How to append number to list in prolog? - list

I am very new to Prolog. My goal is to append integers to a list, up to a bound:
if the function receives N, it outputs a list [N, N-1, ... , 1].
Here is my code:
myAppend(0, L) :- append([],[], L).
myAppend(N, L) :- append([N], [], L), N1 is N - 1, myAppend(N1, L).
invoking the function above returns false for every N=\=0:
51 ?- myAppend(0,L).
L = [] ;
false.
52 ?- myAppend(2,L).
false. <-------------------- was expecting L = [2, 1]
53 ?-
However, when i changed my function to (put a dot . instead of , after call to append in the 2nd rule):
myAppend(0, L) :- append([],[],L).
myAppend(N,L) :- append([N], [], L). N1 is N - 1, myAppend(N1, L).
I got the following output:
51 ?- myAppend(0,L).
L = [] ;
false.
52 ?- myAppend(4,L).
L = [4] . <-------------- was expecting [4, 3, 2, 1]
53 ?-
I am unable to understand why in the 1st implementation I was receiving false, although the logic behind it is correct?

What about
myAppend(0, []).
myAppend(N, [N | L]) :-
N > 0,
N1 is N - 1,
myAppend(N1, L).
?

Related

Remove leading zeros in list in Prolog

I have a list with an unknown number of zeros at the beginning of it, for example [0, 0, 0, 1, 2, 0, 3]. I need this list to be stripped of leading zeros, so that it would look like [1, 2, 0 , 3].
Here's what I have:
lead([Head | _], _) :- Head =\= 0.
lead([0 | Tail], _) :-
lead(Tail, Tail).
The output of which is simply True. Reading the trace shows that it is running until it has a list with no leading zeros, but then the answer doesn't propagate back up the stack. I'm pretty new to Prolog, so I can't figure out how to make it do that.
Here is a solution that works in all directions:
lead([],[]).
lead([H|T],[H|T]) :-
dif(H,0).
lead([0|T],T2) :-
lead(T,T2).
Some queries:
?- lead([0,0,0,1,2,0,3], L).
L = [1, 2, 0, 3] ;
false.
?- lead(L, []).
L = [] ;
L = [0] ;
L = [0, 0] ;
L = [0, 0, 0] ;
...
?- lead(L0, L).
L0 = L, L = [] ;
L0 = L, L = [_G489|_G490],
dif(_G489, 0) ;
L0 = [0],
L = [] ;
L0 = [0, _G495|_G496],
L = [_G495|_G496],
dif(_G495, 0) ;
L0 = [0, 0],
L = [] ;
L0 = [0, 0, _G501|_G502],
L = [_G501|_G502],
dif(_G501, 0) ;
L0 = [0, 0, 0],
L = [] ;
...
EDIT This predicate actually doesn't work for e.g. lead(L0, [0,1,2]).
With library(reif):
:- use_module(reif).
remove_leading_zeros([], []).
remove_leading_zeros([H|T], Rest) :-
if_( H = 0,
remove_leading_zeros(T, Rest),
Rest = [H|T]).
Then:
?- remove_leading_zeros([0,0,0,1,2,0,3], R).
R = [1, 2, 0, 3].
?- remove_leading_zeros([2,0,3], R).
R = [2, 0, 3].
?- remove_leading_zeros(L, R).
L = R, R = [] ;
L = [0],
R = [] ;
L = [0, 0],
R = [] ;
L = [0, 0, 0],
R = [] . % and so on
Here is a solution that actually works for all possible inputs and doesn't leave unnecessary choice points:
lead(L0, L) :-
( nonvar(L),
L = [H|_] ->
dif(H,0)
;
true
),
lead_(L0, L).
lead_([], []).
lead_([H|T], L) :-
if_(H \= 0,
L = [H|T],
lead_(T,L)).
The initial check for nonvar(L) is the only solution I have been able to come up with that would prevent problems with e.g. lead(L0, [0,1,2,3]), while retaining the behavior of the predicate in all other situations.
This uses if_/3, part of library(reif)
if_(If_1, Then_0, Else_0) :-
call(If_1, T),
( T == true -> Then_0
; T == false -> Else_0
; nonvar(T) -> throw(error(type_error(boolean,T),
type_error(call(If_1,T),2,boolean,T)))
; throw(error(instantiation_error,instantiation_error(call(If_1,T),2)))
).
This also uses (\=)/3, that I came up with by simple modification of (=)/3 in library(reif).
\=(X, Y, T) :-
( X \= Y -> T = true
; X == Y -> T = false
; T = true, dif(X, Y)
; T = false,
X = Y
).
Some queries
?- lead([0,0,0,1,2,0,3],L). % No choice point
L = [1, 2, 0, 3].
?- lead([1,2,0,3],L).
L = [1, 2, 0, 3].
?- lead([0,0,0,0],L).
L = [].
?- lead([],L).
L = [].
?- lead(L0,[0,1,2,0,3]). % Correctly fails
false.
?- lead(L0,[1,2,0,3]).
L0 = [1, 2, 0, 3] ;
