%%% -*- Mode: Prolog; -*- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % prefix-trees for managing a DNF % remembers shortest prefix of a conjunction only (i.e. a*b+a*b*c results in a*b only, but b*a+a*b*c is not reduced) % children are sorted, but branches aren't (to speed up search while keeping structure sharing from proof procedure) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% :- module(ptree,[init_ptree/1, delete_ptree/1, rename_ptree/2, member_ptree/2, enum_member_ptree/2, insert_ptree/2, delete_ptree/2, edges_ptree/2, count_ptree/2, prune_check_ptree/2, empty_ptree/1, merge_ptree/3, bdd_ptree/3, bdd_ptree_map/4 ]). :- use_module(library(tries), [ trie_open/1, trie_close/1, trie_stats/4, trie_check_entry/3, trie_get_entry/2, trie_put_entry/3, trie_remove_entry/1, trie_usage/4, trie_dup/2, trie_join/2, trie_traverse/2 ]). :- use_module(library(ordsets), [ ord_subset/2 ]). :- style_check(all). :- yap_flag(unknown,error). :- use_module(flags,[problog_flag/2]). :- ensure_loaded(library(lists)). :- ensure_loaded(library(system)). % name lexicon external - internal sym(1,tree1) :- !. sym(2,tree2) :- !. sym(3,tree3) :- !. sym(N,AN) :- atomic_concat([tree,N],AN). %%%%%%%%%%%%%%%%%%%%%%%% % ptree basics %%%%%%%%%%%%%%%%%%%%%%%% init_ptree(ID) :- sym(ID,Sym), trie_open(Trie), nb_setval(Sym, Trie). delete_ptree(ID) :- sym(ID,Sym), nb_getval(Sym, Trie), !, trie_close(Trie), trie_open(NewTrie), nb_setval(Sym, NewTrie). delete_ptree(_). rename_ptree(OldID,NewID) :- sym(OldID,OldSym), sym(NewID,NewSym), nb_getval(OldSym, Trie), nb_set_shared_val(NewSym, Trie). empty_ptree(ID) :- sym(ID,Sym), nb_getval(Sym, Trie), trie_usage(Trie, 0, 0, 0). %%%%%%%%%%%%%%%%%%%%%%%% % member %%%%%%%%%%%%%%%%%%%%%%%% % non-backtrackable (to check) member_ptree(List,ID) :- sym(ID,Sym), nb_getval(Sym, Trie), trie_check_entry(Trie, List, _). % backtrackable (to list) enum_member_ptree(ID,List) :- sym(ID,Sym), nb_getval(Sym, Tree), trie_path(Tree, List). trie_path(Tree, List) :- trie_traverse(Tree,Ref), trie_get_entry(Ref, List). %%%%%%%%%%%%%%%%%%%%%%%% % insert conjunction %%%%%%%%%%%%%%%%%%%%%%%% insert_ptree(true,ID) :- sym(ID,Sym), !, nb_getval(Sym, Trie), trie_close(Trie), trie_open(NTrie), trie_put_entry(NTrie, true, _). insert_ptree(List,ID) :- sym(ID,Sym), nb_getval(Sym, Trie), trie_put_entry(Trie, List, _). %%%%%%%%%%%%%%%%%%%%%%%% % delete conjunction %%%%%%%%%%%%%%%%%%%%%%%% delete_ptree(List,ID) :- sym(ID,Sym), nb_getval(Sym, Trie), trie_check_entry(Trie, List, Ref), trie_remove_entry(Ref). %%%%%%%% % return list -Edges of all edge labels in ptree % doesn't use any heuristic to order those for the BDD % (automatic reordering has to do the job) %%%%%%%%% edges_ptree(ID,[]) :- empty_ptree(ID), !. edges_ptree(ID,[]) :- sym(ID,Sym), nb_getval(Sym, Trie), trie_check_entry(Trie, true, _), !. edges_ptree(ID,Edges) :- sym(ID,Sym), nb_getval(Sym, Trie), setof(X, trie_literal(Trie, X), Edges). trie_literal(Trie, X) :- trie_traverse(Trie,Ref), trie_get_entry(Ref, List), member(X, List). %%%%%%%% % number of conjunctions in the tree %%%%%%%%% count_ptree(ID,N) :- sym(ID,Sym), nb_getval(Sym, Trie), trie_usage(Trie, N, _, _). %%%%%%%% % check whether some branch of ptree is a subset of conjunction List % useful for pruning the search for proofs (optional due to time overhead) % currently not implemented, just fails %%%%%%% prune_check_ptree(_List,_TreeID) :- format(user,'FAIL: prune check currently not supported~n',[]), flush_output(user), fail. %%%%%%%%%%%%% % merge two ptrees % - take care not to loose proper prefixes that are proofs! %%%%%%%%%%%%%%% merge_ptree(ID1,_,ID3) :- sym(ID1,Sym1), sym(ID3,Sym3), nb_getval(Sym1, T1), trie_check_entry(T1, true, _), !, trie_open(T3), trie_put_entry(T3, true, _), nb_setval(Sym3, T3). merge_ptree(_,ID2,ID3) :- sym(ID2,Sym2), sym(ID3,Sym3), nb_getval(Sym2, T2), trie_check_entry(T2, true, _), !, trie_open(T3), trie_put_entry(T3, true, _), nb_setval(Sym3, T3). merge_ptree(ID1,ID2,ID3) :- sym(ID1,Sym1), sym(ID2,Sym2), sym(ID3,Sym3), nb_getval(Sym1, T1), nb_getval(Sym2, T2), trie_dup(T1, T3), trie_join(T3,T2), nb_setval(Sym3, T3). %%%%%%%%%%%%%%%%%%%%%%%% % write