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I'm creating a predicate enum that takes a list and a number for example [1,2,3,4] and 3 and returns a list that contains lists of length 3 made out of the list introduced. So in the example given enum([1,2,3,4],3,[[1,2,3],[2,3,4]]).
I've created a function take that takes only the first list of length N but I get errors when I try to loop it to get all of the others. Thanks you for helping.
append([],L,L).
append([H|T],L2,[H|L3]):- append(T,L2,L3).
len([],0).
len([_|B],X):- len(B,X1), X is X1+1.
take(_,X,Y) :- X =< 0, !, X =:= 0, Y = [].
take([],_,[]).
take([A|B],X,[A|C]):- Z is X-1, take(B,Z,C).
enum([],_,[]).
enum([N1|N2],N3,N4):-
len([N1|N2],U),
N3=<U,
take([N1|N2],N3,T1),
append([N4],[T1],T2),
!,
enum(N2,N3,T2).
I will focus on the take/3 predicate, which is the core of your question. In order to get a sublist like [2,3,4] of [1,2,3,4], you have to be able to skip the first element and just take a sublist of the rest.
You can achieve this by adding this clause to your definition:
take([_|Xs], N, Ys) :- take(Xs, N, Ys).
With this you now get several different sublists of length 3, but also some other superfluous solutions:
?- take([1,2,3,4], 3, Xs).
Xs = [1, 2, 3] ;
Xs = [1, 2, 4] ;
Xs = [1, 2] ;
Xs = [1, 3, 4] ;
Xs = [1, 3] ;
Xs = [1, 4] ;
Xs = [1] % etc.
This is because your clause take([], _, []) accepts an empty list as a "sublist of any length" of an empty list. I think you only wanted to accept the empty list as a sublist of length 0. If you remove this clause, your first clause will enforce that, and you only get solutions of length exactly 3:
?- take([1,2,3,4], 3, Xs).
Xs = [1, 2, 3] ;
Xs = [1, 2, 4] ;
Xs = [1, 3, 4] ;
Xs = [2, 3, 4] ;
false.
As a side note, your first clause is fine as is, but it can be simplified a bit to:
take(_,X,Y) :- X = 0, !, Y = [].
I would also advise you to use more readable variable names. For numbers like list lengths, we often use N. For lists, it's customary to use names like Xs, Ys, etc., with X, Y, etc. for members of the corresponding list.
Finally, to find all solutions of a predicate, you need to use a system predicate like setof, bagof, or findall. There is no way to write your enum in pure Prolog.
Because I am not sure about the advice in the other answer, here is my take on your problem.
First, don't define your own append/3 and length/2, append/3 is by now Prolog folklore, you can find it in textbooks 30 years old. And length/2 is really difficult to get right on your own, use the built-in.
Now: to take the first N elements at the front of a list L, you can say:
length(Front, N),
append(Front, _, L)
You create a list of the length you need, then use append/3 to split off this the front from the list you have.
With this in mind, it would be enough to define a predicate sliding_window/3:
sliding_window(L, N, [L]) :-
length(L, N).
sliding_window(L, N, [W|Ws]) :-
W = [_|_], % W should be at least one long
length(W, N),
append(W, _, L),
L = [_|L0],
sliding_window(L0, N, Ws).
This kind of works, but it will loop after giving you all useful answers:
?- sliding_window([a,b], N, Ws).
N = 2,
Ws = [[a, b]] ;
N = 1,
Ws = [[a], [b]] ;
% loops
It loops because of the same little snippet:
length(Front, N),
append(Front, _, L)
With length/2, you keep on generating lists of increasing length; once Front is longer than L, the append/3 fails, length/2 makes an even longer list, and so on forever.
One way out of this would be to use between/3 to constrain the length of the front. If you put it in its own predicate:
front_n(L, N, F) :-
length(L, Max),
between(1, Max, N),
length(F, N),
append(F, _, L).
With this:
sliding_window(L, N, [L]) :-
length(L, N).
sliding_window(L, N, [W|Ws]) :-
front_n(L, N, W),
L = [_|L0],
sliding_window(L0, N, Ws).
And now it finally works:
?- sliding_window([a,b,c,d], 3, Ws).
Ws = [[a, b, c], [b, c, d]] ;
false.
?- sliding_window([a,b,c], N, Ws).
N = 3,
Ws = [[a, b, c]] ;
N = 1,
Ws = [[a], [b], [c]] ;
N = 2,
Ws = [[a, b], [b, c]] ;
false.
Exercise: get rid of the harmless, but unnecessary choice point.
I am trying to compute arithmetic calculations and store the results in a new list in Prolog.
The function prototype goes as follows:
calculation(List1, ListofLists, ResultList)
for the first argument I provide a list, for the second argument a list of lists and third the result list. I compute the first argument list with each list of list of lists and store the result in the resulting list.
So can somebody tell me how can I store results in the resulting (empty) list?
