/* Part of SWI-Prolog
Author: Tom Schrijvers, Markus Triska and Jan Wielemaker
E-mail: Tom.Schrijvers@cs.kuleuven.ac.be
WWW: http://www.swi-prolog.org
Copyright (c) 2004-2023, K.U.Leuven
SWI-Prolog Solutions b.v.
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*/
:- module(dif,
[ dif/2 % +Term1, +Term2
]).
:- autoload(library(lists),[append/3, reverse/2, member/2]).
:- set_prolog_flag(generate_debug_info, false).
/** <module> 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.
dif(X,Y) :-
?=(X,Y),
!,
X \== Y.
dif(X,Y) :-
dif_c_c(X,Y,_).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The constraint is helt in an attribute `dif`. A constrained variable
holds a term vardif(L1,L2) where `L1` is a list OrNode-Value for
constraints on this variable and `L2` is the constraint list other
variables have on me.
The `OrNode` is a term node(Pairs), where `Pairs` is a of list Var=Value
terms representing the pending unifications. The original dif/2 call is
represented by a single OrNode.
If a unification related to an OrNode fails the terms are definitely
unequal and thus we can kill all pending constraints and succeed. If a
unequal related to an OrNode succeeds we remove it from the node. If the
node becomes empty the terms are equal and we must fail.
The following invariants must hold
- Any variable involved in a dif/2 constraint has an attribute
vardif(L1,L2), Where each element of both lists is a term
OrNode-Value, L1 represents the values this variable may __not__
become equal to and L2 represents this variable involved in other
constraints. I.e, L2 is only used if a dif/2 requires two variables
to be different.
- An OrNode has an attribute node(Pairs), where Pairs contains the
possible unifications.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
dif_unifiable(X, Y, Us) :-
( current_prolog_flag(occurs_check, error)
-> catch(unifiable(X,Y,Us), error(occurs_check(_,_),_), false)
; unifiable(X, Y, Us)
).
%! 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.
dif_c_c(X,Y,OrNode) :-
( dif_unifiable(X, Y, Unifier)
-> ( Unifier == []
-> or_one_fail(OrNode)
; dif_c_c_l(Unifier,OrNode, U),
subunifier(U, OrNode)
)
; or_succeed(OrNode)
).
subunifier([], _).
subunifier([X=Y|T], OrNode) :-
dif_c_c(X, Y, OrNode),
subunifier(T, OrNode).
%! dif_c_c_l(+Unifier, +OrNode)
%
% Extend OrNode with new elements from the unifier. Note that it is
% possible that a unification against the same variable appears as a
% result of how unifiable acts on sharing subterms. This is prevented
% by simplify_ornode/3.
%
% @see test 14 in src/Tests/attvar/test_dif.pl.
dif_c_c_l(Unifier, OrNode, U) :-
extend_ornode(OrNode, List, Tail),
dif_c_c_l_aux(Unifier, OrNode, List0, Tail),
( simplify_ornode(List0, List, U)
-> true
; List = List0,
or_succeed(OrNode),
U = []
).
extend_ornode(OrNode, List, Vars) :-
( get_attr(OrNode, dif, node(Vars))
-> true
; Vars = []
),
put_attr(OrNode,dif,node(List)).
dif_c_c_l_aux([],_,List,List).
dif_c_c_l_aux([X=Y|Unifier],OrNode,List,Tail) :-
List = [X=Y|Rest],
add_ornode(X,Y,OrNode),
dif_c_c_l_aux(Unifier,OrNode,Rest,Tail).
%! add_ornode(+X, +Y, +OrNode)
%
% Extend the vardif constraints on X and Y with the OrNode.
add_ornode(X,Y,OrNode) :-
add_ornode_var1(X,Y,OrNode),
( var(Y)
-> add_ornode_var2(X,Y,OrNode)
; true
).
add_ornode_var1(X,Y,OrNode) :-
( get_attr(X,dif,Attr)
-> Attr = vardif(V1,V2),
put_attr(X,dif,vardif([OrNode-Y|V1],V2))
; put_attr(X,dif,vardif([OrNode-Y],[]))
).
add_ornode_var2(X,Y,OrNode) :-
( get_attr(Y,dif,Attr)
-> Attr = vardif(V1,V2),
put_attr(Y,dif,vardif(V1,[OrNode-X|V2]))
; put_attr(Y,dif,vardif([],[OrNode-X]))
).
