702 lines
16 KiB
Prolog
702 lines
16 KiB
Prolog
/*
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LPAD and CP-Logic reasoning suite
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File lpadsld.pl
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Goal oriented interpreter for LPADs based on SLDNF
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Copyright (c) 2007, Fabrizio Riguzzi
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*/
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:-dynamic rule/4,def_rule/2,setting/2.
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%:-yap_flag(gc_trace,very_verbose).
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%:-source.
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:-use_module(library(lists)).
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:-use_module(library(ugraphs)).
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:-load_foreign_files(['cplint'],[],init_my_predicates).
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:- op(1150, xfx, <- ).
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:- op(950,xfy, &).
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:- op(900,fy,~).
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:- op(1170,fx,prob).
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/* start of list of parameters that can be set by the user with
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set(Parameter,Value) */
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setting(epsilon_parsing,0.00001).
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setting(save_dot,false).
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setting(ground_body,false).
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/* available values: true, false
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if true, both the head and the body of each clause will be grounded, otherwise
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only the head is grounded. In the case in which the body contains variables
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not appearing in the head, the body represents an existential event */
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setting(min_error,0.01).
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setting(depth_bound,4).
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setting(prob_threshold,0.00001).
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setting(prob_bound,0.01).
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/* end of list of parameters */
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/* s(GoalsLIst,Prob) compute the probability of a list of goals
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GoalsLis can have variables, s returns in backtracking all the solutions with their
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corresponding probability */
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s(GoalsList,Prob):-
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solve(GoalsList,Prob).
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solve(GoalsList,Prob):-
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findall(Deriv,find_deriv(GoalsList,Deriv),L),
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build_formula(L,Formula,[],Var),
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var2numbers(Var,0,NewVar),
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(setting(save_dot,true)->
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format("Variables: ~p~n",[Var]),
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compute_prob(NewVar,Formula,Prob,1)
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;
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compute_prob(NewVar,Formula,Prob,0)
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).
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solve(GoalsList,0.0):-
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\+ find_deriv(GoalsList,_Deriv).
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/* s(GoalsList,Prob,CPUTime1,CPUTime2,WallTime1,WallTime2) compute the probability of a list of goals
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GoalsLis can have variables, s returns in backtracking all the solutions with
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their corresponding probability
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CPUTime1 is the cpu time for performing resolution
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CPUTime2 is the cpu time for elaborating the BDD
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WallTime1 is the wall time for performing resolution
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WallTime2 is the wall time for elaborating the BDD */
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s(GoalsList,Prob,CPUTime1,CPUTime2,WallTime1,WallTime2):-
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solve(GoalsList,Prob,CPUTime1,CPUTime2,WallTime1,WallTime2).
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solve(GoalsList,Prob,CPUTime1,CPUTime2,WallTime1,WallTime2):-
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statistics(cputime,[_,_]),
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statistics(walltime,[_,_]),
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findall(Deriv,find_deriv(GoalsList,Deriv),L)->
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statistics(cputime,[_,CT1]),
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CPUTime1 is CT1/1000,
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statistics(walltime,[_,WT1]),
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WallTime1 is WT1/1000,
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%print_mem,
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build_formula(L,Formula,[],Var,0,Conj),
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length(L,ND),
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length(Var,NV),
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format(user_error,"Disjunctions :~d~nConjunctions: ~d~nVariables ~d~n",[ND,Conj,NV]),
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var2numbers(Var,0,NewVar),
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(setting(save_dot,true)->
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format("Variables: ~p~n",[Var]),
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compute_prob(NewVar,Formula,Prob,1)
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;
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compute_prob(NewVar,Formula,Prob,0)
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),
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statistics(cputime,[_,CT2]),
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CPUTime2 is CT2/1000,
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statistics(walltime,[_,WT2]),
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WallTime2 is WT2/1000,
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format(user_error,"~nMemory after inference~n",[]).
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%print_mem.
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print_mem:-
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statistics(global_stack,[GS,GSF]),
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statistics(local_stack,[LS,LSF]),
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statistics(heap,[HP,HPF]),
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statistics(trail,[TU,TF]),
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format(user_error,"~nGloabal stack used ~d execution stack free: ~d~n",[GS,GSF]),
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format(user_error,"Local stack used ~d execution stack free: ~d~n",[LS,LSF]),
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format(user_error,"Heap used ~d heap free: ~d~n",[HP,HPF]),
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format(user_error,"Trail used ~d Trail free: ~d~n",[TU,TF]).
