recursively unfold function with univ predicate - recursion

I want to replace for example a with 2 in this term f(a,b,g(a,h(a))).
For this I first wanna unfold this term with the univ predicate =...
So far I have:
unfold(T1, T2) :-
T1 =.. T1list,
T2 = T1list.
which is true when T2 is the list represantation of T1.
But in this example I need a way to do this recursively because some arguments are functions as well!
After substitution I need to do all the way back to get f(2,b,g(2,h(2))) as an example
for the substitution I have
replace(X,Y,[],[]).
replace(X,Y,[X|T1],[Y|T2]):-
replace(X,Y,T1,T2).
replace(X,Y,[H|T1],[H|T2]):-
not(X=H),
replace(X,Y,T1,T2).
EDIT: My current Solution: my problem is, it does not work for
replace(a, 1, X, f(1,b,g(1,h(1)))).
replace(_, _, [], []).
replace(X, Y, L1, L2) :-
not(is_list(L1)),
not(is_list(L2)),
unfold(L1, L1unfold),
replace(X,Y, L1unfold, L2sub),
refold(L2sub, L2),
!.
replace(X, Y, [X|T1], [Y|T2]) :-
replace(X, Y, T1, T2),
!.
replace(X, Y, [H|T1], [H|T2]) :-
\+ is_list(H),
replace(X, Y, T1, T2),
!.
replace(X, Y, [H1|T1], [H2|T2]) :-
replace(X, Y, H1, H2),
replace(X, Y, T1, T2).
unfold(T1, [H|T2]) :-
T1 =.. [H|T1Expanded],
maplist(unfold, T1Expanded, T2).
refold([H|T2],T1):-
maplist(refold,T2,R),
T1 =.. [H|R].

You're surprisingly close.
unfold(T1, [H|T2]) :-
T1 =.. [H|T1Expanded],
maplist(unfold, T1Expanded, T2).

Related

List of Nth prime numbers Prolog

I'm trying to learn prolog and now I'm trying to print a list of the Nth primenumber:
primes(N, N).
primes(N, F):-
prime(F),
write(F), nl,
NewF is F + 1,
primes(N, NewF).
primes(N):-
primes(N, 2).
Prime/1 checks wheter the given number is a prime.
The output for primes(10) will be 2, 3 where it should be 2, 3, 5, 7, because when the NewF after 3 (which will be 4) is not a prime. So it will also not execute the write(F) nor the recursive call. I wondered how I could fix this, so it will not write F when it's not a prime but still execute the part after that. Thanks in advance!
You could simply add the clause:
primes(N, F):-
\+prime(F), nl,
NewF is F + 1,
primes(N, NewF).
I know that this answer doesn't exactly respond to the OP question (my getPrimeList(N, L) create a list L with all prime number from zero to N; the OP ask for first N prime numbers) but... just for fun... I've tried to implement the Sieve of Eratosthenes.
getListDisp(Top, Val, []) :-
Val > Top.
getListDisp(Top, V0, [V0 | Tail]) :-
V0 =< Top,
V1 is V0+2,
getListDisp(Top, V1, Tail).
reduceList(_, _, [], []).
reduceList(Step, Exclude, [Exclude | Ti], Lo) :-
NextE is Exclude+Step,
reduceList(Step, NextE, Ti, Lo).
reduceList(Step, Exclude, [H | Ti], [H | To]) :-
Exclude > H,
reduceList(Step, Exclude, Ti, To).
reduceList(Step, Exclude, [H | Ti], [H | To]) :-
Exclude < H,
NextE is Exclude+Step,
reduceList(Step, NextE, Ti, To).
eratSieve([], []).
eratSieve([Prime | Ti], [Prime | To]) :-
Step is 2*Prime,
Exclude is Prime+Step,
reduceList(Step, Exclude, Ti, Lo),
eratSieve(Lo, To).
getPrimeList(Top, []) :-
Top < 2.
getPrimeList(Top, [2 | L]) :-
Top >= 2,
getListDisp(Top, 3, Ld),
eratSieve(Ld, L).
I repeat: not really an answer; just for fun (as the OP, I'm trying to learn Prolog).

