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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.
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   35
   36:- module(dif,
   37          [ dif/2                               % +Term1, +Term2
   38          ]).   39:- autoload(library(lists),[append/3, reverse/2]).   40
   41
   42:- set_prolog_flag(generate_debug_info, false).

The dif/2 constraint

 dif(+Term1, +Term2) is semidet
Constraint that expresses that Term1 and Term2 never become identical (==/2). Fails if Term1 == Term2. Succeeds if Term1 can never become identical to Term2. In other cases the predicate succeeds after attaching constraints to the relevant parts of Term1 and Term2 that prevent the two terms to become identical.
   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    ).
 dif_c_c(+X, +Y, !OrNode)
Enforce dif(X,Y) that is related to the given OrNode. If X and Y are equal we reduce the OrNode. If they cannot unify we are done. Otherwise we extend the OrNode with new pairs and create/extend the vardif/2 terms for the left hand side of the unifier as well as the right hand if this is a variable.
  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)
  109        )
  110    ;   or_succeed(OrNode)
  111    ).
 dif_c_c_l(+Unifier, +OrNode)
Combine the incoming unifier with the OrNode's current pending set, then recompute the most-general unifier for the whole using unifiable/3 over the accumulated left- and right-hand-side lists. That gives canonical propagation and avoids the infinite oscillation pair-wise simplification hits on cyclic terms.

Fails if the recomputed set is empty — that means all pending equations are trivially satisfied and thus the original dif/2 terms are equal, so dif/2 must fail. Calls or_succeed/1 when unifiable/3 itself fails: the pending equations can never all hold, so the two terms are definitely unequal and dif/2 is satisfied.

