,N).
listofitems([A,B|T], Acc,N) :-
* ( related(A,B) -> Acc1 is Acc+1 ; Acc1 = Acc ),
* listofitems([B|T], Acc1,N).
count_list(L,N):-
listofitems(L,0,N).
?- count_list([1], Count).
false.
Even this generalization fails! So now in desperation I try to ask the most general query. It's like when I ask one thing after the other and get a noe after a no. Good this is Prolog, for we can ask: "Say me just everything you know".
?- count_list(Es,Count).
Es = [], Count = 0
; Es = [_,_|_].
So it is only the case for the empty list and lists with at least two elements. But there is no answer for one-elemented lists! You will thus have to generalize the program somehow.
A natural way would be to add a fact
listofitems([_], N, N).
As a minor remark, this isn't called a "terminating condition" but rather a "base case".
And if you really want to trace your code, I recommend these techniques instead of adding manual writes. They are much too prone to error.
If the all list items are integers and your Prolog system supports clpfd, you can proceed like this:
:- use_module(library(clpfd)).
:- use_module(library(lists), [last/3]).
:- use_module(library(maplist), [maplist/4]).
To relate adjacent items, look at two sublists of [E|Es], Es and Fs. If, say,
[E|Es] = [1,2,3,2,1,3,2] holds ...
... then Fs lacks the last item (Fs = [1,2,3,2,1,3,2]) ...
... and Es lacks the first item (Es = [1,2,3,2,1,3,2]).
maplist/4 and i0_i1_gt01/3 map corresponding list items in Fs and Es to 0 / 1:
i_j_gt01(I, J, B) :- % if I #< J then B #= 1
I #< J #<=> B. % if I #>= J then B #= 0
?- maplist(i_j_gt01, [1,2,3,2,1,3], [2,3,2,1,3,2], Bs).
Bs = [1,1,0,0,1,0].
Last, sum up [1,1,0,0,1,0] using sum/3:
?- sum([1,1,0,0,1,0], #=, N).
N = 3.
Let's put it all together!
count_adj_gt([E|Es], N) :-
last(Fs, _, [E|Es]), % or: `append(Fs, [_], [E|Es])`
% or: `list_butlast([E|Es], Fs)`
maplist(i_j_gt01, Es, Fs, Bs),
sum(Bs, #=, N).
Sample query using SICStus Prolog 4.3.2:
?- count_adj_gt([1,2,3,2,1,3,2], N).
N = 3. % succeeds deterministically
not sure about
an elegant terminating condition
my whole code would be
?- Vs=[1,2,3,2,1,3,2], aggregate_all(count, (append(_,[X,Y|_], Vs), X<Y), Count).
That's all...
If you need something more complex, remember that library(clpfd) has more to offer.
I'm trying to create a list in Prolog (SWI Prolog) and check which numbers are powers of 2 and second find how many times a specific number is in the list (in this example I'm trying to find how many times the number 3 is in the list).
For a example, if you ask
?- check([0,2,3,-5,-2,1,8,7,4], MULT2, THREE).
you should see
MULT2=[2,8,4]
THREE=1
My first try to find a solution is to search the list with head and doing head mod 2 = 0 to find all numbers which are powers of 2, but something went wrong and I only get "false" as an answer.
Here's how you can find the "powers of two" in logically-pure way!
Using sicstus-prolog 4.3.5, library(reif) and library(clpz):
:- use_module([library(reif), library(clpz)]).
power_of_two_t(I, T) :-
L #= min(I,1),
M #= I /\ (I-1),
call((L = 1, M = 0), T). % using (=)/3 and (',')/3 of library(reif)
Sample query1 using meta-predicate tfilter/3 in combination with power_of_two_t/2:
?- tfilter(power_of_two_t, [0,2,3,-5,-2,1,8,7,4], Ps).
Ps = [2,1,8,4]. % succeeds deterministically
Here's a more general query suggested by a comment:
?- tfilter(power_of_two_t, [X], Ps).
