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    1/*  Part of SWI-Prolog
    2
    3    Author:        Tom Schrijvers, Markus Triska and Jan Wielemaker
    4    E-mail:        Tom.Schrijvers@cs.kuleuven.ac.be
    5    WWW:           http://www.swi-prolog.org
    6    Copyright (c)  2004-2023, K.U.Leuven
    7                              SWI-Prolog Solutions b.v.
    8    All rights reserved.
    9
   10    Redistribution and use in source and binary forms, with or without
   11    modification, are permitted provided that the following conditions
   12    are met:
   13
   14    1. Redistributions of source code must retain the above copyright
   15       notice, this list of conditions and the following disclaimer.
   16
   17    2. Redistributions in binary form must reproduce the above copyright
   18       notice, this list of conditions and the following disclaimer in
   19       the documentation and/or other materials provided with the
   20       distribution.
   21
   22    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
   23    "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
   24    LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
   25    FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
   26    COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
   27    INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
   28    BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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   30    CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
   31    LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
   32    ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
   33    POSSIBILITY OF SUCH DAMAGE.
   34*/
   35
   36:- module(dif,
   37          [ dif/2                               % +Term1, +Term2
   38          ]).   39:- autoload(library(lists),[append/3, reverse/2, member/2]).   40
   41
   42:- set_prolog_flag(generate_debug_info, false).   43
   44/** <module> The dif/2 constraint
   45*/
   46
   47%!  dif(+Term1, +Term2) is semidet.
   48%
   49%   Constraint that expresses that  Term1   and  Term2  never become
   50%   identical (==/2). Fails if `Term1 ==   Term2`. Succeeds if Term1
   51%   can  never  become  identical  to  Term2.  In  other  cases  the
   52%   predicate succeeds after attaching constraints   to the relevant
   53%   parts of Term1 and Term2 that prevent   the  two terms to become
   54%   identical.
   55
   56dif(X,Y) :-
   57    ?=(X,Y),
   58    !,
   59    X \== Y.
   60dif(X,Y) :-
   61    dif_c_c(X,Y,_).
   62
   63/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   64The constraint is helt in  an   attribute  `dif`. A constrained variable
   65holds a term  vardif(L1,L2)  where  `L1`   is  a  list  OrNode-Value for
   66constraints on this variable  and  `L2`   is  the  constraint list other
   67variables have on me.
   68
   69The `OrNode` is a term node(Pairs), where `Pairs` is a of list Var=Value
   70terms representing the pending unifications. The  original dif/2 call is
   71represented by a single OrNode.
   72
   73If a unification related to an  OrNode   fails  the terms are definitely
   74unequal and thus we can kill all   pending constraints and succeed. If a
   75unequal related to an OrNode succeeds we remove it from the node. If the
   76node becomes empty the terms are equal and we must fail.
   77
   78The following invariants must hold
   79
   80  - Any variable involved in a dif/2 constraint has an attribute
   81    vardif(L1,L2), Where each element of both lists is a term
   82    OrNode-Value, L1 represents the values this variable may __not__
   83    become equal to and L2 represents this variable involved in other
   84    constraints.  I.e, L2 is only used if a dif/2 requires two variables
   85    to be different.
   86  - An OrNode has an attribute node(Pairs), where Pairs contains the
   87    possible unifications.
   88- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
   89
   90dif_unifiable(X, Y, Us) :-
   91    (    current_prolog_flag(occurs_check, error)
   92    ->   catch(unifiable(X,Y,Us), error(occurs_check(_,_),_), false)
   93    ;    unifiable(X, Y, Us)
   94    ).
   95
   96%!  dif_c_c(+X,+Y,!OrNode)
   97%
   98%   Enforce dif(X,Y) that is related to the given OrNode. If X and Y are
   99%   equal we reduce the OrNode.  If  they   cannot  unify  we  are done.
  100%   Otherwise we extend the OrNode with  new pairs and create/extend the
  101%   vardif/2 terms for the left hand side of  the unifier as well as the
  102%   right hand if this is a variable.
  103
  104dif_c_c(X,Y,OrNode) :-
  105    (   dif_unifiable(X, Y, Unifier)
  106    ->  (   Unifier == []
  107        ->  or_one_fail(OrNode)
  108        ;   dif_c_c_l(Unifier,OrNode, U),
  109            subunifier(U, OrNode)
  110        )
  111    ;   or_succeed(OrNode)
  112    ).
