How to express "ancestor" recursively

Question

I'm stuck with this recursion which doesn't work as I expect.

Where is my mistake?

#!/usr/bin/prolog

% Facts

mother( jeanne   , michel  ). % great-grandmother, grandfather
mother( genevieve, aubin   ). % grandmother, father
mother( irene    , alain   ). % great-grandmother, grandfather
mother( emilie   , colette ). % great-grandmother, grandmother
mother( colette  , muriel  ). % grandmother, mother
mother( muriel   , eve     ). % mother, daughter

father( joseph   , michel  ). % great-grandfather, grandfather
father( michel   , aubin   ). % grandfather, father
father( xxx      , alain   ). % great-grandfather, grandfather
father( marcel   , colette ). % great-grandfather, grandmother
father( alain    , muriel  ). % grandfather, mother
father( aubin    , eve     ). % father, daughter

% Rules

parent( Mother, Child ) :- mother( Mother, Child ).
parent( Father, Child ) :- father( Father, Child ).

ancestors( [Parent|Ancestors], Child ) :-
    parent( Parent, Child ),
    ancestors( Ancestors, Parent ).

% Queries

:-
    ancestors( Ancestor, eve ),
    format( 'Eve ancestors: ~w~n', Ancestor ).
% expected answer is [muriel, colette, alain, emilie, marcel, irene, xxx, aubin, michel, genevieve, joseph, jeanne]

EDIT here is the final solution, thank you all.

#!/usr/bin/prolog

/*##- Facts -##*/

mother( jeanne   , michel   ).
mother( genevieve, sylvie   ).
mother( genevieve, brigitte ).
mother( genevieve, aubin    ).
mother( irène    , alain    ).
mother( émilie   , colette  ).
mother( colette  , muriel   ).
mother( colette  , olivier  ).
mother( colette  , audrey   ).
mother( colette  , stéphane ).
mother( muriel   , eve      ).

father( joseph  , michel   ).
father( michel  , sylvie   ).
father( michel  , brigitte ).
father( michel  , aubin    ).
father( séraphin, alain    ).
father( marcel  , colette  ).
father( alain   , muriel   ).
father( alain   , olivier  ).
father( yves    , audrey   ).
father( yves    , stéphane ).
father( aubin   , eve      ).

/*##- Rules -##*/

parent( Mother, Child ) :- mother( Mother, Child ).
parent( Father, Child ) :- father( Father, Child ).

ancestor( Parent, Child ) :- parent( Parent, Child ).
ancestor( GrandParent, Child ) :-
    parent( GrandParent, Parent ),
    ancestor( Parent, Child ).

grandMothers( GrandMother, Child ) :-
    mother( GrandMother, FatherOrMother ),
    parent( FatherOrMother, Child ).

grandsFathers( GrandsFather, Child ) :-
    father( GrandsFather, FatherOrMother ),
    parent( FatherOrMother, Child ).

parents( Mother, Father, Child ) :-
    father( Father, Child ),
    mother( Mother, Child ).

strictSiblings( SisterOrBrother, Child ) :-
    parents( Mother, Father, Child ),
    parents( Mother, Father, SisterOrBrother ),
    SisterOrBrother \= Child.

siblings( SisterOrBrother, Child ) :-
    mother( Mother, Child ), mother( Mother, SisterOrBrother ), SisterOrBrother \= Child ;
    father( Father, Child ), father( Father, SisterOrBrother ), SisterOrBrother \= Child .

/*##- Queries -##*/

theMother :-
    mother( Mother, eve ),
    format( 'Ève\'s mother: ~w~n', [Mother] ).
theFather :-
    father( Father, eve ),
    format( 'Ève\'s father: ~w~n', [Father] ).
theParents :-
    setof( MotherOrFather, parent( MotherOrFather, eve ), MotherAndFather ),
    format( 'Ève\'s parents: ~w~n', [MotherAndFather] ).
theGrandMothers :-
    setof( GrandMother, grandMothers( GrandMother , eve ), GrandMothers ),
    format( 'Ève\'s grand-mothers: ~w~n', [GrandMothers] ).
theGrandFathers :-
    setof( GrandsFather, grandsFathers( GrandsFather , eve ), GrandsPères ),
    format( 'Ève\'s grand-fathers: ~w~n', [GrandsPères] ).
lesEnfants :-
    setof( Child, parents( genevieve, michel, Child ), Children ),
    format( 'Geneviève and Michel children: ~w~n', [Children] ).
theTwoParents :-
    parents( Mother, Father, eve ),
    format( 'Ève\'s mother and father: ~w, ~w~n', [Mother, Father] ).
theStrictSiblings :-
    setof( SisterOrBrother, strictSiblings( SisterOrBrother, muriel ), SistersAndBrothers ),
    format( 'Muriel\'s strict siblings: ~w~n', [SistersAndBrothers] ).
theSiblings :-
    setof( SisterOrBrother, siblings( SisterOrBrother, muriel ), SistersAndBrothers ),
    format( 'Muriel\'s siblings: ~w~n', [SistersAndBrothers] ).
theAncestors :-
    setof( Ancestor, ancestor( Ancestor, eve ), Ancestors ),
    format( 'Ève\'s ancestors: ~w~n', [Ancestors] ).
:-
    theMother,
    theFather,
    theParents,
    theGrandMothers,
    theGrandFathers,
    lesEnfants,
    theTwoParents,
    theStrictSiblings,
    theSiblings,
    theAncestors,
    halt( 0 ).

