/* 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. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ :- module(dif, [ dif/2 % +Term1, +Term2 ]). :- autoload(library(lists),[append/3, reverse/2, member/2]). :- 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. 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).