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find_deriv(GoalsList,Deriv):-
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solve(GoalsList,[],Deriv).
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% remove_duplicates(DerivDup,Deriv).
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/* duplicate can appear in the C set because two different unistantiated clauses may become the
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same clause when instantiated */
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/* sc(Goals,Evidence,Prob) compute the conditional probability of the list of goals
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Goals given the list of goals Evidence
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Goals and Evidence can have variables, sc returns in backtracking all the solutions with their
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corresponding probability
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*/
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sc(Goals,Evidence,Prob):-
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solve_cond(Goals,Evidence,Prob).
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solve_cond(Goals,Evidence,Prob):-
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findall(DerivE,find_deriv(Evidence,DerivE),LE),
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findall(DerivGE,find_deriv_GE(LE,Goals,DerivGE),LGE),
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%print_mem,
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build_formula(LE,FormulaE,[],VarE),
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var2numbers(VarE,0,NewVarE),
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build_formula(LGE,FormulaGE,[],VarGE),
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var2numbers(VarGE,0,NewVarGE),
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compute_prob(NewVarE,FormulaE,ProbE,0),
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call_compute_prob(NewVarGE,FormulaGE,ProbGE),
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(ProbE>0.0->
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Prob is ProbGE/ProbE
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;
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%print_mem,
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Prob=undefined
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),
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format(user_error,"~nMemory after inference~n",[]).
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%print_mem.
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/* sc(Goals,Evidence,Prob,Time1,Time2) compute the conditional probability of the list of goals
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Goals given the list of goals Evidence
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Goals and Evidence can have variables, sc returns in backtracking all the solutions with their
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corresponding probability
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Time1 is the time for performing resolution
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Time2 is the time for elaborating the two BDDs
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*/
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sc(Goals,Evidence,Prob,CPUTime1,CPUTime2,WallTime1,WallTime2):-
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solve_cond(Goals,Evidence,Prob,CPUTime1,CPUTime2,WallTime1,WallTime2).
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solve_cond(Goals,Evidence,Prob,CPUTime1,CPUTime2,WallTime1,WallTime2):-
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statistics(cputime,[_,_]),
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statistics(walltime,[_,_]),
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findall(DerivE,find_deriv(Evidence,DerivE),LE),
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findall(DerivGE,find_deriv_GE(LE,Goals,DerivGE),LGE),
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statistics(cputime,[_,CT1]),
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CPUTime1 is CT1/1000,
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statistics(walltime,[_,WT1]),
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WallTime1 is WT1/1000,
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build_formula(LE,FormulaE,[],VarE),
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var2numbers(VarE,0,NewVarE),
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build_formula(LGE,FormulaGE,[],VarGE),
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var2numbers(VarGE,0,NewVarGE),
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compute_prob(NewVarE,FormulaE,ProbE,0),
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call_compute_prob(NewVarGE,FormulaGE,ProbGE),
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(ProbE>0.0->
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Prob is ProbGE/ProbE,
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statistics(cputime,[_,CT2]),
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CPUTime2 is CT2/1000,
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statistics(walltime,[_,WT2]),
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WallTime2 is WT2/1000
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;
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Prob=undefined,
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statistics(cputime,[_,CT2]),
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CPUTime2 is CT2/1000,
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statistics(walltime,[_,WT2]),
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WallTime2 is WT2/1000
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).
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solve_cond_goals(Goals,LE,0,Time1,0):-
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statistics(runtime,[_,_]),
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\+ find_deriv_GE(LE,Goals,_DerivGE),
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statistics(runtime,[_,T1]),
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Time1 is T1/1000.
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call_compute_prob(NewVarGE,FormulaGE,ProbGE):-
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(setting(save_dot,true)->
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format("Variables: ~p~n",[NewVarGE]),
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compute_prob(NewVarGE,FormulaGE,ProbGE,1)
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;
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compute_prob(NewVarGE,FormulaGE,ProbGE,0)
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).
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find_deriv_GE(LD,GoalsList,Deriv):-
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member(D,LD),
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solve(GoalsList,D,DerivDup),
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remove_duplicates(DerivDup,Deriv).