With library lambda you can write:
:- use_module(library(lambda)).
:- use_module(library(clpfd)).
calculation(L1, L2, Compute, L) :-
maplist([L2,Compute] +\X^Y^call(Compute,L2, X, Y), L1, L).
% my_compute succeeds when R is the list of all the products
% of the numbers component of L with the number V
my_compute(L, V, R) :-
maplist(V +\X^Y^maplist(V +\Z^T^(T #= Z * V), X, Y), L, R).
Here is an example:
?- calculation([1,2,3], [[4,5],[6,7]], my_compute, Zss).
Zss = [[[4, 5], [6, 7]], [[8, 10], [12, 14]], [[12, 15], [18, 21]]].
?- Zss = [[[4,5],[6,7]],[[8,10],[12,14]],[[12,15],[18,21]]],
calculation(Xs, [[4,5],[6,7]], my_compute, Zss).
Xs = [1, 2, 3].
?- Zss = [[[4,5],[6,7]],[[8,10],[12,14]],[[12,15],[18,21]]],
calculation([1,2,3], Xss, my_compute, Zss).
Xss = [[4, 5], [6, 7]].
calculation([], [], []).
calculation([X|Xs], [Y|Ys], [Z|Zs]) :-
calculate(X, Y, Z),
calculation(Xs, Ys, Zs).
which is identical to:
calculation(X, Y, Z) :-
maplist(calculate, X, Y, Z).
either way, you need a predicate calculate/3 that takes a first argument, a list of lists as the second argument, and calculates a result. For example, summing the list in the second argument and multiplying it to the first argument:
calculate(X, Ys, Z) :-
list_sum(Ys, S),
Z is X * S.
If I understood correctly, you want to do some computation on List1 and every member of ListofLists, and get a list of results.
You can do this using findall:
calculation(List1, ListofLists, ResultList) :-
findall(Result, (
member(List2, ListofLists),
your_computation(List1, List2, Result)
), ResultList).
For example, if you replace your_compuation with append, you get:
?- calculation([a,b],[[c,d],[e,f,g],[h]],X).
X = [[a, b, c, d], [a, b, e, f, g], [a, b, h]].
I am new to Prolog and when I query
sortedUnion([1,1,1,2,3,4,4,5], [0,1,3,3,6,7], [0,1,2,3,4,5,6,7]).
I get an error
Exception: (7) unite([_G114, _G162, _G201, _G231, _G243], [_G249, _G297, _G336, _G357, _G369], [0, 1, 2, 3, 4, 5, 6, 7]) ?
So I am hoping someone will be able to tell me where my code is mistaken and why it is wrong?
%undup(L, U) holds precisely when U can be obtained from L by eliminating repeating occurrences of the same element
undup([], []).
undup([X|Xs], [_|B]) :- remove(X,Xs,K), undup(K, B).
remove(_,[],[]).
remove(Y,[Y|T],D) :- remove(Y,T,D).
remove(Y,[S|T],[S|R]) :- not(Y = S), remove(Y,T,R).
%sortedUnion(L1,L2,U) holds when U contains exactly one instance of each element
%of L1 and L2
sortedunion([H|T], [S|R], [F|B]) :- undup([H|T], N), undup([S|R], M), unite(N,M,[F|B]).
unite([], [], []).
unite([X], [], [X]).
unite([], [X], [X]).
unite([H|T], [S|R], [X|Xs]) :- S=H, X is S, unite(T, R, Xs).
unite([H|T], [S|R], [X|Xs]) :- H<S, X is H, unite(T, [S|R], Xs).
unite([H|T], [S|R], [X|Xs]) :- S<H, X is S, unite([H|T], R, Xs).
An advice first: try to keep your code as simple as possible. Your code can reduce to this (that surely works)
sortedunion(A, B, S) :-
append(A, B, C),
sort(C, S).
but of course it's instructive to attempt to solve by yourself. Anyway, try to avoid useless complications.
sortedunion(A, B, S) :-
undup(A, N),
undup(B, M),
unite(N, M, S).
it's equivalent to your code, just simpler, because A = [H|T] and so on.
Then test undup/2:
1 ?- undup([1,1,1,2,3,4,4,5],L).
L = [_G2760, _G2808, _G2847, _G2877, _G2889] ;
false.
Clearly, not what you expect. The culprit should that anon var. Indeed, this works:
undup([], []).
undup([X|Xs], [X|B]) :- remove(X,Xs,K), undup(K, B).
2 ?- undup([1,1,1,2,3,4,4,5],L).
L = [1, 2, 3, 4, 5] ;
false.
Now, unite/3. First of all, is/2 is abused. It introduces arithmetic, then plain unification suffices here: X = S.
Then the base cases are hardcoded to work where lists' length differs at most by 1. Again, simpler code should work better:
unite([], [], []).
unite( X, [], X).
unite([], X, X).
...
Also, note the first clause is useless, being already covered by (both) second and third clauses.
