I would like to create a predicate that returns the element that most often appears, if there are more than one with the same number of occurrences the first:
occ([a,b,c,a,a,a,b],M).
yes M = a
occ([a,b,c,a,b],M).
yes M = a
Note that in Prolog you would generally create rules, not functions to solve this.
There are a number of ways to approach this, I'll provide two.
Recursion
One way is to recurse over the list, keeping a running count of occurrences, and with each call recording what the current max is, an example of use of an accumulator:
% find the X with the most occurrences N in a list L
occ(X,N,L) :-
occ(L,max(null,0),[],max(X,N)).
%% occ(+L, +CurrentMax, +Counts, +FinalMax) is det.
%
% recurse through L, using CurrentMax accumulator to
% store current candidate as a term `max(X,N)`
%
% Counts is a list in which we accumulate counts of
% occurrences to far, as list of element-count pairs X-N
%
% The final argument is unified with the CurrentMax
% accumulator as the base case
occ([], max(Xm, Nm), _, max(Xm, Nm)).
occ([X|L], max(Xm, Nm), Counts, FinalMax) :-
% get the current count of X
( select(X-N, Counts, CountsT)
->
N1 is N+1
;
N1 = 1,
CountsT = Counts),
% make a new list of counts with the
% original entry for X replaced by a new
% one with count of N+1
Counts2 = [X-N1 | CountsT],
% recurse, using either new current best candidate
% or same one depending on whether count is exceeded.
% in case of tie, use same one, thus prioritizing first result
( N1 > Nm
->
occ(L, max(X,N1), Counts2, FinalMax)
;
occ(L, max(Xm,Nm), Counts2, FinalMax)).
Example:
?- occ(X,N,[a,b,c,a,b]).
X = a,
N = 2.
Higher-order aggregate operations
An alternative approach is to use higher-order aggregate predicates. Arguably this leads to more declarative code, although tastes will vary. If you are using SWI-Prolog you can use the aggregate library. We can start with a rule to count occurrences in a list (note I'm going to switch from your occ/2 to more explicit predicates here):
% count number N of instances of X in a list L
element_count(X,N,L) :-
aggregate(count,member(X,L),N).
If you don't want to or can't use aggregate/3 then have a look at the answers to this question previously asked on stack overflow.
Next we can use aggregate/3 to find the maximum number for N, plus a "witness" (i.e. the value of X with the highest value):
% count number N of instances of X in a list L, for highest N
max_element_count(X,N,L) :-
aggregate(max(N1,X1),element_count(X1,N1,L),max(N,X)).
(I'll leave it to you to make an equivalent implementation of this rule if you're not using the aggregate library)
Let's try it:
?- max_element_count(X,N,[a,b,c,a,a,a,b]).
X = a,
N = 4.
With a tie it seems to satisfy your criterion of using the first occurrence in the case of tie-breakers:
?- max_element_count(X,N,[a,b,c,a,b]).
X = a,
N = 2.
But this is not in fact guaranteed - we just happen to choose a here as it is alphabetically before b. Let's try:
?- max_element_count(X,N,[b,a,c,a,b]).
X = a,
N = 2.
Oops!
This time we will find the first member of the list whose number of occurrences is equal to the max:
max_element_count2(X,N,L) :-
aggregate(max(N1),X1,element_count(X1,N1,L),N),
member(X,L),
element_count(X,N,L),
!.
This assumes that member/2 will unify with elements in order, which is the behavior I have always seen with Prologs but don't know off the top of my head if it is mandated by the standard.
To demonstrate:
?- max_element_count2(X,N,[b,a,c,a,b]).
X = b,
N = 2.
Related
I have a large numbers of facts that are already in my file (position(M,P)), M is the name and P is the position of the player , I am asked to do a player_list(L,N), L is the list of players and N is the size of this list. I did it and it works the problem is that it gives the list without the names it gives me numbers and not names
player_list([H|T],N):- L = [H|T],
position(H,P),
\+ member(H,L),
append(L,H),
player_list(T,N).
what I get is:
?- player_list(X,4).
X = [_9176, _9182, _9188, _9194] .
so what should I do ?
