417 lines
11 KiB
Prolog
417 lines
11 KiB
Prolog
/** @defgroup BDDs Binary Decision Diagrams and Friends
|
|
@ingroup packages
|
|
@{
|
|
|
|
This library provides an interface to the BDD package CUDD. It requires
|
|
CUDD compiled as a dynamic library. In Linux this is available out of
|
|
box in Fedora, but can easily be ported to other Linux
|
|
distributions. CUDD is available in the ports OSX package, and in
|
|
cygwin. To use it, call
|
|
|
|
~~~~~
|
|
:-use_module(library(bdd))`.
|
|
~~~~~
|
|
|
|
The following predicates construct a BDD:
|
|
|
|
\toc
|
|
|
|
*/
|
|
|
|
:- module(bdd, [
|
|
bdd_new/2,
|
|
bdd_new/3,
|
|
bdd_from_list/3,
|
|
mtbdd_new/2,
|
|
mtbdd_new/3,
|
|
bdd_eval/2,
|
|
mtbdd_eval/2,
|
|
bdd_tree/2,
|
|
bdd_size/2,
|
|
bdd_print/2,
|
|
bdd_print/3,
|
|
bdd_to_probability_sum_product/2,
|
|
bdd_to_probability_sum_product/3,
|
|
bdd_reorder/2,
|
|
bdd_close/1,
|
|
mtbdd_close/1]).
|
|
|
|
:- use_module(library(lists)).
|
|
|
|
:- use_module(library(maplist)).
|
|
|
|
:- use_module(library(rbtrees)).
|
|
|
|
:- use_module(library(simpbool)).
|
|
|
|
tell_warning :-
|
|
print_message(warning,functionality(cudd)).
|
|
|
|
:- catch(load_foreign_files([cudd], [], init_cudd),_,fail) -> true ; tell_warning.
|
|
|
|
/**
|
|
@pred bdd_new(? _Exp_, - _BddHandle_)
|
|
|
|
create a new BDD from the logical expression _Exp_. The expression
|
|
may include:
|
|
|
|
+ Logical Variables:
|
|
|
|
a leaf-node can be a logical variable.
|
|
|
|
+ `0` and `1`
|
|
|
|
a leaf-node can also be bound to the two boolean constants.
|
|
|
|
+ `or( _X_, _Y_)`, `_X_ \/ _Y_`, `_X_ + _Y_`
|
|
|
|
disjunction
|
|
|
|
+ `and( _X_, _Y_)`, `_X_ /\ _Y_`, `_X_ * _Y_`
|
|
|
|
conjunction
|
|
|
|
+ `nand( _X_, _Y_)`
|
|
|
|
negated conjunction
|
|
|
|
+ `nor( _X_, _Y_)`
|
|
|
|
negated disjunction
|
|
|
|
+ `xor( _X_, _Y_)`
|
|
|
|
exclusive or
|
|
|
|
+ `not( _X_)`, or `-_X_`
|
|
|
|
negation.
|
|
|
|
*/
|
|
bdd_new(T, Bdd) :-
|
|
term_variables(T, Vars),
|
|
bdd_new(T, Vars, Bdd).
|
|
|
|
/**
|
|
@pred bdd_new(? _Exp_, +_Vars_, - _BddHandle_)
|
|
|
|
Same as bdd_new/2, but receives a term of the form
|
|
`vs(V1,....,Vn)`. This allows incremental construction of BDDs.
|
|
|
|
*/
|
|
bdd_new(T, Vars, cudd(M,X,VS,TrueVars)) :-
|
|
term_variables(Vars, TrueVars),
|
|
VS =.. [vs|TrueVars],
|
|
findall(Manager-Cudd, set_bdd(T, VS, Manager, Cudd), [M-X]).
|
|
|
|
/** @pred bdd_from_list(? _List_, ?_Vars_, - _BddHandle_)
|
|
|
|
Convert a _List_ of logical expressions of the form above, that
|
|
includes the set of free variables _Vars_, into a BDD accessible
|
|
through _BddHandle_.
|
|
*/
|
|
% create a new BDD from a list.
|
|
bdd_from_list(List, Vars, cudd(M,X,VS,TrueVars)) :-
|
|
term_variables(Vars, TrueVars),
|
|
VS =.. [vs|TrueVars],
|
|
findall(Manager-Cudd, set_bdd_from_list(List, VS, Manager, Cudd), [M-X]).
|
|
|
|
set_bdd(T, VS, Manager, Cudd) :-
|
|
numbervars(VS,0,_),
|
|
( ground(T)
|
|
->
|
|
term_to_cudd(T,Manager,Cudd)
|
|
;
|
|
writeln(throw(error(instantiation_error,T)))
|
|
).