I want to write a prolog predicate with the following output:
?- all_match([1,2,3,2,3,1,2],L).
L = [[], [1], [1, 2], [2], [2, 3], [3]].
?- all_match([1,1,1,2],L).
L = [[], [1], [1, 1]].
The purpose is to find the sublists that repeat more than once.
So far I found the solution to find all sublists in a list-
subSet(_, []).
subSet(L, [S|T]) :- append(_, L2,L), append([S|T], _, L2).
But I can't figure out how to repeat the search for every element.
Thanks in advance.
This code is a little different from your requirements, in that all_match/2 will omit the empty sequence and fail if there where no repeated subsequences in the input.
repeated(List, Sublist) :-
% For all prefixes, suffixes:
append(Sublist, Tail, List), Sublist \= [],
% For all suffixes of the former suffixes:
append(_, TailTail, Tail),
% Is the head of the latter suffix equal to the head of the input?
append(Sublist, _, TailTail).
repeated([_|List], Sublist) :-
% Strip leading character and continue
repeated(List, Sublist).
all_match(List, Lists) :-
% Aggregate all repeated sequences or fail if there weren't any.
setof(L, repeated(List, L), Lists).
A sketch of the idea of the first clause of repeated/2:
|----------------List------------------| repeated(List, Sublist)
|--Sublist--|------------Tail----------| append(Sublist, Tail, List)
|--Sublist--| |-----TailTail-----| append(_, TailTail, Tail)
|--Sublist--| |--Sublist--| | append(Sublist, _, TailTail)
Result:
?- all_match([1,2,3,2,3,1,2],L).
L = [[1], [1, 2], [2], [2, 3], [3]].
Update to allow overlapping sequences:
repeated([H|List], Sublist) :-
append(Sublist, _, [H|List]), Sublist \= [],
append(_, Tail, List),
append(Sublist, _, Tail).
repeated([_|List], Sublist) :-
repeated(List, Sublist).
I like Kay's answer (+1). Here a variation on thema
all_match(L, M) :-
take(L, M, R),
take(R, M, _).
take(L, [A|B], R) :- % use [A|B] to remove empties
append(_, T, L),
append([A|B], R, T).
yields
?- setof(L,all_match([1,2,3,2,3,1,2],L),R).
R = [[1], [1, 2], [2], [2, 3], [3]].
How do you get the product of a list from left to right?
For example:
?- product([1,2,3,4], P).
P = [1, 2, 6, 24] .
I think one way is to overload the functor and use 3 arguments:
product([H|T], Lst) :- product(T, H, Lst).
I'm not sure where to go from here.
You can use library(lambda) found here : http://www.complang.tuwien.ac.at/ulrich/Prolog-inedit/lambda.pl
Quite unreadable :
:- use_module(library(lambda)).
:- use_module(library(clpfd)).
product(L, R) :-
foldl(\X^Y^Z^(Y = []
-> Z = [X, [X]]
; Y = [M, Lst],
T #= X * M,
append(Lst, [T], Lst1),
Z = [T, Lst1]),
L, [], [_, R]).
Thanks to #Mike_Hartl for his advice, the code is much simple :
product([], []).
product([H | T], R) :-
scanl(\X^Y^Z^( Z #= X * Y), T, H, R).
seems like a list copy, just multiplying by last element handled. Let's start from 1 for the leftmost element:
product(L, P) :-
product(L, 1, P).
product([X|Xs], A, [Y|Ys]) :-
Y is X * A,
product(Xs, Y, Ys).
product([], _, []).
if we use library(clpfd):
:- [library(clpfd)].
product([X|Xs], A, [Y|Ys]) :-
Y #= X * A,
product(Xs, Y, Ys).
product([], _, []).
it works (only for integers) 'backward'
?- product(L, [1,2,6,24]).
L = [1, 2, 3, 4].
Probably very dirty solution (I am new to Prolog):
product([ListHead|ListTail], Answer) :-
product_acc(ListTail, [ListHead], Answer).
product_acc([ListHead|ListTail], [AccHead|AccTail], Answer) :-
Product is ListHead * AccHead,
append([Product, AccHead], AccTail, TempList),
product_acc(ListTail, TempList, Answer).
product_acc([], ReversedList, Answer) :-
reverse(ReversedList, Answer).
So basically at the beginning we call another predicate which has
extra "variable" Acc which is accumulator list.
So we take out head (first number) from original list and put it in
to Accumulator list.
Then we always take head (first number) from original list and
multiply it with head (first number) from accumulator list.
Then we have to append our new number which we got by multiplying
with the head from accumulator and later with the tail
Then we call same predicate again until original list becomes empty
and at the end obviously we need to reverse it.
And it seems to work
?- product([1,2,3,4], L).
L = [1, 2, 6, 24].
?- product([5], L).
L = [5].
?- product([5,4,3], L).
L = [5, 20, 60].
Sorry if my explanation is not very clear. Feel free to comment.