  113
  114subunifier([], _).
  115subunifier([X=Y|T], OrNode) :-
  116    dif_c_c(X, Y, OrNode),
  117    subunifier(T, OrNode).
  118
  119
  120%!  dif_c_c_l(+Unifier, +OrNode)
  121%
  122%   Extend OrNode with new elements from the   unifier.  Note that it is
  123%   possible that a unification against the   same variable appears as a
  124%   result of how unifiable acts on  sharing subterms. This is prevented
  125%   by simplify_ornode/3.
  126%
  127%   @see test 14 in src/Tests/attvar/test_dif.pl.
  128
  129dif_c_c_l(Unifier, OrNode, U) :-
  130    extend_ornode(OrNode, List, Tail),
  131    dif_c_c_l_aux(Unifier, OrNode, List0, Tail),
  132    (   simplify_ornode(List0, List, U)
  133    ->  true
  134    ;   List = List0,
  135        or_succeed(OrNode),
  136        U = []
  137    ).
  138
  139extend_ornode(OrNode, List, Vars) :-
  140    (   get_attr(OrNode, dif, node(Vars))
  141    ->  true
  142    ;   Vars = []
  143    ),
  144    put_attr(OrNode,dif,node(List)).
  145
  146dif_c_c_l_aux([],_,List,List).
  147dif_c_c_l_aux([X=Y|Unifier],OrNode,List,Tail) :-
  148    List = [X=Y|Rest],
  149    add_ornode(X,Y,OrNode),
  150    dif_c_c_l_aux(Unifier,OrNode,Rest,Tail).
  151
  152%!  add_ornode(+X, +Y, +OrNode)
  153%
  154%   Extend the vardif constraints on X and Y with the OrNode.
  155
  156add_ornode(X,Y,OrNode) :-
  157    add_ornode_var1(X,Y,OrNode),
  158    (   var(Y)
  159    ->  add_ornode_var2(X,Y,OrNode)
  160    ;   true
  161    ).
  162
  163add_ornode_var1(X,Y,OrNode) :-
  164    (   get_attr(X,dif,Attr)
  165    ->  Attr = vardif(V1,V2),
  166        put_attr(X,dif,vardif([OrNode-Y|V1],V2))
  167    ;   put_attr(X,dif,vardif([OrNode-Y],[]))
  168    ).
  169
  170add_ornode_var2(X,Y,OrNode) :-
  171    (   get_attr(Y,dif,Attr)
  172    ->  Attr = vardif(V1,V2),
  173        put_attr(Y,dif,vardif(V1,[OrNode-X|V2]))
  174    ;   put_attr(Y,dif,vardif([],[OrNode-X]))
  175    ).
  176
  177%!  simplify_ornode(+OrNode) is semidet.
  178%
  179%   Simplify the possible unifications left on the original dif/2 terms.
  180%   There are two reasons for simplification. First   of all, due to the
  181%   way unifiable works we may end up with variables in the unifier that
  182%   do not refer to the original terms,   but  to variables in subterms,
  183%   e.g. `[V1 = f(a, V2), V2 = b]`.   As a result of subsequent unifying
  184%   variables, the unifier may end up   having  multiple entries for the
  185%   same variable, possibly having different values, e.g.,  `[X = a, X =
  186%   b]`.  As  these  can  never  be  satified  both  we  have  prove  of
  187%   inequality.
  188%
  189%   Finally, we remove elements from the list that have become equal. If
  190%   the OrNode is empty, the original terms   are equal and thus we must
  191%   fail.
  192%
  193%   @tbd The simplification is complicated. Another approach would be to
  194%   turn `[X1=Y1, X2=Y2, ...]` into  `[X1,X2,...]` and `[Y1,Y2,...]` and
  195%   call  unifiable/3  on  these  lists  to    either   end  up  with  a
  196%   contradiction (satisfied) or a  new  unifier.   This  is  a stronger
  197%   propagation. Seems not so easy though.  Both pending constraints and
  198%   reconnecting to the proper variables need attention.
  199
  200simplify_ornode(OrNode) :-
  201    (   get_attr(OrNode, dif, node(Pairs0))
  202    ->  simplify_ornode(Pairs0, Pairs, U),
  203	(   Pairs == [],
  204	    U == []
  205	->  fail
  206        ;   put_attr(OrNode, dif, node(Pairs)),
  207            subunifier(U, OrNode)
  208	)
  209    ;   true
  210    ).