|
|
|
|
set_bdd_from_list(T0, VS, Manager, Cudd) :-
|
|
numbervars(VS,0,_),
|
|
generate_releases(T0, Manager, T),
|
|
% T0 = T,
|
|
% writeln_list(T0),
|
|
list_to_cudd(T,Manager,_Cudd0,Cudd).
|
|
|
|
generate_releases(T0, Manager, T) :-
|
|
rb_empty(RB0),
|
|
reverse(T0, [H|R]),
|
|
add_releases(R, RB0, [H], Manager, T).
|
|
|
|
add_releases([], _, RR, _M, RR).
|
|
add_releases([(X = Ts)|R], RB0, RR0, M, RR) :-
|
|
term_variables(Ts, Vs), !,
|
|
add_variables(Vs, RB0, RR0, M, RBF, RRI),
|
|
add_releases(R, RBF, [(X=Ts)|RRI], M, RR).
|
|
|
|
add_variables([], RB, RR, _M, RB, RR).
|
|
add_variables([V|Vs], RB0, RR0, M, RBF, RRF) :-
|
|
rb_lookup(V, _, RB0), !,
|
|
add_variables(Vs, RB0, RR0, M, RBF, RRF).
|
|
add_variables([V|Vs], RB0, RR0, M, RBF, RRF) :-
|
|
rb_insert(RB0, V, _, RB1),
|
|
add_variables(Vs, RB1, [release_node(M,V)|RR0], M, RBF, RRF).
|
|
|
|
|
|
writeln_list([]).
|
|
writeln_list([B|Bindings]) :-
|
|
writeln(B),
|
|
writeln_list(Bindings).
|
|
|
|
%list_to_cudd(H._List,_Manager,_Cudd0,_CuddF) :- writeln(l:H), fail.
|
|
list_to_cudd([],_Manager,Cudd,Cudd) :- writeln('X').
|
|
list_to_cudd([release_node(M,cudd(V))|T], Manager, Cudd0, CuddF) :- !,
|
|
write('-'), flush_output,
|
|
cudd_release_node(M,V),
|
|
list_to_cudd(T, Manager, Cudd0, CuddF).
|
|
list_to_cudd([(V=0*_Par)|T], Manager, _Cudd0, CuddF) :- !,
|
|
write('0'), flush_output,
|
|
term_to_cudd(0, Manager, Cudd),
|
|
V = cudd(Cudd),
|
|
list_to_cudd(T, Manager, Cudd, CuddF).
|
|
list_to_cudd([(V=0)|T], Manager, _Cudd0, CuddF) :- !,
|
|
write('0'), flush_output,
|
|
term_to_cudd(0, Manager, Cudd),
|
|
V = cudd(Cudd),
|
|
list_to_cudd(T, Manager, Cudd, CuddF).
|
|
list_to_cudd([(V=_Tree*0)|T], Manager, _Cudd0, CuddF) :- !,
|
|
write('0'), flush_output,
|
|
term_to_cudd(0, Manager, Cudd),
|
|
V = cudd(Cudd),
|
|
list_to_cudd(T, Manager, Cudd, CuddF).
|
|
list_to_cudd([(V=Tree*1)|T], Manager, _Cudd0, CuddF) :- !,
|
|
write('.'), flush_output,
|
|
term_to_cudd(Tree, Manager, Cudd),
|
|
V = cudd(Cudd),
|
|
list_to_cudd(T, Manager, Cudd, CuddF).
|
|
list_to_cudd([(V=Tree)|T], Manager, _Cudd0, CuddF) :-
|
|
write('.'), flush_output,
|
|
( ground(Tree) -> true ; throw(error(instantiation_error(Tree))) ),
|
|
term_to_cudd(Tree, Manager, Cudd),
|
|
V = cudd(Cudd),
|
|
list_to_cudd(T, Manager, Cudd, CuddF).
|
|
|
|
/** @pred mtbdd_new(? _Exp_, - _BddHandle_)
|
|
|
|
create a new algebraic decision diagram (ADD) from the logical
|
|
expression _Exp_. The expression may include:
|
|
|
|
+ Logical Variables:
|
|
a leaf-node can be a logical variable, or <em>parameter</em>.
|
|
+ Number
|
|
a leaf-node can also be any number
|
|
+ _X_ \* _Y_
|
|
product
|
|
+ _X_ + _Y_
|
|
sum
|
|
+ _X_ - _Y_
|
|
subtraction
|
|
+ or( _X_, _Y_), _X_ \/ _Y_
|
|
logical or
|
|
|
|
*/
|
|
mtbdd_new(T, Mtbdd) :-
|
|
term_variables(T, Vars),
|
|
mtbdd_new(T, Vars, Mtbdd).
|
|
|
|
mtbdd_new(T, Vars, add(M,X,VS,Vars)) :-
|
|
VS =.. [vs|Vars],
|
|
functor(VS,vs,Sz),
|
|
findall(Manager-Cudd, (numbervars(VS,0,_),term_to_add(T,Sz,Manager,Cudd)), [M-X]).