Decompression of a list in prolog

I need to decompress a list in prolog , like in the example below :
decode([[a,1],[b,2],[c,1],[d,3]],L).
L = [a, b, b, c, d, d, d] ;
I made this code :
divide(L,X,Y):-length(X,1),append(X,Y,L).
divide2(L,X,Y):-divide(L,[X|_],[Y|_]).
makelist(_,N,[]):- N =< 0 .
makelist(X,Y,[X|Result]):-Y1 is Y-1,makelist(X,Y1,Result).
makelist2(L,L2):-divide2(L,X,Y),makelist(X,Y,L2).
decode([],[]).
decode([H|T],L):-makelist2(H,H2),append(H2,L,L2),decode(T,L2).
and when i call
makelist2([a,3],L2).
L2 = [a,a,a].
but when i call
decode([[a,3],[b,1],[c,4]],L)
runs continuously. What am i doing wrong ?
Another variation of the theme, using a slightly modified version of Boris' repeat/3 predicate:
% True when L is a list with N repeats of X
repeat([X, N], L) :-
length(L, N),
maplist(=(X), L).
decode(Encoded, Decoded) :-
maplist(repeat, Encoded, Expanded),
flatten(Expanded, Decoded).
If Encode = [[a,1],[b,2],[c,1],[d,3]], then in the above decode/2, the maplist/3 call will yield Expanded = [[a],[b,b],[c],[d,d,d]], and then the flatten/2 call results in Decoded = [a,b,b,c,d,d,d].
In SWI Prolog, instead of flatten/2, you can use append/2 since you only need a "flattening" at one level.
EDIT: Adding a "bidirectional" version, using a little CLPFD:
rle([], []).
rle([X], [[1,X]]).
rle([X,Y|T], [[1,X]|R]) :-
X \== Y, % use dif(X, Y) here, if available
rle([Y|T], R).
rle([X,X|T], [[N,X]|R]) :-
N #= N1 + 1,
rle([X|T], [[N1,X]|R]).
This will yield:
| ?- rle([a,a,a,b,b], L).
L = [[3,a],[2,b]] ? ;
(1 ms) no
| ?- rle(L, [[3,a],[2,b]]).
L = [a,a,a,b,b] ? ;
no
| ?- rle([a,a,a,Y,Y,Z], [X, [N,b],[M,c]]).
M = 1
N = 2
X = [3,a]
Y = b
Z = c ? a
no
| ?- rle([A,B,C], D).
D = [[1,A],[1,B],[1,C]] ? ;
C = B
D = [[1,A],[2,B]] ? ;
B = A
D = [[2,A],[1,C]] ? ;
B = A
C = A
D = [[3,A]] ? ;
(2 ms) no
| ?- rle(A, [B,C]).
A = [D,E]
B = [1,D]
C = [1,E] ? ;
A = [D,E,E]
B = [1,D]
C = [2,E] ? ;
A = [D,E,E,E]
B = [1,D]
C = [3,E] ? ;
...
| ?- rle(A, B).
A = []
B = [] ? ;
A = [C]
B = [[1,C]] ? ;
A = [C,D]
B = [[1,C],[1,D]] ? ;
...
As #mat suggests in his comment, in Prolog implementations that have dif/2, then dif(X,Y) is preferable to X \== Y above.
The problem is in the order of your append and decode in the last clause of decode. Try tracing it, or even better, trace it "by hand" to see what happens.
Another approach: see this answer. So, with repeat/3 defined as:
% True when L is a list with N repeats of X
repeat(X, N, L) :-
length(L, N),
maplist(=(X), L).
You can write your decode/2 as:
decode([], []).
decode([[X,N]|XNs], Decoded) :-
decode(XNs, Decoded_rest),
repeat(X, N, L),
append(L, Decoded_rest, Decoded).
But this is a slightly roundabout way to do it. You could define a difference-list version of repeat/3, called say repeat/4:
repeat(X, N, Reps, Reps_back) :-
( succ(N0, N)
-> Reps = [X|Reps0],
repeat(X, N0, Reps0, Reps_back)
; Reps = Reps_back
).
And then you can use a difference-list version of decode/2, decode_1/3
decode(Encoded, Decoded) :-
decode_1(Encoded, Decoded, []).
decode_1([], Decoded, Decoded).
decode_1([[X,N]|XNs], Decoded, Decoded_back) :-
repeat(X, N, Decoded, Decoded_rest),
decode_1(XNs, Decoded_rest, Decoded_back).
?- decode([[a,1],[b,2],[c,1],[d,3]],L).
L = [a, b, b, c, d, d, d].
?- decode([[a,3],[b,1],[c,0],[d,3]],L).
L = [a, a, a, b, d, d, d].
?- decode([[a,3]],L).
L = [a, a, a].
?- decode([],L).
