500 lines
12 KiB
Plaintext
500 lines
12 KiB
Plaintext
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%%% -*- Mode: Prolog; -*-
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% prefix-trees for managing a DNF
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% 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)
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% children are sorted, but branches aren't (to speed up search while keeping structure sharing from proof procedure)
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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:- module(ptree,[init_ptree/1,
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delete_ptree/1,
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rename_ptree/2,
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member_ptree/2,
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enum_member_ptree/2,
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insert_ptree/2,
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delete_ptree/2,
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edges_ptree/2,
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count_ptree/2,
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prune_check_ptree/2,
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empty_ptree/1,
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merge_ptree/3,
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bdd_ptree/3,
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bdd_ptree_map/4
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]).
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:- use_module(library(tries),
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[
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trie_open/1,
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trie_close/1,
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trie_stats/4,
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trie_check_entry/3,
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trie_get_entry/2,
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trie_put_entry/3,
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trie_remove_entry/1,
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trie_usage/4,
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trie_dup/2,
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trie_join/2,
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trie_traverse/2
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]).
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:- use_module(library(ordsets),
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[
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ord_subset/2
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]).
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:- style_check(all).
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:- yap_flag(unknown,error).
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:- use_module(flags,[problog_flag/2]).
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:- ensure_loaded(library(lists)).
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:- ensure_loaded(library(system)).
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% name lexicon external - internal
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sym(1,tree1) :- !.
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sym(2,tree2) :- !.
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sym(3,tree3) :- !.
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sym(N,AN) :- atomic_concat([tree,N],AN).
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%%%%%%%%%%%%%%%%%%%%%%%%
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% ptree basics
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%%%%%%%%%%%%%%%%%%%%%%%%
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init_ptree(ID) :-
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sym(ID,Sym),
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trie_open(Trie),
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nb_setval(Sym, Trie).
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delete_ptree(ID) :-
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sym(ID,Sym),
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nb_getval(Sym, Trie), !,
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trie_close(Trie),
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trie_open(NewTrie),
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nb_setval(Sym, NewTrie).
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delete_ptree(_).
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rename_ptree(OldID,NewID) :-
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sym(OldID,OldSym),
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sym(NewID,NewSym),
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nb_getval(OldSym, Trie),
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nb_set_shared_val(NewSym, Trie).
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empty_ptree(ID) :-
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sym(ID,Sym),
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nb_getval(Sym, Trie),
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trie_usage(Trie, 0, 0, 0).
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%%%%%%%%%%%%%%%%%%%%%%%%
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% member
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%%%%%%%%%%%%%%%%%%%%%%%%
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% non-backtrackable (to check)
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member_ptree(List,ID) :-
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sym(ID,Sym),
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nb_getval(Sym, Trie),
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trie_check_entry(Trie, List, _).
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% backtrackable (to list)
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enum_member_ptree(ID,List) :-
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sym(ID,Sym),
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nb_getval(Sym, Tree),
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trie_path(Tree, List).
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trie_path(Tree, List) :-
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trie_traverse(Tree,Ref),
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trie_get_entry(Ref, List).
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%%%%%%%%%%%%%%%%%%%%%%%%
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% insert conjunction
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%%%%%%%%%%%%%%%%%%%%%%%%
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insert_ptree(true,ID) :-
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sym(ID,Sym),
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!,
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nb_getval(Sym, Trie),
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trie_close(Trie),
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trie_open(NTrie),
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trie_put_entry(NTrie, true, _).
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insert_ptree(List,ID) :-
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sym(ID,Sym),
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nb_getval(Sym, Trie),
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trie_put_entry(Trie, List, _).
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%%%%%%%%%%%%%%%%%%%%%%%%
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% delete conjunction
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%%%%%%%%%%%%%%%%%%%%%%%%
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delete_ptree(List,ID) :-
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sym(ID,Sym),
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nb_getval(Sym, Trie),
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trie_check_entry(Trie, List, Ref),
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trie_remove_entry(Ref).
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%%%%%%%%
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% return list -Edges of all edge labels in ptree
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% doesn't use any heuristic to order those for the BDD
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% (automatic reordering has to do the job)
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%%%%%%%%%
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edges_ptree(ID,[]) :-
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empty_ptree(ID),
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!.