L0 = [0, 1, 2, 0, 3] ;
L0 = [0, 0, 1, 2, 0, 3] ;
…
?- lead(L0,L). % Exhaustively enumerates all cases:
L0 = L, L = [] ; % - LO empty
L0 = L, L = [_G2611|_G2612], % - L0 contains no leading 0
dif(_G2611, 0) ;
L0 = [0], % - L0 = [0]
L = [] ;
L0 = [0, _G2629|_G2630], % - L0 contains one leading 0
L = [_G2629|_G2630],
dif(_G2629, 0) ;
L0 = [0, 0], % - L0 = [0, 0]
L = [] ;
L0 = [0, 0, _G2647|_G2648], % - L0 contains two leading 0s
L = [_G2647|_G2648],
dif(_G2647, 0) ;
… % etc.
Here is a solution that doesn't generate any choice points. Its
using freeze/2, in a way that is not anticipated by dif/2. But using
freeze/2 here is quite appropriate, since one rule of thumb for freeze/2
is as follows:
Rule of Thumb for freeze/2: Use freeze/2 where the predicate would
generate uninstantiated solutions and a lot of choice points. The hope
is that a subsequent goal will specify the solution more, and the
freeze/2 will be woken up. Unfortunately doesn't work with CLP(FD) or
dif/2, since freeze/2 does not react to refinements implied by CLP(FD)
or dif/2, only unification will wake it up.
The code is thus:
lead(X, Y) :- var(X), !, freeze(X, lead(X,Y)).
lead([X|Y], Z) :- var(X), !, freeze(X, lead([X|Y],Z)).
lead([0|X], Y) :- !, lead(X, Y).
lead(X, X).
Here are some sample runs (SWI-Prolog without some import, Jekejeke Prolog use Minlog Extension and ?- use_module(library(term/suspend))):
?- lead([0,0,0,1,2,3], X).
X = [1, 2, 3].
?- lead([0,0|X], Y).
freeze(X, lead(X, Y)).
?- lead([0,0|X], Y), X = [0,1,2,3].
X = [0, 1, 2, 3],
Y = [1, 2, 3].
?- lead([Z,0|X], Y), X = [0,1,2,3].
X = [0, 1, 2, 3],
freeze(Z, lead([Z, 0, 0, 1, 2, 3], Y)).
?- lead([Z,0|X], Y), X = [0,1,2,3], Z = 0.
Z = 0,
X = [0, 1, 2, 3],
Y = [1, 2, 3].
In the above lead/2 implemetation only the first argument is handled. To handle multiple arguments simultaneously the predicate when/2 can be used. But for simplicity this is not shown here.
Also when using suspended goals, one might need a labeling like predicate at the end, since suspended goals cannot detect inconsistency among them.
The problem in your code is that the second parameter, your output, is specified as _, so your predicate is true for any output. What you want is a predicate that is true if and only if it is the input minus leading zeroes.
lead([], []).
lead([0 | Tail], Tail2) :- !, lead(Tail, Tail2).
lead([Head | Tail], [Head | Tail]) :- Head =\= 0.
The ! in the first line is optional. It prunes the search tree so Prolog does not consider the second line (which would fail) if the first line matches.
Here's how I'd phrase it. First, establish constraints: either X or Y must be bound to a list. Anything else fails.
If X is bound, we don't care about Y: it can be bound or unbound. We just strip any leading zeros from X and unify the results with Y. This path has a single possible solution.
If X is unbound and Y is bound, we shift into generative mode. This path has an infinite number of possible solutions.
The code:
strip_leading_zeros(X,Y) :- listish(X), !, rmv0( X , Y ) .
strip_leading_zeros(X,Y) :- listish(Y), !, add0( Y , X ) .
rmv0( [] , [] ) .
rmv0( [D|Ds] , R ) :- D \= 0 -> R = [D|Ds] ; rmv0(Ds,R) .
add0( X , X ) .
add0( X , Y ) :- add0([0|X],Y ) .
listish/1 is a simple shallow test for listish-ness. Use is_list/1 if you want to be pedantic about things.
listish( L ) :- var(L), !, fail.
listish( [] ) .
listish( [_|_] ) .
Edited to note: is_list/1 traverses the entire list to ensure that it is testing is a properly constructed list, that is, a ./2 term, whose right-hand child is itself either another ./2 term or the atom [] (which denotes the empty list). If the list is long, this can be an expensive operation.
So, something like [a,b,c] is a proper list and is actually this term: .(a,.(b,.(c,[]))). Something like [a,b|32] is not a proper list: it is the term .(a,.(b,32)).