L = [].
You can deal with both direction with this code :
:- use_module(library(lambda)).
% code from Pascal Bourguignon
packRuns([],[]).
packRuns([X],[[X]]).
packRuns([X|Rest],[XRun|Packed]):-
run(X,Rest,XRun,RRest),
packRuns(RRest,Packed).
run(Var,[],[Var],[]).
run(Var,[Var|LRest],[Var|VRest],RRest):-
run(Var,LRest,VRest,RRest).
run(Var,[Other|RRest],[Var],[Other|RRest]):-
dif(Var,Other).
%end code
pack_1(In, Out) :-
maplist(\X^Y^(X = [V|_],
Y = [V, N],
length(X, N),
maplist(=(V), X)),
In, Out).
decode(In, Out) :-
when((ground(In); ground(Out1)),pack_1(Out1, In)),
packRuns(Out, Out1).
Output :
?- decode([[a,1],[b,2],[c,1],[d,3]],L).
L = [a, b, b, c, d, d, d] .
?- decode(L, [a,b,b,c,d,d,d]).
L = [[a, 1], [b, 2], [c, 1], [d, 3]] .
a compact way:
decode(L,D) :- foldl(expand,L,[],D).
expand([S,N],L,E) :- findall(S,between(1,N,_),T), append(L,T,E).
findall/3 it's the 'old fashioned' Prolog list comprehension facility
decode is a poor name for your predicate: properly done, you predicate should be bi-directional — if you say
decode( [[a,1],[b,2],[c,3]] , L )
You should get
L = [a,b,b,c,c,c].
And if you say
decode( L , [a,b,b,c,c,c] ) .
You should get
L = [[a,1],[b,2],[c,3]].
So I'd use a different name, something like run_length_encoding/2. I might also not use a list to represent individual run lengths as [a,1] is this prolog term: .(a,.(1,[]). Just use a simple term with arity 2 — myself, I like using :/2 since it's defined as an infix operator, so you can simply say a:1.
Try this on for size:
run_length_encoding( [] , [] ) . % the run-length encoding of the empty list is the empty list.
run_length_encoding( [X|Xs] , [R|Rs] ) :- % the run-length encoding of a non-empty list is computed by
rle( Xs , X:1 , T , R ) , % - run-length encoding the prefix of the list
run_length_encoding( T , Rs ) % - and recursively run-length encoding the remainder
. % Easy!
rle( [] , C:N , [] , C:N ) . % - the run is complete when the list is exhausted.
rle( [X|Xs] , C:N , [X|Xs] , C:N ) :- % - the run is complete,
X \= C % - when we encounter a break
. %
rle( [X|Xs] , X:N , T , R ) :- % - the run continues if we haven't seen a break, so....
N1 is N+1 , % - increment the run length,
rle( Xs, X:N1, T, R ) % - and recurse down.
. % Easy!
In direct answer to the original question of, What am I doing wrong?...
When I ran the original code, any expected use case "ran indefinitely" without yielding a result.
Reading through the main predicate:
decode([],[]).
This says that [] is the result of decoding []. Sounds right.
decode([H|T],L) :- makelist2(H,H2), append(H2,L,L2), decode(T,L2).
This says that L is the result of decoding [H|T] if H2 is an expansion of H (which is what makelist2 does... perhaps - we'll go over that below), and H2 appended to this result gives another list L2 which is the decoded form of the original tail T. That doesn't sound correct. If I decode [H|T], I should (1) expand H, (2) decode T giving L2, then (3) append H to L2 giving L.
So the corrected second clause is:
decode([H|T], L) :- makelist2(H, H2), decode(T, L2), append(H2, L2, L).
Note the argument order of append/3 and that the call occurs after the decode of the tail. As Boris pointed out previously, the incorrect order of append and the recursive decode can cause the continuous running without any output as append with more uninstantiated arguments generates a large number of unneeded possibilities before decode can succeed.