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edges_ptree(ID,[]) :-
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sym(ID,Sym),
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nb_getval(Sym, Trie),
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trie_check_entry(Trie, true, _),
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!.
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edges_ptree(ID,Edges) :-
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sym(ID,Sym),
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nb_getval(Sym, Trie),
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setof(X, trie_literal(Trie, X), Edges).
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trie_literal(Trie, X) :-
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trie_traverse(Trie,Ref),
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trie_get_entry(Ref, List),
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member(X, List).
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%%%%%%%%
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% number of conjunctions in the tree
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%%%%%%%%%
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count_ptree(ID,N) :-
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sym(ID,Sym),
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nb_getval(Sym, Trie),
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trie_usage(Trie, N, _, _).
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%%%%%%%%
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% check whether some branch of ptree is a subset of conjunction List
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% useful for pruning the search for proofs (optional due to time overhead)
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% currently not implemented, just fails
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%%%%%%%
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prune_check_ptree(_List,_TreeID) :-
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format(user,'FAIL: prune check currently not supported~n',[]),
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flush_output(user),
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fail.
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%%%%%%%%%%%%%
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% merge two ptrees
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% - take care not to loose proper prefixes that are proofs!
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%%%%%%%%%%%%%%%
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merge_ptree(ID1,_,ID3) :-
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sym(ID1,Sym1),
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sym(ID3,Sym3),
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nb_getval(Sym1, T1),
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trie_check_entry(T1, true, _),
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!,
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trie_open(T3),
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trie_put_entry(T3, true, _),
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nb_setval(Sym3, T3).
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merge_ptree(_,ID2,ID3) :-
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sym(ID2,Sym2),
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sym(ID3,Sym3),
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nb_getval(Sym2, T2),
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trie_check_entry(T2, true, _),
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!,
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trie_open(T3),
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trie_put_entry(T3, true, _),
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nb_setval(Sym3, T3).
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merge_ptree(ID1,ID2,ID3) :-
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sym(ID1,Sym1),
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sym(ID2,Sym2),
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sym(ID3,Sym3),
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nb_getval(Sym1, T1),
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nb_getval(Sym2, T2),
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trie_dup(T1, T3),
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trie_join(T3,T2),
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nb_setval(Sym3, T3).
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%%%%%%%%%%%%%%%%%%%%%%%%
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% write BDD info for given ptree to file
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% - initializes leaf BDDs (=variables) first
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% - then compresses ptree to exploit subtree sharing
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% - bdd_pt/1 does the work on the structure itself
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%%%%%%%%%%%%%%%%%%%%%%%%
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bdd_ptree(ID,FileBDD,FileParam) :-
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bdd_ptree_script(ID,FileBDD,FileParam),
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eraseall(map).
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% version returning variable mapping
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bdd_ptree_map(ID,FileBDD,FileParam,Mapping) :-
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bdd_ptree_script(ID,FileBDD,FileParam),
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findall(X,recorded(map,X,_),Map),
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add_probs(Map,Mapping),
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eraseall(map).
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add_probs([],[]).
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add_probs([m(A,Name)|Map],[m(A,Name,Prob)|Mapping]) :-
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problog:get_fact_probability(A,Prob),
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add_probs(Map,Mapping).
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% number of variables may be to high:
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% counted on trie, but conversion to old tree representation
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% transforms A*B+A to A (prefix-test)
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bdd_ptree_script(ID,FileBDD,FileParam) :-
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edges_ptree(ID,Edges),
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tell(FileParam),
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bdd_vars_script(Edges),
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flush_output,
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told,
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length(Edges,VarCount),
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assert(c_num(1)),
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bdd_pt(ID,CT),
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c_num(NN),
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IntermediateSteps is NN-1,
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tell(FileBDD),
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format('@BDD1~n~w~n~w~n~w~n',[VarCount,0,IntermediateSteps]),
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output_compressed_script(CT),
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told,
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retractall(c_num(_)),
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retractall(compression(_,_)).
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% write parameter file by iterating over all var/not(var) occuring in the tree
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bdd_vars_script(Edges) :-
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bdd_vars_script(Edges,0).
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bdd_vars_script([],_).