Prolog lists of ascending number inside a list

I Have a list of [1,2,3,1,0] at start but need to split it into a number of sub lists where the new lists becomes [[1,2,3],[1],[0]].
The basic concept that I know in prolog is by comparing numbers.
ascending([Head | [HeadTail|TailTail]]) :- Head =< HeadTail.
we can do with basic list' pattern matching
ascending([A], [[A]]).
ascending([A,B|T], R) :-
( A > B -> R = [[A],P|Q] ; P = [M|N], R = [[A,M|N]|Q] ),
ascending([B|T], [P|Q]).
test:
1 ?- ascending([1,2],X).
X = [[1, 2]] ;
false.
2 ?- ascending([2,1],X).
X = [[2], [1]] ;
false.
3 ?- ascending([1,2,3,1,0],X).
X = [[1, 2, 3], [1], [0]] ;
false.
% Trivial base case
asc([],[]).
% Invoke helper
asc([Ah|Ar],B) :- asc(Ar,[Ah],[],B).
% asc(InputList, CurrentSublistReversed, PreviousSublistsReversed, Result )
% No more input; add unreversed CurrentSublist & unreverse result
asc([],A,C,D) :- reverse(A,Ar), reverse([Ar|C],D).
% Next value gets added to head of current reversed sublist
asc([Ah|Ar],[Bh|Bt],C,D) :- Ah >= Bh, asc( Ar, [Ah,Bh|Bt], C, D).
% Unreverse current sblist, add to head of reversed list of previous sublists; start new sublist
asc([Ah|Ar],[Bh|Bt],C,D) :- Ah < Bh, reverse( [Bh|Bt], Br ), asc( Ar, [Ah], [Br|C], D ).