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/* solve(GoalsList,CIn,COut) takes a list of goals and an input C set
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and returns an output C set
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The C set is a list of triple (N,R,S) where
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- N is the index of the head atom used, starting from 0
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- R is the index of the non ground rule used, starting from 1
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- S is the substitution of rule R, in the form of a list whose elements
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are of the form 'VarName'=value
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*/
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solve([],C,C):-!.
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solve([\+ H|T],CIn,COut):-
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builtin(H),!,
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call((\+ H)),
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solve(T,CIn,COut).
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solve([\+ H |T],CIn,COut):-!,
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list2and(HL,H),
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findall(D,solve(HL,CIn,D),L),
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choose_clauses(CIn,L,C1),
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solve(T,C1,COut)
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.
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solve([H|T],CIn,COut):-
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builtin(H),!,
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call(H),
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solve(T,CIn,COut).
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solve([H|T],CIn,COut):-
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def_rule(H,B),
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append(B,T,NG),
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solve(NG,CIn,COut).
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solve([H|T],CIn,COut):-
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find_rule(H,(R,S,N),CIn),
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solve_pres(R,S,N,T,CIn,COut).
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solve_pres(R,S,N,T,CIn,COut):-
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member_eq((N,R,S),CIn),!,
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solve(T,CIn,COut).
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solve_pres(R,S,N,T,CIn,COut):-
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% format("a",[]),
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solve(T,[(N,R,S)|CIn],COut).
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/*
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solve_pres(R,S,N,T,CIn,COut):-
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append(CIn,[(N,R,S)],C1),
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solve(T,C1,COut).
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*/
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/* find_rule(G,(R,S,N),Body,C) takes a goal G and the current C set and
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returns the index R of a disjunctive rule resolving with G together with
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the index N of the resolving head, the substitution S and the Body of the
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rule */
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find_rule(H,(R,S,N),C):-
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rule(H,_P,N,R,S,_NH,_Head),
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not_already_present_with_a_different_head(N,R,S,C).
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not_already_present_with_a_different_head(_N,_R,_S,[]).
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not_already_present_with_a_different_head(N,R,S,[(N1,R,S1)|T]):-
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not_different(N,N1,S,S1),!,
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not_already_present_with_a_different_head(N,R,S,T).
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not_already_present_with_a_different_head(N,R,S,[(_N1,R1,_S1)|T]):-
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R\==R1,
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not_already_present_with_a_different_head(N,R,S,T).
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not_different(_N,_N1,S,S1):-
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S\=S1,!.
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not_different(N,N,S,S).
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/* choose_clauses(CIn,LC,COut) takes as input the current C set and
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the set of C sets for a negative goal and returns a new C set that
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excludes all the derivations for the negative goals */
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choose_clauses(C,[],C).
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choose_clauses(CIn,[D|T],COut):-
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set_diff(D,Cin,D1),
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member((N,R,S),D1),
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add_inc(N,R,S,CIn,T,COut).
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add_inc(N,R,S,CIn,T,COut):-
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already_present_with_a_different_head(N,R,S,CIn),!,
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choose_clauses(CIn,T,COut).
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add_inc(N,R,S,CIn,T,COut):-
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\+ member((N,R,S),CIn),
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new_head(N,R,S,N1),
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choose_clauses([(N1,R,S)|CIn],T,COut).
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set_diff([H|_T],[H|_S],[]):-!.
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set_diff([H|T],S,[H|R]):-
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set_diff(T,S,R).
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set_diff(T,_S,T).
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/*
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set_diff([H|T],[H|S],R):-!,
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set_diff(T,S,R).
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set_diff(T,_S,T).
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*/
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/*
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set_diff([],_S,[]).
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set_diff([H|T],S,R):-
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member(H,S),!,
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set_diff(T,S,R).
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set_diff([H|T],S,[H|R]):-
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set_diff(T,S,R).
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*/
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/* select a head different from N for rule R with
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substitution S, return it in N1 */
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new_head(N,R,S,N1):-
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rule_by_num(R,S,Numbers,Head,_Body),
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Head\=uniform(_,_,_),!,
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nth0(N, Numbers, _Elem, Rest),
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member(N1,Rest).
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already_present_with_a_different_head(N,R,S,[(NH,R,SH)|_T]):-
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S=SH,NH \= N,!.
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already_present_with_a_different_head(N,R,S,[_H|T]):-
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already_present_with_a_different_head(N,R,S,T).