%! simplify_ornode(+OrNode) is semidet.
%
% Simplify the possible unifications left on the original dif/2 terms.
% There are two reasons for simplification. First of all, due to the
% way unifiable works we may end up with variables in the unifier that
% do not refer to the original terms, but to variables in subterms,
% e.g. `[V1 = f(a, V2), V2 = b]`. As a result of subsequent unifying
% variables, the unifier may end up having multiple entries for the
% same variable, possibly having different values, e.g., `[X = a, X =
% b]`. As these can never be satified both we have prove of
% inequality.
%
% Finally, we remove elements from the list that have become equal. If
% the OrNode is empty, the original terms are equal and thus we must
% fail.
%
% @tbd The simplification is complicated. Another approach would be to
% turn `[X1=Y1, X2=Y2, ...]` into `[X1,X2,...]` and `[Y1,Y2,...]` and
% call unifiable/3 on these lists to either end up with a
% contradiction (satisfied) or a new unifier. This is a stronger
% propagation. Seems not so easy though. Both pending constraints and
% reconnecting to the proper variables need attention.
simplify_ornode(OrNode) :-
( get_attr(OrNode, dif, node(Pairs0))
-> simplify_ornode(Pairs0, Pairs, U),
( Pairs == [],
U == []
-> fail
; put_attr(OrNode, dif, node(Pairs)),
subunifier(U, OrNode)
)
; true
).
simplify_ornode(List0, List, U) :-
sort(1, @=<, List0, Sorted),
simplify_ornode_(Sorted, List, U).
simplify_ornode_([], List, U) =>
List = [],
U = [].
simplify_ornode_([V1=V2|T], List, U), V1 == V2 =>
simplify_ornode_(T, List, U).
simplify_ornode_([V1=Val1,V2=Val2|T], List, U), var(V1), V1 == V2 =>
( ?=(Val1, Val2)
-> Val1 == Val2,
simplify_ornode_([V1=Val2|T], List, U)
; U = [Val1=Val2|UT],
simplify_ornode_([V2=Val2|T], List, UT)
).
simplify_ornode_([H|T], List, U) =>
List = [H|Rest],
simplify_ornode_(T, Rest, U).
%! attr_unify_hook(+VarDif, +Other)
%
% If two dif/2 variables are unified we must join the two vardif/2
% terms. To do so, we filter the vardif terms for the ones involved in
% this unification. Those that are represent OrNodes that have a
% unification satisfied. For the rest we remove the unifications with
% _self_, append them and use this as new vardif term.
%
% On unification with a value, we recursively call dif_c_c/3 using the
% existing OrNodes.
attr_unify_hook(vardif(V1,V2),Other) :-
( get_attr(Other, dif, vardif(OV1,OV2))
-> ( ( or_nodes_completed(V1)
; or_nodes_completed(V2)
)
-> true
; reverse_lookups(V1, Other, OrNodes1, NV1),
or_one_fails(OrNodes1),
reverse_lookups(OV1, Other, OrNodes2, NOV1),
or_one_fails(OrNodes2),
remove_obsolete(V2, Other, NV2),
remove_obsolete(OV2, Other, NOV2),
append(NV1, NOV1, CV1),
append(NV2, NOV2, CV2),
( CV1 == [], CV2 == []
-> del_attr(Other, dif)
; put_attr(Other, dif, vardif(CV1,CV2))
)
)
; var(Other) % unrelated variable
-> put_attr(Other, dif, vardif(V1,V2))
; verify_compounds(V1, Other), % concrete value
verify_compounds(V2, Other)
).
%! or_nodes_completed(+List) is semidet.