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bdd_vars_script([A|B],N) :-
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problog:get_fact_probability(A,P),
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get_var_name(A,NameA),
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format('@~w~n~12f~n',[NameA,P]),
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NN is N+1,
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bdd_vars_script(B,NN).
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%%%%%%%%%%%%%%%%%%%%%%%%
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% find top level symbol for script
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%%%%%%%%%%%%%%%%%%%%%%%%
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% special cases: variable-free formulae
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bdd_pt(ID,false) :-
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empty_ptree(ID),
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!,
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once(retractall(c_num(_))),
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once(assert(c_num(2))).
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bdd_pt(ID,true) :-
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sym(ID,Sym),
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nb_getval(Sym, Trie),
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trie_check_entry(Trie, true, _),
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!,
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once(retractall(c_num(_))),
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once(assert(c_num(2))).
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% general case: transform trie to nested tree structure for compression
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bdd_pt(ID,CT) :-
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sym(ID,Sym),
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nb_getval(Sym, Trie),
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trie_to_tree(Trie, Tree),
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compress_pt(Tree,CT).
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trie_to_tree(Trie, Tree) :-
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findall(Path,trie_path(Trie, Path), Paths),
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add_trees(Paths, [], Tree).
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add_trees([], Tree, Tree).
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add_trees([List|Paths], Tree0, Tree) :-
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ins_pt(List, Tree0, TreeI),
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add_trees(Paths, TreeI, Tree).
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ins_pt([],_T,[]) :- !.
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ins_pt([A|B],[s(A1,AT)|OldT],NewT) :-
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compare(Comp, A1, A),
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(Comp == = ->
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(AT == [] ->
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NewT=[s(A1,AT)|OldT]
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;
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NewT = [s(A1,NewAT)|OldT],
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ins_pt(B, AT, NewAT))
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;
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Comp == > ->
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NewT = [s(A1,AT)|Tree],
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ins_pt([A|B], OldT, Tree)
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;
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NewT = [s(A,BTree),s(A1,AT)|OldT],
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ins_pt(B,[],BTree)
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).
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ins_pt([A|B],[],[s(A,NewAT)]) :-
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ins_pt(B,[],NewAT).
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%%%%%%%%%%%%
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% BDD compression: alternates and- and or-levels to build BDD bottom-up
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% each sub-BDD will be either a conjunction of a one-node BDD with some BDD or a disjunction of BDDs
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% uses the internal database to temporarily store a map of components
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%%%%%%%%%%%%
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% T is completely compressed and contains single variable
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% i.e. T of form x12
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compress_pt(T,TT) :-
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atom(T),
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test_var_name(T),
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!,
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get_next_name(TT),
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assertz(compression(TT,[T])).
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% T is completely compressed and contains subtrees
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% i.e. T of form 'L56'
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compress_pt(T,T) :-
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atom(T).
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% T not yet compressed
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% i.e. T is a tree-term (nested list & s/2 structure)
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% -> execute one layer of compression, then check again
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compress_pt(T,CT) :-
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\+ atom(T),
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and_or_compression(T,IT),
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compress_pt(IT,CT).
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% transform tree-term T into tree-term CT where last two layers have been processed
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% i.e. introduce names for subparts (-> Map) and replace (all occurrenes of) subparts by this names
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and_or_compression(T,CT) :-
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and_comp(T,AT),
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or_comp(AT,CT).
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% replace leaves that are single child by variable representing father-AND-child
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and_comp(T,AT) :-
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all_leaves_pt(T,Leaves),
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compression_mapping(Leaves,Map),
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replace_pt(T,Map,AT).
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% replace list of siblings by variable representing their disjunction
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or_comp(T,AT) :-
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all_leaflists_pt(T,Leaves),
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compression_mapping(Leaves,Map),
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replace_pt(T,Map,AT).
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all_leaves_pt(T,L) :-
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all(X,some_leaf_pt(T,X),L).
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some_leaf_pt([s(A,[])|_],s(A,[])).
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some_leaf_pt([s(A,L)|_],s(A,L)) :-
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atom(L).
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some_leaf_pt([s(_,L)|_],X) :-
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some_leaf_pt(L,X).
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some_leaf_pt([_|L],X) :-
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some_leaf_pt(L,X).
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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).
|