Prolog: Take the first "N" elements of a list

I need to write a Prolog predicate take(L, N, L1) which succeeds if list L1 contains the first N elements of list L, in the same order. For example:
?- take([5,1,2,7], 3, L1).
L1 = [5,1,2]
?- take([5,1,2,7], 10, L1).
L1 = [5,1,2,7]
Prolog thus far is making little sense to me, and I'm having a hard time breaking it down. Here is what I have so far:
take([H|T], 0, []).
take([H|T], N, L1) :-
take(T, X, L2),
X is N-1.
Can you please explain what I did wrong here?
Here is a definition that implements the relational counterpart to take in functional languages like Haskell1. First, the argument order should be different which facilitates partial application. There is a cut, but only after the error checking built-in (=<)/2 which produces an instantiation_error should the argument contain a variable.
take(N, _, Xs) :- N =< 0, !, N =:= 0, Xs = [].
take(_, [], []).
take(N, [X|Xs], [X|Ys]) :- M is N-1, take(M, Xs, Ys).
?- take(2, Xs, Ys).
Xs = [], Ys = []
; Xs = [_A], Ys = [_A]
; Xs = [_A,_B|_C], Ys = [_A,_B].
Note how above query reads:
How can one take 2 elements from Xs to get Ys?
And there are 3 different answers. If Xs is empty, then so is Ys. If Xs is a list with one element, then so is Ys. If Xs has at least 2 elements, then those two are Ys.
1) The only difference being that take(-1, Xs,Ys) fails (for all Xs, Ys). Probably the best would be to issue a domain_error similar to arg(-1,s(1),2)
findall/3 it's a bit the 'swiss knife' of Prolog. I would use this snippet:
take(Src,N,L) :- findall(E, (nth1(I,Src,E), I =< N), L).
The code by #CapelliC works if the instantiation is right; if not, it can show erratic behavior:
?- take(Es, 0, Xs).
**LOOPS** % trouble: goal does not terminate
?- take([A,_], 1, [x]).
true. % trouble: variable A remains unbound
To safeguard against this you can use
iwhen/2 like so:
take(Src, N, L) :-
iwhen(ground(N+Src), findall(E, (nth1(I,Src,E), I =< N), L)).
Sample queries run with SWI-Prolog 8.0.0:
?- take([a,b,c,d,e,f], 3, Ls).
Ls = [a,b,c].
?- take([a,b,c,d,e,f], N, Ls).
ERROR: Arguments are not sufficiently instantiated
?- take(Es, 0, Xs).
ERROR: Arguments are not sufficiently instantiated
?- take([A,_], 1, [x]).
ERROR: Arguments are not sufficiently instantiated
Safer now!
The obvious solution would be:
take(List, N, Prefix) :-
length(List, Len),
( Len =< N
-> Prefix = List
; length(Prefix, N),
append(Prefix, _, List)
).
Less thinking means less opportunity for mistakes. It also makes the predicate more general.
your base case is fine
take([H|T], 0, []).
And also you can say what if N is 1
take([H|T],1,[H]).
But you recursive case some variable is not defined like L2. So we can write this as
take([X|T1],N,[X|T2]):-
N>=0,
N1 is N-1,
take(T1,N1,T2).
which case all varibles are pattern-matched.
take(L, N, L1) :- length(L1, N), append(L1, _, L).
This is performant, general and deterministic:
first_elements_of_list(IntElems, LongLst, ShortLst) :-
LongLst = [H|T],
( nonvar(IntElems) -> Once = true
; is_list(ShortLst) -> Once = true
; Once = false
),
first_elements_of_list_(T, H, 1, IntElems, ShortLst),
(Once = true -> ! ; true).
first_elements_of_list_([], H, I, I, [H]).
first_elements_of_list_([_|_], H, I, I, [H]).
first_elements_of_list_([H|LongLst], PrevH, Upto, IntElems, [PrevH|ShortLst]) :-
Upto1 is Upto + 1,
first_elements_of_list_(LongLst, H, Upto1, IntElems, ShortLst).
Result in swi-prolog:
?- first_elements_of_list(N, [a, b, c], S).
N = 1,
S = [a] ;
N = 2,
S = [a,b] ;
N = 3,
S = [a,b,c].
?- first_elements_of_list(2, [a, b, c], S).
S = [a,b].
Below is a variant which also supports:
?- first_elements_of_list_more(10, [5, 1, 2, 7], L1).
L1 = [5,1,2,7].
first_elements_of_list_more(IntElems, [H|LongLst], [H|ShortLst]) :-
once_if_nonvar(IntElems, first_elements_of_list_more_(LongLst, 1, IntElems, ShortLst)).
first_elements_of_list_more_([], Inc, Elems, []) :-
(var(Elems) -> Inc = Elems
; Elems >= Inc).
first_elements_of_list_more_([_|_], E, E, []).
first_elements_of_list_more_([H|LongLst], Upto, IntElems, [H|ShortLst]) :-
succ(Upto, Upto1),
first_elements_of_list_more_(LongLst, Upto1, IntElems, ShortLst).
once_if_nonvar(Var, Expr) :-
nonvar(Var, Bool),
call(Expr),
(Bool == true -> ! ; true).
nonvar(Var, Bool) :-
(nonvar(Var) -> Bool = true ; Bool = false).