%
% Unification may have made some of the or nodes internally
% inconsistent. This code checks for that and makes the or node
% succeed if this is the case.
or_nodes_completed(List) :-
member(Or-_Value, List),
get_attr(Or, dif, node(Unifiers0)),
copy_term_nat(Unifiers0, Unifiers),
\+ unify_list(Unifiers),
!,
or_succeed(Or).
unify_list([]).
unify_list([A=A|T]) :-
unify_list(T).
remove_obsolete([], _, []).
remove_obsolete([N-Y|T], X, L) :-
( Y==X
-> remove_obsolete(T, X, L)
; L=[N-Y|RT],
remove_obsolete(T, X, RT)
).
reverse_lookups([],_,[],[]).
reverse_lookups([N-X|NXs],Value,Nodes,Rest) :-
( X == Value
-> Nodes = [N|RNodes],
Rest = RRest
; Nodes = RNodes,
Rest = [N-X|RRest]
),
reverse_lookups(NXs,Value,RNodes,RRest).
%! verify_compounds(+Nodes, +Value)
%
% Unification to a concrete Value (no variable)
verify_compounds([],_).
verify_compounds([OrNode-Y|Rest],X) :-
( var(Y)
-> true
; OrNode == (-)
-> true
; dif_c_c(X,Y,OrNode)
),
verify_compounds(Rest,X).
%! 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.
or_succeed(OrNode) :-
( get_attr(OrNode,dif,Attr)
-> Attr = node(Pairs),
del_attr(OrNode,dif),
OrNode = (-),
del_or_dif(Pairs)
; true
).
del_or_dif([]).
del_or_dif([X=Y|Xs]) :-
cleanup_dead_nodes(X),
cleanup_dead_nodes(Y), % JW: what about embedded variables?
del_or_dif(Xs).
cleanup_dead_nodes(X) :-
( get_attr(X,dif,Attr)
-> Attr = vardif(V1,V2),
filter_dead_ors(V1,NV1),
filter_dead_ors(V2,NV2),
( NV1 == [], NV2 == []
-> del_attr(X,dif)
; put_attr(X,dif,vardif(NV1,NV2))
)
; true
).
filter_dead_ors([],[]).
filter_dead_ors([Or-Y|Rest],List) :-
( var(Or)
-> List = [Or-Y|NRest]
; List = NRest
),
filter_dead_ors(Rest,NRest).
%! or_one_fail(+OrNode) is semidet.
%
% Some unification related to OrNode succeeded.
or_one_fail(OrNode) :-
simplify_ornode(OrNode).
or_one_fails([]).
or_one_fails([N|Ns]) :-
or_one_fail(N),
or_one_fails(Ns).
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
The attribute of a variable X is vardif/2. The first argument is a
list of pairs. The first component of each pair is an OrNode. The
attribute of each OrNode is node/2. The second argument of node/2
is a list of equations A = B. If the LHS of the first equation is
X, then return a goal, otherwise don't because someone else will.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
attribute_goals(Var) -->
( { get_attr(Var, dif, vardif(Ors,_)) }
-> or_nodes(Ors, Var)
; or_node(Var)
).
or_node(O) -->
( { get_attr(O, dif, node(Pairs)) }
-> { eqs_lefts_rights(Pairs, As, Bs) },
mydif(As, Bs),
{ del_attr(O, dif) }
; []
).
or_nodes([], _) --> [].
or_nodes([O-_|Os], X) -->
( { get_attr(O, dif, node(Eqs)) }
-> ( { Eqs = [LHS=_|_], LHS == X }
-> { eqs_lefts_rights(Eqs, As, Bs) },
mydif(As, Bs),
{ del_attr(O, dif) }
; []
)
; [] % or-node already removed
),
or_nodes(Os, X).
mydif([X], [Y]) --> !, dif_if_necessary(X, Y).
mydif(Xs0, Ys0) -->
{ reverse(Xs0, Xs), reverse(Ys0, Ys), % follow original order
X =.. [f|Xs], Y =.. [f|Ys]
},
dif_if_necessary(X, Y).
dif_if_necessary(X, Y) -->
( { dif_unifiable(X, Y, _) }
-> [dif(X,Y)]
; []
).
eqs_lefts_rights([], [], []).
eqs_lefts_rights([A=B|ABs], [A|As], [B|Bs]) :-
eqs_lefts_rights(ABs, As, Bs).