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/* checks that a rule R with head N and selection S is already
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present in C (or a generalization of it is in C) */
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already_present(N,R,S,[(N,R,SH)|_T]):-
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S=SH.
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already_present(N,R,S,[_H|T]):-
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already_present(N,R,S,T).
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/* rem_dup_lists removes the C sets that are a superset of
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another C sets further on in the list of C sets */
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/* rem_dup_lists removes the C sets that are a superset of
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another C sets further on in the list of C sets */
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rem_dup_lists([],L,L).
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rem_dup_lists([H|T],L0,L):-
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(member_subset(H,T);member_subset(H,L0)),!,
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rem_dup_lists(T,L0,L).
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rem_dup_lists([H|T],L0,L):-
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rem_dup_lists(T,[H|L0],L).
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member_subset(E,[H|_T]):-
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subset_my(H,E),!.
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member_subset(E,[_H|T]):-
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member_subset(E,T).
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/* predicates for building the formula to be converted into a BDD */
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/* build_formula(LC,Formula,VarIn,VarOut) takes as input a set of C sets
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LC and a list of Variables VarIn and returns the formula and a new list
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of variables VarOut
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Formula is of the form [Term1,...,Termn]
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Termi is of the form [Factor1,...,Factorm]
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Factorj is of the form (Var,Value) where Var is the index of
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the multivalued variable Var and Value is the index of the value
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*/
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build_formula([],[],Var,Var,C,C).
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build_formula([D|TD],[F|TF],VarIn,VarOut,C0,C1):-
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length(D,NC),
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C2 is C0+NC,
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%reverse(D,D1),
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D1=D,
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build_term(D1,F,VarIn,Var1),
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build_formula(TD,TF,Var1,VarOut,C2,C1).
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build_formula([],[],Var,Var).
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build_formula([D|TD],[F|TF],VarIn,VarOut):-
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build_term(D,F,VarIn,Var1),
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build_formula(TD,TF,Var1,VarOut).
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build_term([],[],Var,Var).
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build_term([(_,pruned,_)|TC],TF,VarIn,VarOut):-!,
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build_term(TC,TF,VarIn,VarOut).
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build_term([(N,R,S)|TC],[[NVar,N]|TF],VarIn,VarOut):-
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(nth0_eq(0,NVar,VarIn,(R,S))->
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Var1=VarIn
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;
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append(VarIn,[(R,S)],Var1),
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length(VarIn,NVar)
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),
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build_term(TC,TF,Var1,VarOut).
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/* nth0_eq(PosIn,PosOut,List,El) takes as input a List,
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an element El and an initial position PosIn and returns in PosOut
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the position in the List that contains an element exactly equal to El
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*/
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nth0_eq(N,N,[H|_T],El):-
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H==El,!.
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nth0_eq(NIn,NOut,[_H|T],El):-
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N1 is NIn+1,
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nth0_eq(N1,NOut,T,El).
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/* var2numbers converts a list of couples (Rule,Substitution) into a list
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of triples (N,NumberOfHeadsAtoms,ListOfProbabilities), where N is an integer
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starting from 0 */
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var2numbers([],_N,[]).
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var2numbers([(R,S)|T],N,[[N,ValNumber,Probs]|TNV]):-
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find_probs(R,S,Probs),
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length(Probs,ValNumber),
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N1 is N+1,
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var2numbers(T,N1,TNV).
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find_probs(R,S,Probs):-
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rule_by_num(R,S,_N,Head,_Body),
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get_probs(Head,Probs).
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get_probs(uniform(_A:1/Num,_P,_Number),ListP):-
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Prob is 1/Num,
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list_el(Num,Prob,ListP).
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get_probs([],[]).
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get_probs([_H:P|T],[P1|T1]):-
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P1 is P,
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get_probs(T,T1).
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list_el(0,_P,[]):-!.
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list_el(N,P,[P|T]):-
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N1 is N-1,
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list_el(N1,P,T).
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/* end of predicates for building the formula to be converted into a BDD */list_el(0,_P,[]):-!.
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/* start of predicates for parsing an input file containing a program */
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/* p(File) parses the file File.cpl. It can be called more than once without
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exiting yap */
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p(File):-
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parse(File).