Fill list in SWI-Prolog

I am trying to fill a list of given length N with numbers 1,2,3,...,N.
I thought this could be done this way:
create_list(N,L) :-
length(L,N),
forall(between(1,N,X), nth1(X,L,X)).
However, this does not seem to work. Can anyone say what I am doing wrong?
First things first: Use clpfd!
:- use_module(library(clpfd)).
In the following I present zs_between_and/3, which (in comparison to my previous answer) offers some more features.
For a start, let's define some auxiliary predicates first!
equidistant_stride([] ,_).
equidistant_stride([Z|Zs],D) :-
equidistant_prev_stride(Zs,Z,D).
equidistant_prev_stride([] ,_ ,_). % internal predicate
equidistant_prev_stride([Z1|Zs],Z0,D) :-
Z1 #= Z0+D,
equidistant_prev_stride(Zs,Z1,D).
Let's run a few queries to get a picture of equidistant_stride/2:
?- Zs = [_,_,_], equidistant_stride(Zs,D).
Zs = [_A,_B,_C], _A+D#=_B, _B+D#=_C.
?- Zs = [1,_,_], equidistant_stride(Zs,D).
Zs = [1,_B,_C], _B+D#=_C, 1+D#=_B.
?- Zs = [1,_,_], equidistant_stride(Zs,10).
Zs = [1,11,21].
So far, so good... moving on to the actual "fill list" predicate zs_between_and/3:
zs_between_and([Z0|Zs],Z0,Z1) :-
Step in -1..1,
Z0 #= Z1 #<==> Step #= 0,
Z0 #< Z1 #<==> Step #= 1,
Z0 #> Z1 #<==> Step #= -1,
N #= abs(Z1-Z0),
( fd_size(N,sup)
-> true
; labeling([enum,up],[N])
),
length(Zs,N),
labeling([enum,down],[Step]),
equidistant_prev_stride(Zs,Z0,Step).
A bit baroque, I must confess...
Let's see what features were gained---in comparison to my previous answer!
?- zs_between_and(Zs,1,4). % ascending consecutive integers
Zs = [1,2,3,4]. % (succeeds deterministically)
?- zs_between_and(Zs,3,1). % descending consecutive integers (NEW)
Zs = [3,2,1]. % (succeeds deterministically)
?- zs_between_and(Zs,L,10). % enumerates fairly
L = 10, Zs = [10] % both ascending and descenting (NEW)
; L = 9, Zs = [9,10]
; L = 11, Zs = [11,10]
; L = 8, Zs = [8,9,10]
; L = 12, Zs = [12,11,10]
; L = 7, Zs = [7,8,9,10]
...
?- L in 1..3, zs_between_and(Zs,L,6).
L = 3, Zs = [3,4,5,6]
; L = 2, Zs = [2,3,4,5,6]
; L = 1, Zs = [1,2,3,4,5,6].
Want some more? Here we go!
?- zs_between_and([1,2,3],From,To).
From = 1, To = 3
; false.
?- zs_between_and([A,2,C],From,To).
A = 1, From = 1, C = 3, To = 3 % ascending
; A = 3, From = 3, C = 1, To = 1. % descending
I don't have a prolog interpreter available right now, but wouldn't something like...
isListTo(N, L) :- reverse(R, L), isListFrom(N, R).
isListFrom(0, []).
isListFrom(N, [H|T]) :- M is N - 1, N is H, isListFrom(M, T).
reverse can be done by using e.g. http://www.webeks.net/prolog/prolog-reverse-list-function.html
So tracing isListTo(5, [1, 2, 3, 4, 5])...
isListTo(5, [1, 2, 3, 4, 5])
<=> isListFrom(5, [5, 4, 3, 2, 1])
<=> 5 is 5 and isListFrom(4, [4, 3, 2, 1])
<=> 4 is 4 and isListFrom(3, [3, 2, 1])
<=> 3 is 3 and isListFrom(2, [2, 1])
<=> 2 is 2 and isListFrom(1, [1])
<=> 1 is 1 and isListFrom(0, [])