BDD info for given ptree to file % - initializes leaf BDDs (=variables) first % - then compresses ptree to exploit subtree sharing % - bdd_pt/1 does the work on the structure itself %%%%%%%%%%%%%%%%%%%%%%%% bdd_ptree(ID,FileBDD,FileParam) :- bdd_ptree_script(ID,FileBDD,FileParam), eraseall(map). % version returning variable mapping bdd_ptree_map(ID,FileBDD,FileParam,Mapping) :- bdd_ptree_script(ID,FileBDD,FileParam), findall(X,recorded(map,X,_),Map), add_probs(Map,Mapping), eraseall(map). add_probs([],[]). add_probs([m(A,Name)|Map],[m(A,Name,Prob)|Mapping]) :- problog:get_fact_probability(A,Prob), add_probs(Map,Mapping). % number of variables may be to high: % counted on trie, but conversion to old tree representation % transforms A*B+A to A (prefix-test) bdd_ptree_script(ID,FileBDD,FileParam) :- edges_ptree(ID,Edges), tell(FileParam), bdd_vars_script(Edges), flush_output, told, length(Edges,VarCount), assert(c_num(1)), bdd_pt(ID,CT), c_num(NN), IntermediateSteps is NN-1, tell(FileBDD), format('@BDD1~n~w~n~w~n~w~n',[VarCount,0,IntermediateSteps]), output_compressed_script(CT), told, retractall(c_num(_)), retractall(compression(_,_)). % write parameter file by iterating over all var/not(var) occuring in the tree bdd_vars_script(Edges) :- bdd_vars_script(Edges,0). bdd_vars_script([],_). bdd_vars_script([A|B],N) :- problog:get_fact_probability(A,P), get_var_name(A,NameA), format('@~w~n~12f~n',[NameA,P]), NN is N+1, bdd_vars_script(B,NN). %%%%%%%%%%%%%%%%%%%%%%%% % find top level symbol for script %%%%%%%%%%%%%%%%%%%%%%%% % special cases: variable-free formulae bdd_pt(ID,false) :- empty_ptree(ID), !, once(retractall(c_num(_))), once(assert(c_num(2))). bdd_pt(ID,true) :- sym(ID,Sym), nb_getval(Sym, Trie), trie_check_entry(Trie, true, _), !, once(retractall(c_num(_))), once(assert(c_num(2))). % general case: transform trie to nested tree structure for compression bdd_pt(ID,CT) :- sym(ID,Sym), nb_getval(Sym, Trie), trie_to_tree(Trie, Tree), compress_pt(Tree,CT). trie_to_tree(Trie, Tree) :- findall(Path,trie_path(Trie, Path), Paths), add_trees(Paths, [], Tree). add_trees([], Tree, Tree). add_trees([List|Paths], Tree0, Tree) :- ins_pt(List, Tree0, TreeI), add_trees(Paths, TreeI, Tree). ins_pt([],_T,[]) :- !. ins_pt([A|B],[s(A1,AT)|OldT],NewT) :- compare(Comp, A1, A), (Comp == = -> (AT == [] -> NewT=[s(A1,AT)|OldT] ; NewT = [s(A1,NewAT)|OldT], ins_pt(B, AT, NewAT)) ; Comp == > -> NewT = [s(A1,AT)|Tree], ins_pt([A|B], OldT, Tree) ; NewT = [s(A,BTree),s(A1,AT)|OldT], ins_pt(B,[],BTree) ). ins_pt([A|B],[],[s(A,NewAT)]) :- ins_pt(B,[],NewAT). %%%%%%%%%%%% % BDD compression: alternates and- and or-levels to build BDD bottom-up % each sub-BDD will be either a conjunction of a one-node BDD with some BDD or a disjunction of BDDs % uses the internal database to temporarily store a map of components %%%%%%%%%%%% % T is completely compressed and contains single variable % i.e. T of form x12 compress_pt(T,TT) :- atom(T), test_var_name(T), !, get_next_name(TT), assertz(compression(TT,[T])). % T is completely compressed and contains subtrees % i.e. T of form 'L56' compress_pt(T,T) :- atom(T). % T not yet compressed % i.e. T is a tree-term (nested list & s/2 structure) % -> execute one layer of compression, then check again compress_pt(T,CT) :- \+ atom(T), and_or_compression(T,IT), compress_pt(IT,CT). % transform tree-term T into tree-term CT where last two layers have been processed % i.e. introduce names for subparts (-> Map) and replace (all occurrenes of) subparts by this names and_or_compression(T,CT) :- and_comp(T,AT), or_comp(AT,CT). % replace leaves that are single child by variable representing father-AND-child and_comp(T,AT) :- all_leaves_pt(T,Leaves), compression_mapping(Leaves,Map), replace_pt(T,Map,AT). % replace