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parse(File):-
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atom_concat(File,'.cil',FilePl),
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open(FilePl,read,S),
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read_clauses(S,C),
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close(S),
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retractall(rule_by_num(_,_,_,_,_)),
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retractall(rule(_,_,_,_,_,_,_)),
|
|
retractall(def_rule(_,_)),
|
|
process_clauses(C,1).
|
|
|
|
process_clauses([(end_of_file,[])],_N).
|
|
|
|
process_clauses([((H <- B),_V)|T],N):-!,
|
|
convert_body(B,BL),
|
|
assert(def_rule(H,BL)),
|
|
process_clauses(T,N).
|
|
|
|
|
|
process_clauses([((prob H),V)|T],N):-!,
|
|
list2and(HL1,H),
|
|
process_head(HL1,HL),
|
|
length(HL,LH),
|
|
listN(0,LH,NH),
|
|
assert_rules(HL,0,HL,[],NH,N,V),
|
|
assertz(rule_by_num(N,V,NH,HL,[])),
|
|
N1 is N+1,
|
|
process_clauses(T,N1).
|
|
|
|
process_clauses([(H,_V)|T],N):-
|
|
assert(def_rule(H,[])),
|
|
process_clauses(T,N).
|
|
|
|
|
|
assert_rules([],_Pos,_HL,_BL,_Nh,_N,_V1):-!.
|
|
|
|
assert_rules(['':_P],_Pos,_HL,_BL,_Nh,_N,_V1):-!.
|
|
|
|
assert_rules([H:P|T],Pos,HL,BL,NH,N,V1):-
|
|
assertz(rule(H,P,Pos,N,V1,NH,HL)),
|
|
Pos1 is Pos+1,
|
|
assert_rules(T,Pos1,HL,BL,NH,N,V1).
|
|
|
|
|
|
/* if the annotation in the head are not ground, the null atom is not added
|
|
and the eventual formulas are not evaluated */
|
|
|
|
process_head(HL,NHL):-
|
|
(ground_prob(HL)->
|
|
process_head_ground(HL,0,NHL)
|
|
;
|
|
NHL=HL
|
|
).
|
|
|
|
ground_prob([]).
|
|
|
|
ground_prob([_H:PH|T]):-
|
|
ground(PH),
|
|
ground_prob(T).
|
|
|
|
process_head_ground([H:PH],P,[H:PH1|Null]):-
|
|
PH1 is PH,
|
|
PNull is 1-P-PH1,
|
|
setting(epsilon_parsing,Eps),
|
|
EpsNeg is - Eps,
|
|
PNull > EpsNeg,
|
|
(PNull>Eps->
|
|
Null=['':PNull]
|
|
;
|
|
Null=[]
|
|
).
|
|
|
|
process_head_ground([H:PH|T],P,[H:PH1|NT]):-
|
|
PH1 is PH,
|
|
P1 is P+PH1,
|
|
process_head_ground(T,P1,NT).
|
|
|
|
/* predicates for reading in the program clauses */
|
|
read_clauses(S,Clauses):-
|
|
(setting(ground_body,true)->
|
|
read_clauses_ground_body(S,Clauses)
|
|
;
|
|
read_clauses_exist_body(S,Clauses)
|
|
).
|
|
|
|
|
|
read_clauses_ground_body(S,[(Cl,V)|Out]):-
|
|
read_term(S,Cl,[variable_names(V)]),
|
|
(Cl=end_of_file->
|
|
Out=[]
|
|
;
|
|
read_clauses_ground_body(S,Out)
|
|
).
|
|
|
|
|
|
read_clauses_exist_body(S,[(Cl,V)|Out]):-
|
|
read_term(S,Cl,[variable_names(VN)]),
|
|
extract_vars_cl(Cl,VN,V),
|
|
(Cl=end_of_file->
|
|
Out=[]
|
|
;
|
|
read_clauses_exist_body(S,Out)
|
|
).
|
|
|
|
|
|
extract_vars_cl(end_of_file,[]).
|
|
|
|
extract_vars_cl(Cl,VN,Couples):-
|
|
(Cl=(H:-_B)->
|
|
true
|
|
;
|
|
H=Cl
|
|
),
|
|
extract_vars(H,[],V),
|
|
pair(VN,V,Couples).
|
|
|
|
|
|
pair(_VN,[],[]).
|
|
|
|
pair([VN= _V|TVN],[V|TV],[VN=V|T]):-
|
|
pair(TVN,TV,T).
|
|
|
|
|
|
extract_vars(Var,V0,V):-
|
|
var(Var),!,
|
|
(member_eq(Var,V0)->
|
|
V=V0
|
|
;
|
|
append(V0,[Var],V)
|
|
).