But now the result is:
| ?- decode([[a,3]], L).
L = [a,a,a] ? ;
L = [a,a,a,a] ? ;
...
If you try out our other predicates by hand in the Prolog interpreter, you'll find that makelist2/2 has an issue:
It produces the correct result, but also a bunch of incorrect results. Let's have a look at makelist2/2. We can try this predicate by itself and see what happens:
| ?- makelist2([a,3], L).
L = [a,a,a] ? ;
L = [a,a,a,a] ? ;
...
There's an issue: makelist2/2 should only give the first solution, but it keeps going, giving incorrect solutions. Let's look closer at makelist/2:
makelist2(L,L2) :- divide2(L,X,Y), makelist(X,Y,L2).
It takes a list L of the form [A,N], divides it (via divide2/3) into X = A and Y = N, then calls an auxiliary, makelist(X, Y, L2).
makelist(_,N,[]):- N =< 0 .
makelist(X,Y,[X|Result]):-Y1 is Y-1,makelist(X,Y1,Result).
makelist/3 is supposed to generate a list (the third argument) by replicating the first argument the number of times given in the second argument. The second, recursive clause appears to be OK, but has one important flaw: it will succeed even if the value of Y is less than or equal to 0. Therefore, even though a correct solution is found, it keeps succeeding on incorrect solutions because the base case allows the count to be =< 0:
| ?- makelist(a,2,L).
L = [a,a] ? ;
L = [a,a,a] ? ;
We can fix makelist/2 as follows:
makelist(_,N,[]):- N =< 0 .
makelist(X,Y,[X|Result]):- Y > 0, Y1 is Y-1, makelist(X,Y1,Result).
Now the code will generate a correct result. We just needed to fix the second clause of decode/2, and the second clause of makelist/3.
| ?- decode([[a,3],[b,4]], L).
L = [a,a,a,b,b,b,b]
yes
The complete, original code with just these couple of corrections looks like this:
divide(L, X, Y) :- length(X, 1), append(X, Y, L).
divide2(L, X, Y) :- divide(L, [X|_], [Y|_]).
makelist(_, N, []) :- N =< 0 .
makelist(X, Y, [X|Result]) :- Y > 0, Y1 is Y-1, makelist(X,Y1,Result).
makelist2(L, L2) :- divide2(L, X, Y), makelist(X, Y, L2).
decode([], []).
decode([H|T], L) :- makelist2(H,H2), decode(T,L2), append(H2,L2,L).
Note some simple, direct improvements. The predicate, divide2(L, X, Y) takes a list L of two elements and yields each, individual element, X and Y. This predicate is unnecessary because, in Prolog, you can obtain these elements by simple unification: L = [X, Y]. You can try this right in the Prolog interpreter:
| ?- L = [a,3], L = [X,Y].
L = [a,3]
X = a
Y = 3
yes
We can then completely remove the divide/3 and divide2/3 predicates, and replace a call to divide2(L, X, Y) with L = [X,Y] and reduce makelist2/2 to:
makelist2(L, L2) :- L = [X, Y], makelist(X, Y, L2).
Or more simply (because we can do the unification right in the head of the clause):
makelist2([X,Y], L2) :- makelist(X, Y, L2).
You could just remove makelist2/2 and call makelist/2 directly from decode/2 by unifying H directly with its two elements, [X, N]. So the original code simplifies to:
makelist(_, N, []) :- N =< 0 .
makelist(X, Y, [X|Result]) :- Y > 0, Y1 is Y-1, makelist(X,Y1,Result).
decode([], []).
decode([[X,N]|T], L) :- makelist(X, N, H2), decode(T, L2), append(H2, L2, L).
And makelist/3 can be performed a bit more clearly using one of the methods provided in the other answers (e.g., see Boris' repeat/3 predicate).