You could use an additional list as an argument to keep track of the players you already have. This list is empty at the beginning, so the calling predicate calls the predicate describing the actual relation with [] as an additional argument:
player_list(PLs,L) :-
pl_l_(PLs,L,[]). % <- actual relation
The definition you posted is missing a base case, that is, if you already have the desired amount of players, you can stop adding others. In this case the number of players to add is zero otherwise it is greater than zero. You also have to describe that the head of the list (PL) is a player (whose position you don't care about, so the variable is preceded by an underscore (_P), otherwise the goal is just like in your code) and is not in the accumulator yet (as opposed to your code, where you check if PL is not in L) but in the recursive call it is in the accumulator. You can achieve the latter by having [PL|Acc0] in the recursive goal, so you don't need append/2. Putting all this together, your code might look something like this:
pl_l_([],0,_). % base case
pl_l_([PL|PLs],L1,Acc0) :-
L1 > 0, % number of players yet to add
L0 is L1-1, % new number of players to add
position(PL,_P), % PL is a player and
\+ member(PL,Acc0), % not in the accumulator yet
pl_l_(PLs,L0,[PL|Acc0]). % the relation holds for PLs, L0 and [PL|Acc0] as well
With respect to your comment, I assume that your code contains the following four facts:
position(zlatan,center).
position(rooney,forward).
position(ronaldo,forward).
position(messi,forward).
Then your example query yields the desired results:
?- player_list(X,4).
X = [zlatan,rooney,ronaldo,messi] ? ;
X = [zlatan,rooney,messi,ronaldo] ? ;
...
If you intend to use the predicate the other way around as well, I suggest the use of CLP(FD). To see why, consider the most general query:
?- player_list(X,Y).
X = [],
Y = 0 ? ;
ERROR at clause 2 of user:pl_l_/3 !!
INSTANTIATION ERROR- =:=/2: expected bound value
You get this error because >/2 expects both arguments to be ground. You can modify the predicate pl_l_/3 to use CLP(FD) like so:
:- use_module(library(clpfd)).
pl_l_([],0,_).
pl_l_([PL|PLs],L1,Acc0) :-
L1 #> 0, % <- new
L0 #= L1-1, % <- new
position(PL,_P),
\+ member(PL,Acc0),
pl_l_(PLs,L0,[PL|Acc0]).
With these modifications the predicate is more versatile:
?- player_list([zlatan,messi,ronaldo],Y).
Y = 3
?- player_list(X,Y).
X = [],
Y = 0 ? ;
X = [zlatan],
Y = 1 ? ;
X = [zlatan,rooney],
Y = 2 ?
...
So I have this mathematical language, it goes like this:
E -> number
[+,E,E,E] //e.g. [+,1,2,3] is 1+2+3 %we can put 2 to infinite Es here.
[-,E,E,E] //e.g. [-,1,2,3] is 1-2-3 %we can put 2 to infinite Es here.
[*,E,E,E] //e.g. [*,1,2,3] is 1*2*3 %we can put 2 to infinite Es here.
[^,E,E] //e.g. [^,2,3] is 2^3
[sin,E] //e.g. [sin,0] is sin 0
[cos,E] //e.g. [cos,0] is cos 0
and I want to write the set of rules that finds the numeric value of a mathematical expression written by this language in prolog.
I first wrote a function called "check", it checks to see if the list is written in a right way according to the language we have :
check1([]).
check1([L|Ls]):- number(L),check1(Ls).
check([L|Ls]):-atom(L),check1(Ls).
now I need to write the function "evaluate" that takes a list that is an expression written by this language, and a variable that is the numeric value corresponding to this language.
example:
?-evaluate([*,1,[^,2,2],[*,2,[+,[sin,0],5]]]],N) -> N = 40
so I wrote this:
sum([],0).
sum([L|Ls],N):- not(is_list(L)),sum(Ls,No),N is No + L.
min([],0).
min([L|Ls],N):-not(is_list(L)), min(Ls,No),N is No - L.
pro([],0).
pro([X],[X]).
pro([L|Ls],N):-not(is_list(L)), pro(Ls,No), N is No * L.
pow([L|Ls],N):-not(is_list(L)), N is L ^ Ls.
sin_(L,N):-not(is_list(L)), N is sin(L).
cos_(L,N):-not(is_list(L)), N is cos(L).
d([],0).
d([L|Ls],N):- L == '+' ,sum(Ls,N);
L == '-',min(Ls,N);
L == '*',pro(Ls,N);
L == '^',pow(Ls,N);
L == 'sin',sin_(Ls,N);
L == 'cos',cos_(Ls,N).
evaluate([],0).
evaluate([L|Ls],N):-
is_list(L) , check(L) , d(L,N),L is N,evaluate(Ls,N);
is_list(L), not(check(L)) , evaluate(Ls,N);
not(is_list(L)),not(is_list(Ls)),check([L|Ls]),d([L|Ls],N),
L is N,evaluate(Ls,N);
is_list(Ls),evaluate(Ls,N).
and it's working for just a list and returning the right answer , but not for multiple lists inside the main list, how should my code be?