  211
  212simplify_ornode(List0, List, U) :-
  213    sort(1, @=<, List0, Sorted),
  214    simplify_ornode_(Sorted, List, U).
  215
  216simplify_ornode_([], List, U) =>
  217    List = [],
  218    U = [].
  219simplify_ornode_([V1=V2|T], List, U), V1 == V2 =>
  220    simplify_ornode_(T, List, U).
  221simplify_ornode_([V1=Val1,V2=Val2|T], List, U), var(V1), V1 == V2 =>
  222    (   ?=(Val1, Val2)
  223    ->  Val1 == Val2,
  224        simplify_ornode_([V1=Val2|T], List, U)
  225    ;   U = [Val1=Val2|UT],
  226        simplify_ornode_([V2=Val2|T], List, UT)
  227    ).
  228simplify_ornode_([H|T], List, U) =>
  229    List = [H|Rest],
  230    simplify_ornode_(T, Rest, U).
  231
  232
  233%!  attr_unify_hook(+VarDif, +Other)
  234%
  235%   If two dif/2 variables are unified  we   must  join the two vardif/2
  236%   terms. To do so, we filter the vardif terms for the ones involved in
  237%   this unification. Those that  are  represent   OrNodes  that  have a
  238%   unification satisfied. For the rest we  remove the unifications with
  239%   _self_, append them and use this as new vardif term.
  240%
  241%   On unification with a value, we recursively call dif_c_c/3 using the
  242%   existing OrNodes.
  243
  244attr_unify_hook(vardif(V1,V2),Other) :-
  245    (   get_attr(Other, dif, vardif(OV1,OV2))
  246    ->  (   (   or_nodes_completed(V1)
  247	    ;   or_nodes_completed(V2)
  248	    )
  249	->  true
  250	;   reverse_lookups(V1, Other, OrNodes1, NV1),
  251	    or_one_fails(OrNodes1),
  252	    reverse_lookups(OV1, Other, OrNodes2, NOV1),
  253	    or_one_fails(OrNodes2),
  254	    remove_obsolete(V2, Other, NV2),
  255	    remove_obsolete(OV2, Other, NOV2),
  256	    append(NV1, NOV1, CV1),
  257	    append(NV2, NOV2, CV2),
  258	    (   CV1 == [], CV2 == []
  259	    ->  del_attr(Other, dif)
  260	    ;   put_attr(Other, dif, vardif(CV1,CV2))
  261	    )
  262        )
  263    ;   var(Other)			% unrelated variable
  264    ->  put_attr(Other, dif, vardif(V1,V2))
  265    ;   verify_compounds(V1, Other),    % concrete value
  266        verify_compounds(V2, Other)
  267    ).
  268
  269%!  or_nodes_completed(+List) is semidet.
  270%
  271%   Unification  may  have  made  some  of  the  or  nodes  internally
  272%   inconsistent.  This  code checks  for that and  makes the  or node
  273%   succeed if this is the case.
  274
  275or_nodes_completed(List) :-
  276    member(Or-_Value, List),
  277    get_attr(Or, dif, node(Unifiers0)),
  278    copy_term_nat(Unifiers0, Unifiers),
  279    \+ unify_list(Unifiers),
  280    !,
  281    or_succeed(Or).
  282
  283unify_list([]).
  284unify_list([A=A|T]) :-
  285    unify_list(T).
  286
  287
  288remove_obsolete([], _, []).
  289remove_obsolete([N-Y|T], X, L) :-
  290    (   Y==X
  291    ->  remove_obsolete(T, X, L)
  292    ;   L=[N-Y|RT],
  293        remove_obsolete(T, X, RT)
  294    ).
  295
  296reverse_lookups([],_,[],[]).
  297reverse_lookups([N-X|NXs],Value,Nodes,Rest) :-
  298    (   X == Value
  299    ->  Nodes = [N|RNodes],
  300        Rest = RRest
  301    ;   Nodes = RNodes,
  302        Rest = [N-X|RRest]
  303    ),
  304    reverse_lookups(NXs,Value,RNodes,RRest).
  305
  306%!  verify_compounds(+Nodes, +Value)
  307%
  308%   Unification to a concrete Value (no variable)
  309
  310verify_compounds([],_).