Prolog predicate makelist

Define a Prolog predicate makelist/3 such that makelist(Start, End, List) is true if
List is a list of all integers from the integer Start to the integer End. For example:
makelist(3, 7, [3, 4, 5, 6, 7]) should be true.
Can't understand why my code doesn't work
makelist(H, L, _) :-
L is H+1.
makelist(H, L, List) :-
append([], [H], List), H1 is H+1.
makelist(H1, L, List) :-
append(List, [H1], List1), last(List1, R),
R \= L+1, makelist(N, L, List1), N is H1+1.
You can simplify your code, let's take your predicate and examine what is what you really need to do:
% makelist(X,Y,L)
Since your recursive call is increasing by 1 the first parameter, let's call it X, then your base case would be when X is the same than Y:
makelist(X,X,[X]) .
and your recursive call: it will be when X is smaller than Y, you need to increase X and add the value to the list:
makelist(X,Y,[X|L]) :- X < Y ,
X1 is X + 1 ,
makelist(X1, Y, L).

Infinite recursion in SWI-Prolog

I am trying to define a family tree and the relationships between its nodes basing their definitions on three predicates: male/1, female/1 and parent_of/2.
I have defined the notions of ascendant, descendant, father, mother, son, daughter, grandfather, grandmother, aunt, uncle and cousin. Any new definition can't be based on the notion of "brother/sister of", but only on the previous ones.
This is the code:
male(daniel).
male(miguelangel).
male(mario).
male(mahmoud).
male(esteban).
male(enrique).
male(javier).
male(miguelin).
female(diana).
female(hengameh).
female(vicenta).
female(mahvash).
female(angeles).
female(mexicana).
female(eloina).
female(esmeralda).
female(cristina).
female(otilia).
parent_of(miguelangel, daniel).
parent_of(miguelangel, diana).
parent_of(hengameh, daniel).
parent_of(hengameh, diana).
parent_of(mario, miguelangel).
parent_of(mario, esteban).
parent_of(mario, eloina).
parent_of(mario, angeles).
parent_of(mario, otilia).
parent_of(vicenta, miguel).
parent_of(vicenta, esteban).
parent_of(vicenta, eloina).
parent_of(vicenta, angeles).
parent_of(vicenta, otilia).
parent_of(mahmoud, hengameh).
parent_of(mahvash, hengameh).
parent_of(enrique, javier).
parent_of(angeles, javier).
parent_of(cristina, miguelin).
parent_of(otilia, cristina).
parent_of(eloina, esmeralda).
% Rules
ancestor(X, Y) :-
parent_of(X, Y);
parent_of(X, Z),
ancestor(Z, Y).
descendant(X, Y) :-
ancestor(Y, X).
father(X, Y) :-
parent_of(X, Y),
male(X).
mother(X, Y) :-
parent_of(X, Y),
female(X).
son(X, Y) :-
parent_of(Y, X),
male(X).
daughter(X, Y) :-
parent_of(Y, X),
female(X).
grandfather(X, Y) :-
parent_of(X, Z),
parent_of(Z, Y),
male(X).
grandmother(X, Y) :-
parent_of(X, Z),
parent_of(Z, Y),
female(X).
aunt(X, Y) :-
(grandfather(Z, Y) ; grandmother(Z, Y)),
(father(Z, X) ; mother(Z, X)),
not(parent_of(X, Y)),
female(X).
uncle(X, Y) :-
(grandfather(Z, Y) ; grandmother(Z, Y)),
(father(Z, X) ; mother(Z, X)),
not(parent_of(X, Y)),
male(X).
cousin(X, Y) :-
((uncle(Z, Y), parent_of(Z, X)) ; (cousin(P, Y), descendant(X, P)));
((aunt(Z, Y), parent_of(Z, X)) ; (cousin(P, Y), descendant(X, P))).
For the sake of clarity I have represented through an image the part of the tree where I'm having issues:
When I write
cousin(X, Y) :-
((uncle(Z, Y), parent_of(Z, X)));
((aunt(Z, Y), parent_of(Z, X))).
instead of
cousin(X, Y) :-
((uncle(Z, Y), parent_of(Z, X)) ; (cousin(P, Y), descendant(X, P)));
((aunt(Z, Y), parent_of(Z, X)) ; (cousin(P, Y), descendant(X, P))).
I get
?- cousin(miguelin, daniel).
false.
?- cousin(cristina, daniel).
true .
which are valid results. But when I introduce the recursive definitions on the right, as stated on the first (big) code, for saying that the descendants of the cousins of Y are also the cousins of Y, the program crashes:
?- cousin(miguelin, daniel).
ERROR: Out of local stack
I don't understand why. If I look at the image, it makes sense (at least to me) that recursive definition, and miguelin should be now the cousin of daniel (since he is a descendant of another cousin of daniel, which is cristina). I also tested it "manually" and I got the right result:
?- cousin(cristina, daniel), descendant(X, cristina).
X = miguelin ;
What's wrong with the definition?
One problem with the cousin/2 predicate is that the recursion is occurring before you resolve the descendant/2, and cousin/2 is having an infinite recursion issue in this context. As a simple way to fix that, you can swap them around. Also, you have one redundant recursive subclause. So the modified cousin/2 predicate would be:
cousin(X, Y) :-
(uncle(Z,Y), parent_of(Z,X)) ;
(aunt(W,Y), parent_of(W,X)) ;
(descendant(X,P), cousin(P,Y)).
And then you get:
?- cousin(miguelin, daniel).
true ;
false.
?- cousin(cristina, daniel).
true ;
false.
?-