And the output is:

Ève's mother: muriel
Ève's father: aubin
Ève's parents: [aubin,muriel]
Ève's grand-mothers: [colette,genevieve]
Ève's grand-fathers: [alain,michel]
Geneviève and Michel children: [aubin,brigitte,sylvie]
Ève's mother and father: muriel, aubin
Muriel's strict siblings: [olivier]
Muriel's siblings: [audrey,olivier,stéphane]
Ève's ancestors: [alain,aubin,colette,genevieve,irène,jeanne,joseph,marcel,michel,muriel,séraphin,émilie]

before reading the post itself, recursion is easy, it's there to help us find solutions easily. :) — Will Ness, Sep 24 '20 at 18:11
I recommend picking a title that describes the problem specifically. — ggorlen, Sep 24 '20 at 18:53

David Tonhofer · Accepted Answer · 2020-09-24T21:07:16.217

Let's do this interactively (in SWI Prolog) instead of in a script which prints the answers at the end using format/2.

We want all possible ancestors of eve in a list.

So we have to

query the Prolog program for all possible solutions to the goal ancestor(A,eve)
and then collect them into a list

This is done using one of the predicates bagof/3, setof/3 or findall/3, which backtrack over answers to a goal and unify a variable with a list containing all the answers (with duplicate answers for bagof/3, without duplicate answers for setof/3, and with "no possible answer" yielding [] instead of failure for findall/3).

So we just need to make sure the goal to find any ancestor is correct.

We can state that A is an ancestor of C if

A is a parent of C or
A is a parent of some D, and D is an ancestor of C

(Note: just 'if', not 'if an only if'. However, it is assumed there are no other ways in which A could possibly be an ancestor of C ... a reasonable "closed world assumption")

The above formulation is well adapted to the search strategy of Prolog, which attempts to resolve a leftmost sub-goal in the body first:

ancestor(A,C) :- parent(A,C).
ancestor(A,C) :- parent(A,D),ancestor(D,C).

Doing it in the way "check for ancestor on the left":

ancestor(A,C) :- parent(A,C).
ancestor(A,C) :- ancestor(A,D),parent(D,C).

should lead to the same result but actually does not: After initially giving good answer, the Prolog Processor will eventually enter an infinite loop, where ancestor(A,C) calls ancestor(A,D). (This would work in the simpler "Datalog" language).

Anyway, are we done?

?- ancestor(X,eve).
X = muriel ;
X = aubin ;
X = jeanne ;
X = genevieve ;
X = irene ;
X = emilie ;
X = colette ;
X = joseph ;
X = michel ;
X = xxx ;
X = marcel ;
X = alain ;
false.

Now collect everything into a list:

(In SWI-Prolog, you have to say that you want long lists printed, not replaced by ellipses, so):

?- set_prolog_flag(answer_write_options,[max_depth(0)]).
true.

And then:

?- bagof(X,ancestor(X,eve),Out).
Out = [muriel,aubin,jeanne,genevieve,irene,emilie,
       colette,joseph,michel,xxx,marcel,alain].

Thank you very much, I've integrated your advices into my sample (study) with long names (I don't like A,C,D) and was surprised to write ancestor( GrandParent, Child ). My mistake was here. Your solution is crystal clear. — Aubin, Sep 25 '20 at 08:19
@Aubin I have switched from "long names" to "short names" in recent months unless the logic is tricky and needs "in place documentation". It is easier to scan source code afterwards and to pick out the variables ... less visual noise. And as variables are always clause-local, there aren't that many in a given context. (But I would really like to see would be editor support for variable coloring). — David Tonhofer, Sep 25 '20 at 09:17

How to express "ancestor" recursively

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