QED
Since PROLOG will not only evaluate truth, but find satisfying solutions, this should work. I know this is a vastly different approach from the one you are trying, and apologize if your question is specifically about doing loops in PROLOG (if that is the case, perhaps re-tag the question?).
Here's a logically pure implementation of predicate zs_from_to/3 using clpfd:
:- use_module(library(clpfd)).
zs_from_to([],I0,I) :-
I0 #> I.
zs_from_to([I0|Is],I0,I) :-
I0 #=< I,
I1 #= I0 + 1,
zs_from_to(Is,I1,I).
Let's use it! First, some ground queries:
?- zs_from_to([1,2,3],1,3).
true.
?- zs_from_to([1,2,3],1,4).
false.
Next, some more general queries:
?- zs_from_to(Zs,1,7).
Zs = [1,2,3,4,5,6,7]
; false.
?- zs_from_to([1,2,3],From,To).
From = 1, To = 3.
Now, let's have some even more general queries:
?- zs_from_to(Zs,From,2).
Zs = [], From in 3..sup
; Zs = [2], From = 2
; Zs = [1,2], From = 1
; Zs = [0,1,2], From = 0
; Zs = [-1,0,1,2], From = -1
; Zs = [-2,-1,0,1,2], From = -2
...
?- zs_from_to(Zs,0,To).
Zs = [], To in inf.. -1
; Zs = [0], To = 0
; Zs = [0,1], To = 1
; Zs = [0,1,2], To = 2
; Zs = [0,1,2,3], To = 3
; Zs = [0,1,2,3,4], To = 4
...
What answers do we get for the most general query?
?- zs_from_to(Xs,I,J).
Xs = [], J#=<I+ -1
; Xs = [I], I+1#=_A, J#>=I, J#=<_A+ -1
; Xs = [I,_A], I+1#=_A, J#>=I, _A+1#=_B, J#>=_A, J#=<_B+ -1
; Xs = [I,_A,_B], I+1#=_A, J#>=I, _A+1#=_B, J#>=_A, _B+1#=_C, J#>=_B, J#=<_C+ -1
...
Edit 2015-06-07
To improve on above implementation of zs_from_to/3, let's do two things:
Try to improve determinism of the implementation.
Extract a more general higher-order idiom, and implement zs_from_to/3 on top of it.
Introducing the meta-predicates init0/3 and init1/3:
:- meta_predicate init0(2,?,?).
:- meta_predicate init1(2,?,?).
init0(P_2,Expr,Xs) :- N is Expr, length(Xs,N), init_aux(Xs,P_2,0).
init1(P_2,Expr,Xs) :- N is Expr, length(Xs,N), init_aux(Xs,P_2,1).
:- meta_predicate init_aux(?,2,+). % internal auxiliary predicate
init_aux([] , _ ,_ ).
init_aux([Z|Zs],P_2,I0) :-
call(P_2,I0,Z),
I1 is I0+1,
init_aux(Zs,P_2,I1).
Let's see init0/3 and init1/3 in action!
?- init0(=,5,Zs). % ?- numlist(0,4,Xs),maplist(=,Xs,Zs).
Zs = [0,1,2,3,4].
?- init1(=,5,Zs). % ?- numlist(1,5,Xs),maplist(=,Xs,Zs).
Zs = [1,2,3,4,5].
Ok, where do we go from here? Consider the following query:
?- init0(plus(10),5,Zs). % ?- numlist(0,4,Xs),maplist(plus(10),Xs,Zs).
Zs = [10,11,12,13,14].
Almost done! Putting it together, we define zs_from_to/2 like this:
z_z_sum(A,B,C) :- C #= A+B.
zs_from_to(Zs,I0,I) :-
N #= I-I0+1,
init0(z_z_sum(I0),N,Zs).
At last, let's see if determinism has improved!
?- zs_from_to(Zs,1,7).
Zs = [1,2,3,4,5,6,7]. % succeeds deterministically
If I understood correctly, the built-in predicate numlist/3 would do.
http://www.swi-prolog.org/pldoc/man?predicate=numlist/3

How do I find the longest list in a list of lists?