The specification you work with looks like a production rule that describes that E (presumably short for Expression) might be a number or one of the 6 specified operations. That is the empty list [] is not an expression. So the fact
evaluate([],0).
should not be in your code. Your predicate sum/2 almost works the way you wrote it, except for the empty list and a list with a single element, that are not valid inputs according to your specification. But the predicates min/2 and pro/2 are not correct. Consider the following examples:
?- sum([1,2,3],X).
X = 6 % <- correct
?- sum([1],X).
X = 1 % <- incorrect
?- sum([],X).
X = 0 % <- incorrect
?- min([1,2,3],X).
X = -6 % <- incorrect
?- pro([1,2,3],X).
X = 6 ? ; % <- correct
X = 0 % <- incorrect
Mathematically speaking, addition and multiplication are associative but subtraction is not. In programming languages all three of these operations are usually left associative (see e.g. Operator associativity) to yield the mathematically correct result. That is, the sequence of subtractions in the above query would be calculated:
1-2-3 = (1-2)-3 = -4
The way you define a sequence of these operations resembles the following calculation:
[A,B,C]: ((0 op C) op B) op A
That works out fine for addition:
[1,2,3]: ((0 + 3) + 2) + 1 = 6
But it doesn't for subtraction:
[1,2,3]: ((0 - 3) - 2) - 1 = -6
And it is responsible for the second, incorrect solution when multiplying:
[1,2,3]: ((0 * 3) * 2) * 1 = 0
There are also some other issues with your code (see e.g. #lurker's comments), however, I won't go into further detail on that. Instead, I suggest a predicate that adheres closely to the specifying production rule. Since the grammar is describing expressions and you want to know the corresponding values, let's call it expr_val/2. Now let's describe top-down what an expression can be: It can be a number:
expr_val(X,X) :-
number(X).
It can be an arbitrarily long sequence of additions or subtractions or multiplications respectively. For the reasons above all three sequences should be evaluated in a left associative way. So it's tempting to use one rule for all of them:
expr_val([Op|Es],V) :-
sequenceoperator(Op), % Op is one of the 3 operations
exprseq_op_val(Es,Op,V). % V is the result of a sequence of Ops
The power function is given as a list with three elements, the first being ^ and the others being expressions. So that rule is pretty straightforward:
expr_val([^,E1,E2],V) :-
expr_val(E1,V1),
expr_val(E2,V2),
V is V1^V2.
The expressions for sine and cosine are both lists with two elements, the first being sin or cos and the second being an expression. Note that the argument of sin and cos is the angle in radians. If the second argument of the list yields the angle in radians you can use sin/1 and cos/2 as you did in your code. However, if you get the angle in degrees, you need to convert it to radians first. I include the latter case as an example, use the one that fits your application.
expr_val([sin,E],V) :-
expr_val(E,V1),
V is sin(V1*pi/180). % radians = degrees*pi/180
expr_val([cos,E],V) :-
expr_val(E,V1),
V is cos(V1*pi/180). % radians = degrees*pi/180
For the second rule of expr_val/2 you need to define the three possible sequence operators:
sequenceoperator(+).
sequenceoperator(-).
sequenceoperator(*).
And subsequently the predicate exprseq_op_val/3. As the leading operator has already been removed from the list in expr_val/2, the list has to have at least two elements according to your specification. In order to evaluate the sequence in a left associative way the value of the head of the list is passed as an accumulator to another predicate exprseq_op_val_/4
exprseq_op_val([E1,E2|Es],Op,V) :-
expr_val(E1,V1),
exprseq_op_val_([E2|Es],Op,V,V1).
that is describing the actual evaluation. There are basically two cases: If the list is empty then, regardless of the operator, the accumulator holds the result. Otherwise the list has at least one element. In that case another predicate, op_val_args/4, delivers the result of the respective operation (Acc1) that is then recursively passed as an accumulator to exprseq_op_val_/4 alongside with the tail of the list (Es):
exprseq_op_val_([],_Op,V,V).
exprseq_op_val_([E1|Es],Op,V,Acc0) :-
expr_val(E1,V1),
op_val_args(Op,Acc1,Acc0,V1),
exprseq_op_val_(Es,Op,V,Acc1).