|
|
|
|
/** @pred bdd_eval(+ _BDDHandle_, _Val_)
|
|
|
|
Unify _Val_ with the value of the logical expression compiled in
|
|
_BDDHandle_ given an assignment to its variables.
|
|
|
|
~~~~~
|
|
bdd_new(X+(Y+X)*(-Z), BDD),
|
|
[X,Y,Z] = [0,0,0],
|
|
bdd_eval(BDD, V),
|
|
writeln(V).
|
|
~~~~~
|
|
would write 0 in the standard output stream.
|
|
|
|
The Prolog code equivalent to <tt>bdd_eval/2</tt> is:
|
|
|
|
~~~~~
|
|
Tree = bdd(1, T, _Vs),
|
|
reverse(T, RT),
|
|
foldl(eval_bdd, RT, _, V).
|
|
|
|
eval_bdd(pp(P,X,L,R), _, P) :-
|
|
P is ( X/\L ) \/ ( (1-X) /\ R ).
|
|
eval_bdd(pn(P,X,L,R), _, P) :-
|
|
P is ( X/\L ) \/ ( (1-X) /\ (1-R) ).
|
|
~~~~~
|
|
First, the nodes are reversed to implement bottom-up evaluation. Then,
|
|
we use the `foldl` list manipulation predicate to walk every node,
|
|
computing the disjunction of the two cases and binding the output
|
|
variable. The top node gives the full expression value. Notice that
|
|
`(1- _X_)` implements negation.
|
|
|
|
|
|
*/
|
|
bdd_eval(cudd(M, X, Vars, _), Val) :-
|
|
cudd_eval(M, X, Vars, Val).
|
|
bdd_eval(add(M, X, Vars, _), Val) :-
|
|
add_eval(M, X, Vars, Val).
|
|
|
|
mtbdd_eval(add(M,X, Vars, _), Val) :-
|
|
add_eval(M, X, Vars, Val).
|
|
|
|
% get the BDD as a Prolog list from the CUDD C object
|
|
/** @pred bdd_tree(+ _BDDHandle_, _Term_)
|
|
|
|
Convert the BDD or ADD represented by _BDDHandle_ to a Prolog term
|
|
of the form `bdd( _Dir_, _Nodes_, _Vars_)` or `mtbdd( _Nodes_, _Vars_)`, respectively. The arguments are:
|
|
|
|
+
|
|
_Dir_ direction of the BDD, usually 1
|
|
+
|
|
_Nodes_ list of nodes in the BDD or ADD.
|
|
|
|
In a BDD nodes may be <tt>pp</tt> (both terminals are positive) or <tt>pn</tt>
|
|
(right-hand-side is negative), and have four arguments: a logical
|
|
variable that will be bound to the value of the node, the logical
|
|
variable corresponding to the node, a logical variable, a 0 or a 1 with
|
|
the value of the left-hand side, and a logical variable, a 0 or a 1
|
|
with the right-hand side.
|
|
|
|
+
|
|
_Vars_ are the free variables in the original BDD, or the parameters of the BDD/ADD.
|
|
|
|
As an example, the BDD for the expression `X+(Y+X)\*(-Z)` becomes:
|
|
|
|
~~~~~
|
|
bdd(1,[pn(N2,X,1,N1),pp(N1,Y,N0,1),pn(N0,Z,1,1)],vs(X,Y,Z))
|
|
~~~~~
|
|
|
|
|
|
*/
|
|
bdd_tree(cudd(M, X, Vars, _Vs), bdd(Dir, List, Vars)) :-
|
|
cudd_to_term(M, X, Vars, Dir, List).
|
|
bdd_tree(add(M, X, Vars, _), mtbdd(Tree, Vars)) :-
|
|
add_to_term(M, X, Vars, Tree).
|
|
|
|
/** @pred bdd_to_probability_sum_product(+ _BDDHandle_, - _Prob_)
|
|
|
|
Each node in a BDD is given a probability _Pi_. The total
|
|
probability of a corresponding sum-product network is _Prob_.
|
|
|
|
|
|
*/
|
|
bdd_to_probability_sum_product(cudd(M,X,_,Probs), Prob) :-
|
|
cudd_to_probability_sum_product(M, X, Probs, Prob).
|
|
|
|
/** @pred bdd_to_probability_sum_product(+ _BDDHandle_, - _Probs_, - _Prob_)
|
|
Each node in a BDD is given a probability _Pi_. The total
|
|
probability of a corresponding sum-product network is _Prob_, and
|
|
the probabilities of the inner nodes are _Probs_.
