solver.ml 22.5 KB
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(*-----------------------------------------------------------------------
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** Copyright (C) 2001, 2002 - Verimag.
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** This file may only be copied under the terms of the GNU Library General
** Public License 
**-----------------------------------------------------------------------
**
** File: solver.ml
** Main author: jahier@imag.fr
*)

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open List
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open Formula
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open Util
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open Hashtbl
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open Gne
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open Rnumsolver
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(****************************************************************************)
	  
let (formula_list_to_conj: formula list -> formula) =
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  fun fl -> 
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    (** Transform a (non-empty) list of formula to the conjunction
       made of those formula.  
    *)
    match fl with
	[] -> assert false
      | f::[] -> f
      | f1::f2::tail -> 
          List.fold_left (fun x y -> And(x, y)) (And(f1, f2)) tail

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let (lookup: env_in -> subst list -> var_name -> var_value option) = 
  fun input pre vn ->  
    try Some(Hashtbl.find input vn)
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    with Not_found -> 
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      try Some(List.assoc vn pre)
      with Not_found -> None

(****************************************************************************)

type comp = SupZero | SupEqZero | EqZero | NeqZero


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let rec (formula_to_bdd : env_in -> formula -> Bdd.t * bool) =
  fun input f ->
    (** Replaces input and pre variables by their values in the
      formula [f], and translates it into a bdd.

      Also returns a flag telling whether or not the formula depends
      on input and pre vars. If this flag is true, the formula is
      stored (cached) in a global table ([env_state.bdd_tbl]);
      otherwise, it is stored in a table that is cleared at each new
      step ([env_state.bdd_tbl_global]).

    *)
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    try (Env_state.bdd f, true)
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    with Not_found -> 
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      try (Env_state.bdd_global f, false)
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      with Not_found -> 
	let (bdd, dep) =
	  match f with 
	      Not(f1) ->
		let (bdd_not, dep) =  (formula_to_bdd input f1) in
		  (Bdd.dnot bdd_not, dep)

	    | Or(f1, f2) ->
		let (bdd1, dep1) = (formula_to_bdd input f1)
		and (bdd2, dep2) = (formula_to_bdd input f2)
		in
		  (Bdd.dor bdd1 bdd2, dep1 || dep2)

	    | And(f1, f2) -> 
		let (bdd1, dep1) = (formula_to_bdd input f1)
		and (bdd2, dep2) = (formula_to_bdd input f2)
		in
		  (Bdd.dand bdd1 bdd2, dep1 || dep2)

	    | IteB(f1, f2, f3) -> 
		let (bdd1, dep1) = (formula_to_bdd input f1)
		and (bdd2, dep2) = (formula_to_bdd input f2)
		and (bdd3, dep3) = (formula_to_bdd input f3) 
		in
		  ((Bdd.dor (Bdd.dand bdd1 bdd2) 
		      (Bdd.dand (Bdd.dnot bdd1) bdd3)),
		   dep1 || dep2 || dep3 )
		  
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	    | True ->  (Bdd.dtrue  (Env_state.bdd_manager ()), false)
	    | False -> (Bdd.dfalse (Env_state.bdd_manager ()), false)
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	    | Bvar(vn) ->    
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		( match (lookup input (Env_state.pre ()) vn) with 
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		      Some(B(bool)) -> 
			if bool 
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			then (Bdd.dtrue  (Env_state.bdd_manager ()), true) 
			else (Bdd.dfalse (Env_state.bdd_manager ()), true)
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		    | Some(_) -> 
			print_string (vn ^ " is not a boolean!\n");
			assert false
		    | None ->
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			if List.mem vn (Env_state.pre_var_names ())
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			then failwith 
			  ("*** " ^ vn ^ " is unknown at this stage.\n "
			   ^ "*** Make sure you have not used "
			   ^ "a pre on a output var at the 1st step, \n "
			   ^ "*** or a pre on a input var at the second step in "
			   ^ "your formula in the environment.\n ")
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			else (Bdd.ithvar (Env_state.bdd_manager ()) 
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			 (Env_state.atomic_formula_to_index (Bv(vn))), false)
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		)
		
	    | Eq(e1, e2) -> 
		let (gne, dep) = expr_to_gne (Diff(e1, e2)) input in 
		  (gne_to_bdd gne EqZero, dep)
		  
	    | Neq(e1, e2) -> 
		let (gne, dep) = expr_to_gne (Diff(e1, e2)) input in
		  (gne_to_bdd gne NeqZero, dep)
		  