list of siblings by variable representing their disjunction or_comp(T,AT) :- all_leaflists_pt(T,Leaves), compression_mapping(Leaves,Map), replace_pt(T,Map,AT). all_leaves_pt(T,L) :- all(X,some_leaf_pt(T,X),L). some_leaf_pt([s(A,[])|_],s(A,[])). some_leaf_pt([s(A,L)|_],s(A,L)) :- atom(L). some_leaf_pt([s(_,L)|_],X) :- some_leaf_pt(L,X). some_leaf_pt([_|L],X) :- some_leaf_pt(L,X). all_leaflists_pt(L,[L]) :- atomlist(L),!. all_leaflists_pt(T,L) :- all(X,some_leaflist_pt(T,X),L),!. all_leaflists_pt(_,[]). some_leaflist_pt([s(_,L)|_],L) :- atomlist(L). some_leaflist_pt([s(_,L)|_],X) :- some_leaflist_pt(L,X). some_leaflist_pt([_|L],X) :- some_leaflist_pt(L,X). atomlist([]). atomlist([A|B]) :- atom(A), atomlist(B). % for each subtree that will be compressed, add its name % only introduce 'L'-based names when subtree composes elements, store these in compression/2 for printing the script compression_mapping([],[]). compression_mapping([First|B],[N-First|BB]) :- ( First = s(A,[]) % subtree is literal -> use variable's name x17 from map -> recorded(map,m(A,N),_) ; (First = s(A,L),atom(L)) % subtree is node with single completely reduced child -> use next 'L'-based name -> (get_next_name(N), assertz(compression(N,s(A,L)))) ; (First = [L],atom(L)) % subtree is an OR with a single completely reduced element -> use element's name -> N=L ; (atomlist(First), % subtree is an OR with only (>1) completely reduced elements -> use next 'L'-based name get_next_name(N), assertz(compression(N,First))) ), compression_mapping(B,BB). % replace_pt(+T,+Map,-NT) % given the tree-term T and the Map of Name-Subtree entries, replace each occurence of Subtree in T with Name -> result NT replace_pt(T,[],T). replace_pt([],_,[]). replace_pt(L,M,R) :- atomlist(L), member(R-L,M), !. replace_pt([L|LL],[M|MM],R) :- replace_pt_list([L|LL],[M|MM],R). replace_pt_list([T|Tree],[M|Map],[C|Compr]) :- replace_pt_single(T,[M|Map],C), replace_pt_list(Tree,[M|Map],Compr). replace_pt_list([],_,[]). replace_pt_single(s(A,T),[M|Map],Res) :- atomlist(T), member(Res-s(A,T),[M|Map]), !. replace_pt_single(s(A,T),[M|Map],s(A,Res)) :- atomlist(T), member(Res-T,[M|Map]), !. replace_pt_single(s(A,T),[M|Map],Res) :- member(Res-s(A,T),[M|Map]), !. replace_pt_single(s(A,T),[M|Map],s(A,TT)) :- replace_pt_list(T,[M|Map],TT). replace_pt_single(A,_,A) :- atom(A). %%%%%%%%%%%% % output for script % input argument is compressed tree, i.e. true/false or name assigned in last compression step %%%%%%%%%%%% output_compressed_script(false) :- !, format('L1 = FALSE~nL1~n',[]). output_compressed_script(true) :- !, format('L1 = TRUE~nL1~n',[]). % for each name-subtree pair, write corresponding line to script, e.g. L17 = x4 * L16 % stop after writing definition of root (last entry in compression/2), add it's name to mark end of script output_compressed_script(T) :- once(retract(compression(Short,Long))), (T = Short -> format('~w = ',[Short]), format_compression_script(Long), format('~w~n',[Short]) ; format('~w = ',[Short]), format_compression_script(Long), output_compressed_script(T)). format_compression_script(s(A,B)) :- recorded(map,m(A,C),_), format('~w * ~w~n',[C,B]). format_compression_script([A]) :- format('~w~n',[A]). format_compression_script([A,B|C]) :- format('~w + ',[A]), format_compression_script([B|C]). %%%%%%%%%%%%%%%%%%%%%%%% % auxiliaries for translation to BDD %%%%%%%%%%%%%%%%%%%%%%%% % prefix the current counter with "L" get_next_name(Name) :- retract(c_num(N)), NN is N+1, assert(c_num(NN)), atomic_concat('L',N,Name). % create BDD-var as fact id prefixed by x % learning.yap relies on this format! % when changing, also adapt test_var_name/1 below get_var_name(A,NameA) :- atomic_concat([x,A],NameA), recorda(map,m(A,NameA),_). % test used by base case of compression mapping to detect single-variable tree % has to match above naming scheme test_var_name(T) :- atomic_concat(x,_,T).