I have a list of lists, and I need to find the longest one of them. If there are more than one with the same length it's the same which it returns. Thanks.
Here is a general predicate that scans a list to find a single member defined by a given goal.
select_element(Goal, [Head | Tail], Selected) :-
select_element(Goal, Tail, Head, Selected).
select_element(_Goal, [], Selected, Selected).
select_element(Goal, [Head | Tail], Current, FinalSelected) :-
call(Goal, Head, Current, Selected),
select_element(Goal, Tail, Selected, FinalSelected).
Lets say you define a predicate
get_bigger_number(N1, N2, N) :-
N is max(N1, N2).
Now you can execute:
?- select_element(get_bigger_number, [5, 1, -2, 10, 3.2, 0], Selected).
Selected = 10
So all you need to do now is define a predicate get_longer_list(L1, L2, L),
and use it instead of get_bigger_number/3.
Of course, using a general predicate like select_element/3 might not be very efficient. For example, you should try to avoid calculating the length of the same list several times, because this calculation is slow in Prolog (at least if implemented in Prolog in the standard way).
Please consider my aproach.
longest([L], L) :-
!.
longest([H|T], H) :-
length(H, N),
longest(T, X),
length(X, M),
N > M,
!.
longest([H|T], X) :-
longest(T, X),
!.
Then you can consult it:
?- longest([[1]], N).
N = [1] ;
?- longest([[1],[2]], N).
N = [2] .
?- longest([[1],[2], [3,3,3], [2]], N).
N = [3, 3, 3] ;
?- longest([[1],[2], [3,3,3], [2]], N).
N = [3, 3, 3].
?- longest([[1],[2], [3,3,3], [2], [4,4,4,4]], N).
N = [4, 4, 4, 4] .
?- longest([[1],[2], [3,3,3], [2], [4,4,4,4]], N).
N = [4, 4, 4, 4] ;
Greets!
We define longest/2 based on meta-predicate max_of_by/3 used in tandem with length/2:
longest(Xss,Ys) :-
max_of_by(Ys,Xss,length).
Sample queries:
?- longest([[1],[2]],Xs). % we expect multiple solutions
Xs = [1]
; Xs = [2]. % we _get_ multiple solutions
?- longest([[2,1,3],[7,5],[1,8,2,3,1],[2,7,1,4]],Xs).
Xs = [1,8,2,3,1]. % succeeds deterministically
Here is another approach that is efficient and easy to understand. The idea is to find the lengths of all lists in the list, use max_list to get the length of the longest list, and then find a list that is that long. This has the benefit that it will return all lists of the longest length.
lengths([],[]).
lengths([H|T], [LH|LengthsT]) :-
length(H, LH),
lengths(T, LengthsT).
lengthLongest(ListOfLists, Max) :-
lengths(ListOfLists, Lengths),
max_list(Lengths, Max).
longestList(ListOfLists, Longest) :-
lengthLongest(ListOfLists, Len),
member(Longest, ListOfLists),
length(Longest, Len).
% Correct again.
longest(LL,LX) :-
findmax(Len,(append(_,[L|_],LL),length(L,Len)),MaxLen),
append(_,[LX|_],LL),
length(LX,MaxLen).
findmax(V,P,Max) :-
findall(V,P,L),
max(L,Max).
max([N],N) :- !.
max([N|R],Max) :-
max(R,Max2),
max3(N,Max2,Max).
max3(N,Max2,N) :- N > Max2,!.
max3(N,Max2,Max2).
To have the length of longest list:
%sample: longest([[2,1,3],[7,5],[1,8,2,3,1],[2,7,1,4]],L,LEN).
longest([L], L, _) :-
!.
longest([H|T], H, _) :-
length(H, N),
longest(T, X, N),
length(X, M),
N > M,
!.
longest([_|T], X, LEN) :-
length(X, LEN),
longest(T, X, LEN),
!.