  311verify_compounds([OrNode-Y|Rest],X) :-
  312    (   var(Y)
  313    ->  true
  314    ;   OrNode == (-)
  315    ->  true
  316    ;   dif_c_c(X,Y,OrNode)
  317    ),
  318    verify_compounds(Rest,X).
  319
  320%!  or_succeed(+OrNode) is det.
  321%
  322%   The dif/2 constraint related  to  OrNode   is  complete,  i.e., some
  323%   (sub)terms can definitely not become equal.   Next,  we can clean up
  324%   the constraints. We do so by setting   the  OrNode to `-` and remove
  325%   this _dead_ OrNode from every vardif/2 attribute we can find.
  326
  327or_succeed(OrNode) :-
  328    (   get_attr(OrNode,dif,Attr)
  329    ->  Attr = node(Pairs),
  330        del_attr(OrNode,dif),
  331        OrNode = (-),
  332        del_or_dif(Pairs)
  333    ;   true
  334    ).
  335
  336del_or_dif([]).
  337del_or_dif([X=Y|Xs]) :-
  338    cleanup_dead_nodes(X),
  339    cleanup_dead_nodes(Y),              % JW: what about embedded variables?
  340    del_or_dif(Xs).
  341
  342cleanup_dead_nodes(X) :-
  343    (   get_attr(X,dif,Attr)
  344    ->  Attr = vardif(V1,V2),
  345        filter_dead_ors(V1,NV1),
  346        filter_dead_ors(V2,NV2),
  347        (   NV1 == [], NV2 == []
  348        ->  del_attr(X,dif)
  349        ;   put_attr(X,dif,vardif(NV1,NV2))
  350        )
  351    ;   true
  352    ).
  353
  354filter_dead_ors([],[]).
  355filter_dead_ors([Or-Y|Rest],List) :-
  356    (   var(Or)
  357    ->  List = [Or-Y|NRest]
  358    ;   List = NRest
  359    ),
  360    filter_dead_ors(Rest,NRest).
  361
  362
  363%!  or_one_fail(+OrNode) is semidet.
  364%
  365%   Some unification related to OrNode succeeded.
  366
  367or_one_fail(OrNode) :-
  368    simplify_ornode(OrNode).
  369
  370or_one_fails([]).
  371or_one_fails([N|Ns]) :-
  372    or_one_fail(N),
  373    or_one_fails(Ns).
  374
  375
  376/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  377   The attribute of a variable X is vardif/2. The first argument is a
  378   list of pairs. The first component of each pair is an OrNode. The
  379   attribute of each OrNode is node/2. The second argument of node/2
  380   is a list of equations A = B. If the LHS of the first equation is
  381   X, then return a goal, otherwise don't because someone else will.
  382- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  383
  384attribute_goals(Var) -->
  385    (   { get_attr(Var, dif, vardif(Ors,_)) }
  386    ->  or_nodes(Ors, Var)
  387    ;   or_node(Var)
  388    ).
  389
  390or_node(O) -->
  391    (   { get_attr(O, dif, node(Pairs)) }
  392    ->  { eqs_lefts_rights(Pairs, As, Bs) },
  393        mydif(As, Bs),
  394        { del_attr(O, dif) }
  395    ;   []
  396    ).
  397
  398or_nodes([], _)       --> [].
  399or_nodes([O-_|Os], X) -->
  400    (   { get_attr(O, dif, node(Eqs)) }
  401    ->  (   { Eqs = [LHS=_|_], LHS == X }
  402        ->  { eqs_lefts_rights(Eqs, As, Bs) },
  403            mydif(As, Bs),
  404            { del_attr(O, dif) }
  405        ;   []
  406        )
  407    ;   [] % or-node already removed
  408    ),
  409    or_nodes(Os, X).
  410
  411mydif([X], [Y]) --> !, dif_if_necessary(X, Y).
  412mydif(Xs0, Ys0) -->
  413    { reverse(Xs0, Xs), reverse(Ys0, Ys), % follow original order
  414      X =.. [f|Xs], Y =.. [f|Ys]
  415    },
  416    dif_if_necessary(X, Y).
  417
  418dif_if_necessary(X, Y) -->
  419    (   { dif_unifiable(X, Y, _) }
  420    ->  [dif(X,Y)]
  421    ;   []
  422    ).
  423
  424eqs_lefts_rights([], [], []).
  425eqs_lefts_rights([A=B|ABs], [A|As], [B|Bs]) :-
  426    eqs_lefts_rights(ABs, As, Bs)