|
|
|
|
extract_vars(Term,V0,V):-
|
|
Term=..[_F|Args],
|
|
extract_vars_list(Args,V0,V).
|
|
|
|
|
|
extract_vars_list([],V,V).
|
|
|
|
extract_vars_list([Term|T],V0,V):-
|
|
extract_vars(Term,V0,V1),
|
|
extract_vars_list(T,V1,V).
|
|
|
|
|
|
listN(N,N,[]):-!.
|
|
|
|
listN(NIn,N,[NIn|T]):-
|
|
N1 is NIn+1,
|
|
listN(N1,N,T).
|
|
/* end of predicates for parsing an input file containing a program */
|
|
|
|
/* start of utility predicates */
|
|
list2or([X],X):-
|
|
X\=;(_,_),!.
|
|
|
|
list2or([H|T],(H ; Ta)):-!,
|
|
list2or(T,Ta).
|
|
|
|
list2and([X],X):-
|
|
X\=(_,_),!.
|
|
|
|
list2and([H|T],(H,Ta)):-!,
|
|
list2and(T,Ta).
|
|
|
|
member_eq(A,[H|_T]):-
|
|
A==H,!.
|
|
|
|
member_eq(A,[_H|T]):-
|
|
member_eq(A,T).
|
|
|
|
subset_my([],_).
|
|
|
|
subset_my([H|T],L):-
|
|
member_eq(H,L),
|
|
subset_my(T,L).
|
|
|
|
remove_duplicates_eq([],[]).
|
|
|
|
remove_duplicates_eq([H|T],T1):-
|
|
member_eq(H,T),!,
|
|
remove_duplicates_eq(T,T1).
|
|
|
|
remove_duplicates_eq([H|T],[H|T1]):-
|
|
remove_duplicates_eq(T,T1).
|
|
|
|
builtin(_A is _B).
|
|
builtin(_A > _B).
|
|
builtin(_A < _B).
|
|
builtin(_A >= _B).
|
|
builtin(_A =< _B).
|
|
builtin(_A =:= _B).
|
|
builtin(_A =\= _B).
|
|
builtin(true).
|
|
builtin(false).
|
|
builtin(_A = _B).
|
|
builtin(_A==_B).
|
|
builtin(_A\=_B).
|
|
builtin(_A\==_B).
|
|
builtin(length(_L,_N)).
|
|
builtin(member(_El,_L)).
|
|
builtin(average(_L,_Av)).
|
|
builtin(max_list(_L,_Max)).
|
|
builtin(min_list(_L,_Max)).
|
|
builtin(nth0(_,_,_)).
|
|
builtin(nth(_,_,_)).
|
|
average(L,Av):-
|
|
sum_list(L,Sum),
|
|
length(L,N),
|
|
Av is Sum/N.
|
|
|
|
clique(Graph,Clique):-
|
|
vertices(Graph,Candidates),
|
|
extend_cycle(Graph,Candidates,[],[],Clique).
|
|
|
|
extend_cycle(G,[H|T],Not,CS,CSOut):-
|
|
neighbours(H, G, Neigh),
|
|
intersection(Neigh,T,NewCand),
|
|
intersection(Neigh,Not,NewNot),
|
|
extend(G,NewCand,NewNot,[H|CS],CSOut).
|
|
|
|
extend_cycle(G,[H|T],Not,CS,CSOut):-
|
|
extend_cycle(G,T,[H|Not],CS,CSOut).
|
|
|
|
extend(_G,[],[],CompSub,CompSub):-!.
|
|
|
|
extend(G,Cand,Not,CS,CSOut):-
|
|
extend_cycle(G,Cand,Not,CS,CSOut).
|
|
|
|
convert_body((~ A & B),[\+ A|B1]):-!,
|
|
convert_body(B,B1).
|
|
|
|
convert_body((A & B),[A|B1]):-!,
|
|
convert_body(B,B1).
|
|
|
|
convert_body(~ A,[\+ A]):-!.
|
|
|
|
convert_body(A,[A]).
|
|
|
|
/* set(Par,Value) can be used to set the value of a parameter */
|
|
set(Parameter,Value):-
|
|
retract(setting(Parameter,_)),
|
|
assert(setting(Parameter,Value)).
|
|
|
|
/* end of utility predicates */
|