|
|
|
|
In Prolog, this predicate would correspond to computing the value of a
|
|
BDD. The input variables will be bound to probabilities, eg
|
|
`[ _X_, _Y_, _Z_] = [0.3.0.7,0.1]`, and the previous
|
|
`eval_bdd` would operate over real numbers:
|
|
|
|
~~~~~
|
|
Tree = bdd(1, T, _Vs),
|
|
reverse(T, RT),
|
|
foldl(eval_prob, RT, _, V).
|
|
|
|
eval_prob(pp(P,X,L,R), _, P) :-
|
|
P is X * L + (1-X) * R.
|
|
eval_prob(pn(P,X,L,R), _, P) :-
|
|
P is X * L + (1-X) * (1-R).
|
|
~~~~~
|
|
|
|
*/
|
|
bdd_to_probability_sum_product(cudd(M,X,_,_Probs), Probs, Prob) :-
|
|
cudd_to_probability_sum_product(M, X, Probs, Prob).
|
|
|
|
|
|
/** @pred bdd_close( _BDDHandle_)
|
|
|
|
close the BDD and release any resources it holds.
|
|
|
|
*/
|
|
bdd_close(cudd(M,_,_Vars, _)) :-
|
|
cudd_die(M).
|
|
bdd_close(add(M,_,_Vars, _)) :-
|
|
cudd_die(M).
|
|
|
|
/** @pred bdd_close( _BDDHandle_)
|
|
|
|
close the BDD and release any resources it holds.
|
|
|
|
*/
|
|
bdd_reorder(cudd(M,Top,_Vars, _), How) :-
|
|
cudd_reorder(M, Top,How).
|
|
|
|
/** @pred bdd_size(+ _BDDHandle_, - _Size_)
|
|
|
|
Unify _Size_ with the number of nodes in _BDDHandle_.
|
|
|
|
|
|
*/
|
|
bdd_size(cudd(M,Top,_Vars, _), Sz) :-
|
|
cudd_size(M,Top,Sz).
|
|
bdd_size(add(M,Top,_Vars, _), Sz) :-
|
|
cudd_size(M,Top,Sz).
|
|
|
|
/** @pred bdd_print(+ _BDDHandle_, + _File_)
|
|
|
|
Output bdd _BDDHandle_ as a dot file to _File_.
|
|
|
|
|
|
*/
|
|
bdd_print(cudd(M,Top,_Vars, _), File) :-
|
|
absolute_file_name(File, AFile, []),
|
|
cudd_print(M, Top, AFile).
|
|
bdd_print(add(M,Top,_Vars, _), File) :-
|
|
absolute_file_name(File, AFile, []),
|
|
cudd_print(M, Top, AFile).
|
|
|
|
bdd_print(cudd(M,Top, Vars, _), File, Names) :-
|
|
Vars =.. [_|LVars],
|
|
%trace,
|
|
maplist( fetch_name(Names), LVars, Ss),
|
|
absolute_file_name(File, AFile, []),
|
|
cudd_print(M, Top, AFile, Ss).
|
|
bdd_print(add(M,Top, Vars, _), File, Names) :-
|
|
Vars =.. [_|LVars],
|
|
maplist( fetch_name(Names), LVars, Ss),
|
|
absolute_file_name(File, AFile, []),
|
|
cudd_print(M, Top, AFile, Ss).
|
|
|
|
fetch_name([S=V1|_], V2, SN) :- V1 == V2, !,
|
|
( atom(S) -> SN = S ; format(atom(SN), '~w', [S]) ).
|
|
fetch_name([_|Y], V, S) :- !,
|
|
fetch_name(Y, V, S).
|
|
fetch_name([], V, V).
|
|
|
|
mtbdd_close(add(M,_,_Vars,_)) :-
|
|
cudd_die(M).
|
|
|
|
/* algorithm to compute probabilitie in Prolog */
|
|
bdd_to_sp(bdd(Dir, Tree, _Vars, IVars), Binds, Prob) :-
|
|
findall(P, sp(Dir, Tree, IVars, Binds, P), [Prob]).
|
|
|
|
sp(Dir, Tree, Vars, Vars, P) :-
|
|
run_sp(Tree),
|
|
fetch(Tree, Dir, P).
|
|
|
|
run_sp([]).
|
|
run_sp(pp(P,X,L,R).Tree) :-
|
|
run_sp(Tree),
|
|
P is X*L+(1-X)*R.
|
|
run_sp(pn(P,X,L,R).Tree) :-
|
|
run_sp(Tree),
|
|
P is X*L+(1-X)*(1-R).
|
|
|
|
fetch(pp(P,_,_,_)._Tree, 1, P).
|
|
fetch(pp(P,_,_,_)._Tree, -1, N) :- N is 1-P.
|
|
fetch(pn(P,_,_,_)._Tree, 1, P).
|
|
fetch(pn(P,_,_,_)._Tree, -1, N) :- N is 1-P.
|
|
|
|
%% @}
|