  128dif_c_c_l(_Unifier, OrNode) :-
  129    nonvar(OrNode),                          % dead (or_succeed'd) node
  130    !.
  131dif_c_c_l(Unifier, OrNode) :-
  132    (   get_attr(OrNode, dif, node(OldPairs))
  133    ->  true
  134    ;   OldPairs = []
  135    ),
  136    append(Unifier, OldPairs, All),
  137    (   All == []
  138    ->  true                                 % nothing pending
  139    ;   eqs_lefts_rights(All, Xs, Ys),
  140        (   dif_unifiable(Xs, Ys, NewPairs)
  141        ->  NewPairs \== [],                 % [] ⇒ all satisfied ⇒ fail
  142            remove_ornode_from_pairs(OldPairs, OrNode),
  143            add_ornode_pairs(NewPairs, OrNode),
  144            put_attr(OrNode, dif, node(NewPairs))
  145        ;   or_succeed(OrNode)
  146        )
  147    ).
  148
  149remove_ornode_from_pairs([], _).
  150remove_ornode_from_pairs([X=Y|T], OrNode) :-
  151    (   var(X) -> remove_ornode_v1(X, OrNode) ; true ),
  152    (   var(Y) -> remove_ornode_v2(Y, OrNode) ; true ),
  153    remove_ornode_from_pairs(T, OrNode).
  154
  155remove_ornode_v1(X, OrNode) :-
  156    (   get_attr(X, dif, vardif(V1, V2))
  157    ->  filter_out_ornode(V1, OrNode, NV1),
  158        (   NV1 == [], V2 == []
  159        ->  del_attr(X, dif)
  160        ;   put_attr(X, dif, vardif(NV1, V2))
  161        )
  162    ;   true
  163    ).
  164
  165remove_ornode_v2(Y, OrNode) :-
  166    (   get_attr(Y, dif, vardif(V1, V2))
  167    ->  filter_out_ornode(V2, OrNode, NV2),
  168        (   V1 == [], NV2 == []
  169        ->  del_attr(Y, dif)
  170        ;   put_attr(Y, dif, vardif(V1, NV2))
  171        )
  172    ;   true
  173    ).
  174
  175filter_out_ornode([], _, []).
  176filter_out_ornode([N-Y|T], OrNode, L) :-
  177    (   N == OrNode
  178    ->  filter_out_ornode(T, OrNode, L)
  179    ;   L = [N-Y|LT],
  180        filter_out_ornode(T, OrNode, LT)
  181    ).
  182
  183add_ornode_pairs([], _).
  184add_ornode_pairs([X=Y|T], OrNode) :-
  185    add_ornode(X, Y, OrNode),
  186    add_ornode_pairs(T, OrNode).
 add_ornode(+X, +Y, +OrNode)
Extend the vardif constraints on X and Y with the OrNode.
  192add_ornode(X,Y,OrNode) :-
  193    add_ornode_var1(X,Y,OrNode),
  194    (   var(Y)
  195    ->  add_ornode_var2(X,Y,OrNode)
  196    ;   true
  197    ).
  198
  199add_ornode_var1(X,Y,OrNode) :-
  200    (   get_attr(X,dif,Attr)
  201    ->  Attr = vardif(V1,V2),
  202        put_attr(X,dif,vardif([OrNode-Y|V1],V2))
  203    ;   put_attr(X,dif,vardif([OrNode-Y],[]))
  204    ).
  205
  206add_ornode_var2(X,Y,OrNode) :-
  207    (   get_attr(Y,dif,Attr)
  208    ->  Attr = vardif(V1,V2),
  209        put_attr(Y,dif,vardif(V1,[OrNode-X|V2]))
  210    ;   put_attr(Y,dif,vardif([],[OrNode-X]))
  211    ).
 attr_unify_hook(+VarDif, +Other)
Called after the attributed variable has been unified with Other. Collects every OrNode this variable (and, for a var-var unification, Other) is involved in and recomputes each one's MGU. The rebuild inside dif_c_c_l/2 keeps the OrNode's pending list, this variable's vardif and Other's vardif consistent — the current bindings show through variable dereferencing when eqs_lefts_rights/3 walks the pending list.
  223attr_unify_hook(vardif(V1, V2), Other) :-
  224    live_ornodes(V1, V2, MyOrNodes),
  225    (   var(Other),
  226        get_attr(Other, dif, vardif(OV1, OV2))
  227    ->  live_ornodes(OV1, OV2, TheirOrNodes),
  228        append(MyOrNodes, TheirOrNodes, OrNodes0),
  229        sort(OrNodes0, OrNodes)              % dedup by identity
  230    ;   OrNodes = MyOrNodes
  231    ),
  232    recompute_ornodes(OrNodes).
  233
  234live_ornodes(V1, V2, OrNodes) :-
  235    live_ornodes_(V1, L1, T1),
  236    live_ornodes_(V2, T1, []),
  237    OrNodes = L1.
  238
  239live_ornodes_([], T, T).
  240live_ornodes_([O-_|R], L, T) :-
  241    (   var(O)
  242    ->  L = [O|L1]
  243    ;   L = L1
  244    ),
  245    live_ornodes_(R, L1, T).
  246
  247recompute_ornodes([]).
  248recompute_ornodes([O|T]) :-
  249    or_one_fail(O),
  250    recompute_ornodes(T).
 or_succeed(+OrNode) is det
The dif/2 constraint related to OrNode is complete, i.e., some (sub)terms can definitely not become equal. Next, we can clean up the constraints. We do so by setting the OrNode to - and remove this dead OrNode from every vardif/2 attribute we can find.
  259or_succeed(OrNode) :-
  260    (   get_attr(OrNode,dif,Attr)
  261    ->  Attr = node(Pairs),
  262        del_attr(OrNode,dif),
  263        OrNode = (-),
  264        del_or_dif(Pairs)
  265    ;   true
  266    ).
  267
  268del_or_dif([]).
  269del_or_dif([X=Y|Xs]) :-
  270    cleanup_dead_nodes(X),
  271    cleanup_dead_nodes(Y),              % JW: what about embedded variables?
  272    del_or_dif(Xs).
  273
  274cleanup_dead_nodes(X) :-
  275    (   get_attr(X,dif,Attr)
  276    ->  Attr = vardif(V1,V2),
  277        filter_dead_ors(V1,NV1),
  278        filter_dead_ors(V2,NV2),
  279        (   NV1 == [], NV2 == []
  280        ->  del_attr(X,dif)
  281        ;   put_attr(X,dif,vardif(NV1,NV2))
  282        )
  283    ;   true
  284    ).
  285
  286filter_dead_ors([],[]).
  287filter_dead_ors([Or-Y|Rest],List) :-
  288    (   var(Or)
  289    ->  List = [Or-Y|NRest]
  290    ;   List = NRest
  291    ),
  292    filter_dead_ors(Rest,NRest).
 or_one_fail(+OrNode) is semidet
Recompute the MGU for OrNode's pending set without adding any new equations. Fails when the set becomes empty (dif/2 fails).
  300or_one_fail(OrNode) :-
  301    dif_c_c_l([], OrNode).
  302
  303
  304/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
  305   The attribute of a variable X is vardif/2. The first argument is a
  306   list of pairs. The first component of each pair is an OrNode. The
  307   attribute of each OrNode is node/2. The second argument of node/2
  308   is a list of equations A = B. If the LHS of the first equation is
  309   X, then return a goal, otherwise don't because someone else will.
  310- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
  311
  312attribute_goals(Var) -->
  313    (   { get_attr(Var, dif, vardif(Ors,_)) }
  314    ->  or_nodes(Ors, Var)
  315    ;   or_node(Var)
  316    ).
  317
  318or_node(O) -->
  319    (   { get_attr(O, dif, node(Pairs)) }
  320    ->  { eqs_lefts_rights(Pairs, As, Bs) },
  321        mydif(As, Bs),
  322        { del_attr(O, dif) }
  323    ;   []
  324    ).
  325
  326or_nodes([], _)       --> [].
  327or_nodes([O-_|Os], X) -->
  328    (   { get_attr(O, dif, node(Eqs)) }
  329    ->  (   { Eqs = [LHS=_|_], LHS == X }
  330        ->  { eqs_lefts_rights(Eqs, As, Bs) },
  331            mydif(As, Bs),
  332            { del_attr(O, dif) }
  333        ;   []
  334        )
  335    ;   [] % or-node already removed
  336    ),
  337    or_nodes(Os, X).
  338
  339mydif([X], [Y]) --> !, dif_if_necessary(X, Y).
  340mydif(Xs0, Ys0) -->
  341    { reverse(Xs0, Xs), reverse(Ys0, Ys), % follow original order
  342      X =.. [f|Xs], Y =.. [f|Ys]
  343    },
  344    dif_if_necessary(X, Y).
  345
  346dif_if_necessary(X, Y) -->
  347    (   { dif_unifiable(X, Y, _) }
  348    ->  [dif(X,Y)]
  349    ;   []
  350    ).
  351
  352eqs_lefts_rights([], [], []).
  353eqs_lefts_rights([A=B|ABs], [A|As], [B|Bs]) :-
  354    eqs_lefts_rights(ABs, As, Bs)