At last you have to define op_val_args/4, that is again pretty straightforward:
op_val_args(+,V,V1,V2) :-
V is V1+V2.
op_val_args(-,V,V1,V2) :-
V is V1-V2.
op_val_args(*,V,V1,V2) :-
V is V1*V2.
Now let's see how this works. First your example query:
?- expr_val([*,1,[^,2,2],[*,2,[+,[sin,0],5]]],V).
V = 40.0 ? ;
no
The simplest expression according to your specification is a number:
?- expr_val(-3.14,V).
V = -3.14 ? ;
no
The empty list is not an expression:
?- expr_val([],V).
no
The operators +, - and * need at least 2 arguments:
?- expr_val([-],V).
no
?- expr_val([+,1],V).
no
?- expr_val([*,1,2],V).
V = 2 ? ;
no
?- expr_val([-,1,2,3],V).
V = -4 ? ;
no
The power function has exactly two arguments:
?- expr_val([^,1,2,3],V).
no
?- expr_val([^,2,3],V).
V = 8 ? ;
no
?- expr_val([^,2],V).
no
?- expr_val([^],V).
no
And so on...
sumPicker([[]|_], Y, Z).
sumPicker([X|X1], Y, Z):-
downList(Y, X, Sum),
Total is Z,
Z is Total + Sum,
sumPicker(X1,Y, Z).
downList([Z|_], 1, Z).
downList([_|B],Count, Number):- Count > 1,
SendCount is Count - 1,
downList(B, SendCount, Number).
So this code is basically suppose to take in Two lists sumPicker([3,5], [1,2,3,4,5,6], X). The program then takes the first list and depending on the value of the number, so in this case 3, it will find the third number in the second list then it will find the 5th number of the second list and add them together.
ERROR: is/2: Arguments are not sufficiently instantiated is what i am getting
I'm assuming that your instructor would like you to work out the recursion yourself, rather than using built-in list operations. To that end, you could approach it something like this, using no built-ins at all.
A common prolog idiom is to have a simple "public" predicate that invokes a "helper" predicate that carries state (in this case, the current position in the list and the running sum). Often, that "helper" predicate will have the same functor (name) as the public predicate, with a higher arity (number of arguments).
So, first we have the public predicate, sum_of_desired/3:
sum_of_desired( Indices , Numbers , Sum ) :- % to sum certain list elements,
sum_of_desired( Indices , Numbers , 0 , Sum ) - % invoke the helper
. %
All it does is invoke the helper, sum_of_desired/4. This helper predicate carries an extra argument that is its state: an accumulator that contains the running sum. When it succeeds, that running sum is unified with the final total. This is because, in Prolog, you can't change the value of a variable: once you assign a value to a variable, it ceases to be variable. It become that with which it was unified (that's it's called unification). The only way to undo that assignment is via backtracking.
Typically, a recursive problem has a few special cases and a more general case. So, here, our helper predicate has 2 clauses:
The first clause is the special case: the list of desired indices is empty, in which case the finally sum is the current value of the accumulator (0 initially).
the second clause is the recursive general case: here we find the desired list item, add it to the running total and recurse down, moving on to the next item in the list of desired list items.
sum_of_desired( [] , _ , S , S ) . % the list of desired indices is empty: unify the accumulator with the result.
sum_of_desired( [I|Is] , L , T , S ) :- % otherwise...
get_nth_item(I,L,N) , % - get the nth item from the list
T1 is T+N , % - add it to the running total
sum_of_desired(Is,T1,S) % - and recurse down
. %
Finally, this predicate, get_nth_item/3, simple recursively walks the list, looking for the nth item in the list, where n is relative to 1 (e.g., the first item in the list is at index 1). When it finds it, it's returned as the 3rd argument of the predicate.
Again, here you will note that we have a single terminating special case and the more general recursive special case:
get_nth_item( 1 , [X|_] , X ) . % found it!
get_nth_item( N , [_|Xs] , R ) :- % otherwise...