Prolog Family Tree Blood Relations, Recursion? [duplicate]

I have to write a small prolog program which checks if a given person is a ancestor of a second one.
These are the facts and rules:
mother(tim, anna).
mother(anna, fanny).
mother(daniel, fanny).
mother(celine, gertrude).
father(tim, bernd).
father(anna, ephraim).
father(daniel, ephraim).
father(celine, daniel).
parent(X,Y) :- mother(X,Y).
parent(X,Y) :- father(X,Y).
The test if a person is an ancestor of another person is easy:
ancestor(X, Y) :- parent(X, Y).
ancestor(X, Y) :- parent(X, Z), ancestor(Z, Y).
But now I have to write a method ancestor(X,Y,Z) which also prints out the relationship between two persons. It should look like this
?- ancestor(ephraim, tim, X).
false.
?- ancestor(tim, ephraim, X).
X = father(mother(tim)).
And that is the problem: I have no clue how do to this.
You can use an accumulator to adapt #Scott Hunter's solution :
mother(anna, fanny).
mother(daniel, fanny).
mother(celine, gertrude).
father(tim, bernd).
father(anna, ephraim).
father(daniel, ephraim).
father(celine, daniel).
ancestor(X, Y, Z) :- ancestor(X, Y, X, Z).
ancestor(X, Y, Acc, father(Acc)) :- father(X, Y).
ancestor(X, Y, Acc, mother(Acc)) :- mother(X, Y).
ancestor(X, Y, Acc, Result) :-
father(X, Z),
ancestor(Z, Y, father(Acc), Result).
ancestor(X, Y, Acc, Result) :-
mother(X, Z),
ancestor(Z, Y, mother(Acc), Result).
edit : as Scott Hunter showed in his edit, there's no need for an explicit accumulator here, since we can left the inner part of the term unbound easily at each iteration. His solution is therefore better !
A term manipulation alternative to the accumulator tecnique by #Mog:
parent(X, Y, mother(X)) :- mother(X, Y).
parent(X, Y, father(X)) :- father(X, Y).
ancestor(X, Y, R) :-
parent(X, Y, R).
ancestor(X, Y, R) :-
parent(X, Z, P),
ancestor(Z, Y, A),
eldest(A, P, R).
eldest(A, P, R) :-
A =.. [Af, Aa],
( atom(Aa)
-> T = P
; eldest(Aa, P, T)
),
R =.. [Af, T].
To test, I made tim a father: father(ugo, tim).
?- ancestor(tim, ephraim, X).
X = father(mother(tim)) .
?- ancestor(ugo, ephraim, X).
X = father(mother(father(ugo))) .
Simply add a term which tracts what kind of parent is used at each step (edited to get result in proper order):
ancestor(X,Y,father(X)) :- father(X,Y).
ancestor(X,Y,mother(X)) :- mother(X,Y).
ancestor(X,Y,father(Z2)) :- father(Z,Y), ancestor(X,Z,Z2).
ancestor(X,Y,mother(Z2)) :- mother(Z,Y), ancestor(X,Z,Z2).

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