Ps = [X], 0#=X/\_A, _A+1#=X, X in 1..sup, _A in 0..sup
; Ps = [], dif(_A,0), _A#=X/\_B, _B+1#=X, X in 1..sup, _B in 0..sup
; Ps = [], dif(_A,1), _A#=min(X,1), _B#=X/\_C, _C+1#=X, X#>=_A, _A in inf..1.
Footnote 1: The answer sequences shown above were brushed up to indicate the determinism of calls.
Footnote 2: To reproduce the results use call_det/2 which is defined like this:
call_det(G_0, Det) :-
call_cleanup(G_0, Flag = set),
( nonvar(Flag)
-> Det = true
; Det = false
).
It's a strange thing to have two such a different tasks to do in one predicate. You should probably have two separate predicates, one for counting number of powers of 2 and one to count 3s. Then you can combine them in one predicate like:
check(Nums, MULT2, THREE) :-
count2powers(Nums, MULT2),
count3s(Nums, THREE).
After that you can decompose further and have a separate predicate to check if a number is a power of 2:
is2power(1).
is2power(N) :-
N > 0,
N2 is N // 2,
N2 * 2 =:= N,
is2power(N2).
This is basic software engineering and this way you can build your program step by step and you will be able to ask more concrete and meaningful questions than just "The whole program returns false."
Im new to Prolog and was looking for some assistance. What i am trying to do is basically get a list L consisting of elements that repeat at least twice in a given list L'
Example
L'=[1,2,1,3,4,3,2] => L=[1,2,3].
So far I am able to compute the occurrence of every consecutive variables
% pack(L1,L2) :- the list L2 is obtained from the list L1 by packing
% repeated occurrences of elements into separate sublists.
% (list,list) (+,?)
pack([],[]).
pack([X|Xs],[Z|Zs]) :- transfer(X,Xs,Ys,Z), pack(Ys,Zs).
% transfer(X,Xs,Ys,Z) Ys is the list that remains from the list Xs
% when all leading copies of X are removed and transfered to Z
transfer(X,[],[],[X]).
transfer(X,[Y|Ys],[Y|Ys],[X]) :- X \= Y.
transfer(X,[X|Xs],Ys,[X|Zs]) :- transfer(X,Xs,Ys,Zs).
% encode(L1,L2) :- the list L2 is obtained from the list L1 by run-length
% encoding. Consecutive duplicates of elements are encoded as terms [N,E],
% where N is the number of duplicates of the element E.
% (list,list) (+,?)
encode(L1,L2) :- pack(L1,L), transform(L,L2).
transform([],[]).
transform([[X|Xs]|Ys],[[N,X]|Zs]) :- length([X|Xs],N), transform(Ys,Zs).
which will return the following list of touples
?- encode([a,a,a,a,b,c,c,a,a,d,e,e,e,e],X).
X = [[4,a],[1,b],[2,c],[2,a],[1,d][4,e]]
But there still remains the problem of building a list that will contain distinct elements that repeat at least twice.
If anyone can help me or point me in the general direction that would be great.
Thanks in advance
an element E of list L should:
be a member of list L',
be a member of list L'' where L'' is list L' if we remove element E.
check select/3, member/2, findall/3 and/or setof/3
You could write a procedure:
% E it's the list of are elements from L that repeat at least twice
elements_that_repeat_at_least_twice(L, E) :-
elements_that_repeat_at_least_twice(L, [], E).
elements_that_repeat_at_least_twice([H|Ls], Dupl, E) :-
...
In elements_that_repeat_at_least_twice the added list Dupl will keep each element you verify it's present multiple times. Examine each element of L, using [H|Ls].
Use memberchk/2 to verify if H is in L: then it's at least duplicate. If it's not yet in Dupl, add to it, and recurse. Remember to write the recursion base case (stop at empty list []).
Now I see you have added some code: then I complete suggestion:
elements_that_repeat_at_least_twice([], Dupl, Dupl).
elements_that_repeat_at_least_twice([H|Ls], Dupl, E) :-
( memberchk(H, Ls)
-> ( \+ memberchk(H, Dupl)
-> Dupl1 = [H|Dupl]
; Dupl1 = Dupl
)
; Dupl1 = Dupl
),
elements_that_repeat_at_least_twice(Ls, Dupl1, E).
Remember to reverse the list of duplicates when done.