N > 1 , % - if N > 1 ,
N1 is N-1 , % - decrement N
nth_item( N1 , Xs , R ) % - recurse down.
. % - easy!
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.
I want to implement a predicate (vecLine2BitLine) which does the following:
get two lists and a number the first list is the length of blocks (the elements of the blocks are '$') and the second list contains the indexes that these blocks should be placed at meaning:
vecLine2BitLine([1,2,1],[2,5,9],12,BitLine).
BitLine=[' ','$',' ',' ','$','$',' ',' ','$',' ',' ',' '].
explanation:a block of length 1 is at index 2
and a block of length 2 is at index 5 and so on..
insert_at_mul : inserts an element N times (it works perfectly,dupli and my_flatten were implemented previously so i used them)
Ive been trying to activate insert_at_mul N times when N is the length of the list X and Y
in the predicate vecLine2BitLine.
dupli(L1,N,L2) :- dupli(L1,N,L2,N).
dupli([],_,[],_).
dupli([_|Xs],N,Ys,0) :- dupli(Xs,N,Ys,N).
dupli([X|Xs],N,[X|Ys],K) :- K > 0, K1 is K - 1, dupli([X|Xs],N,Ys,K1).
my_flatten(X,[X]) :- \+ is_list(X).
my_flatten([],[]).
my_flatten([X|Xs],Zs) :- my_flatten(X,Y), my_flatten(Xs,Ys), append(Y,Ys,Zs).
insert_at_mul(L,X,K,R,N):-dupli([X],N,XX) , insert_at(L,XX,K,L1) , my_flatten(L1,R).
get_num_spaces(L,N,X):-sum(L,S), X is N-S.
generate_spaces(N,L,X):- insert_at_mul(L,'',1,X,N).
vecLine2BitLineAux([],[],_,_,_).
vecLine2BitLineAux([X|Tail1],[Y|Tail2],N,L,Lnew):- insert_at_mul(L,'*',Y,Lnew,X) ,vecLine2BitLineAux(Tail1,Tail2,N,Lnew,R). // problem here!!!
vecLine2BitLine(X,Y,N,L):- get_num_spaces(X,N,Z) , generate_spaces(Z,[],ZZ) , vecLine2BitLineAux(X,Y,N,ZZ,L).
now the problem is that in the function vecLine2BitLine i cant activate insert_at_mul N times(thats what i tried to do in this code, but failed).
how can I fix vecLine2BitLine for it to work properly as in returning the correct output by actually activating the predicate insert_at_mul N times??
THANKS!
added :
vecLine2BitLine : input parameters : (L1,L2,N,Result)
N: after activating the predicate Result will be N in length.
L1: L1 is a list of numbers each number indicates the length of a block, a block is comprised of a Sequence of '$'.
L2: L2 is a list of numbers the numbers are indices for where the blocks in L1 should be placed.
example:
vecLine2BitLine([3,2],[1,5],9,BitLine).
we can look at the input better as tuples :
vecLine2BitLine[(3,1),(2,5)],9,BitLine).
(3,1) : there is a sequence of '' 3 times at index 1
(2,5) : there is a sequence of '' 2 times at index 5
in our example 9 is the length of BitLine at the end and we have to insert into the
list BitLine 3+2 of the "special chars" '*' but we have 9-(3+2) places left in the list
so we add '' in those places and then we get:
BitLine=['$','$','$','','$','$','','','',''].
This is kind of a nice problem because you can use the arguments as loop counters. The K argument gets you to the proper index. Let's just traverse the list and find a particular index as an example. Notice the base case is that you're at the right element, and the inductive case is prior to the right element.
traverse(1, [X|_], X).
traverse(N, [_|Xs], X) :- N > 0, N0 is N-1, traverse(N0, Xs, X).
We're going to apply that pattern to insert_at/4 to get to the right location in the list. Now let's write a repeat/3 predicate that repeats X N times in a new list L. This time the base case is when we've added all the repetitions we care to, and the inductive case is that we'll add another instance.
repeat(1, X, [X]).
repeat(N, X, [X|Xs]) :- N > 0, N0 is N-1, repeat(N0, X, Xs).
You can see the similarity of structure between these two. Try to combine them into a single predicate. Since this is homework, I'll stop here. You're inches from the goal.