	    | SupEq(e1, e2) ->
		let (gne, dep) = expr_to_gne (Diff(e1, e2)) input in
		  (gne_to_bdd gne SupEqZero, dep)
		  
	    | Sup(e1, e2)   ->
		let (gne, dep) = expr_to_gne (Diff(e1, e2)) input in
		  (gne_to_bdd gne SupZero, dep)
		  
	    | InfEq(e1, e2) ->  
		let (gne, dep) = expr_to_gne (Diff(e2, e1)) input in
		  (gne_to_bdd gne SupEqZero, dep)
		  
	    | Inf(e1, e2)   ->  
		let (gne, dep) =  expr_to_gne (Diff(e2, e1)) input in
		  (gne_to_bdd gne SupZero, dep)
		  
	in
	  if dep
	  then 
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	    ( Env_state.set_bdd f bdd;	
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	      match f with 
		  Not(nf) -> () (* Already in the tbl thanks to the rec call *)
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		| _  -> Env_state.set_bdd (Not(f)) (Bdd.dnot bdd) 
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	    ) 
	  else 
	    (* [f] does not depend on pre nor input vars *)
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	    ( Env_state.set_bdd_global f bdd ;	
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	      match f with 
		  Not(nf) -> () (* Already in the table thanks to the rec call *)
		| _  -> 
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		    Env_state.set_bdd_global (Not(f)) (Bdd.dnot bdd)
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	    );

	  (bdd, dep)
and
  (expr_to_gne: expr -> env_in -> Gne.gn_expr * bool) =
  fun e input -> 
    (** Evaluates pre and input vars appearing in [e] and tranlates
      it into a so-called garded normal form. Also returns a flag
      that is true iff [e] depends on pre or input vars. *)
    let (gne, dep) =
      match e with  
	  Sum(e1, e2) ->
	    let (gne1, dep1) = (expr_to_gne e1 input)
	    and (gne2, dep2) = (expr_to_gne e2 input) 
	    in
	      (Gne.add  gne1 gne2, dep1 || dep2)

	| Diff(e1, e2) -> 
	    let (gne1, dep1) = (expr_to_gne e1 input)
	    and (gne2, dep2) = (expr_to_gne e2 input) 
	    in
	      (Gne.diff gne1 gne2, dep1 || dep2)

	| Prod(e1, e2) -> 
	    let (gne1, dep1) = (expr_to_gne e1 input)
	    and (gne2, dep2) = (expr_to_gne e2 input) 
	    in
	      (Gne.mult gne1 gne2, dep1 || dep2)

	| Quot(e1, e2) -> 
	    let (gne1, dep1) = (expr_to_gne e1 input)
	    and (gne2, dep2) = (expr_to_gne e2 input) 
	    in
	      (Gne.quot gne1 gne2, dep1 || dep2)

	| Mod(e1, e2)  -> 
	    let (gne1, dep1) = (expr_to_gne e1 input)
	    and (gne2, dep2) = (expr_to_gne e2 input) 
	    in
	      (Gne.modulo gne1 gne2, dep1 || dep2)

	| Ivar(str) ->
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	    ( match (lookup input (Env_state.pre ()) str) with 
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		  Some(N(I(i))) ->
		    ( (GneMap.add 
			(NeMap.add "" (I(i)) NeMap.empty) 
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			(Bdd.dtrue (Env_state.bdd_manager ()))
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			GneMap.empty),
		      true
		    )
		| None ->
		    ( (GneMap.add 
			(NeMap.add str (I(1)) NeMap.empty) 
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			(Bdd.dtrue (Env_state.bdd_manager ())) 
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			GneMap.empty),
		      false
		    )     
		| Some(N(F(f))) -> 
		    print_string ((string_of_float f) 
				  ^ "is a float, but an int is expected.\n");
		    assert false
		| Some(B(f)) -> 
		    print_string ((string_of_bool f) 
				  ^ "is a bool, but an int is expected.\n");
		    assert false
	    )

	| Fvar(str) ->
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	    ( match (lookup input (Env_state.pre ()) str) with 
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		  Some(N(F(f))) ->
		    ( (GneMap.add 
			(NeMap.add "" (F(f)) NeMap.empty) 
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			(Bdd.dtrue (Env_state.bdd_manager ())) 
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			GneMap.empty),
		      true
		    )
		| None ->
		    ( (GneMap.add 
			(NeMap.add str (F(1.)) NeMap.empty) 
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			(Bdd.dtrue (Env_state.bdd_manager ())) 
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			GneMap.empty),
		      false
		    )
		| Some(N(I(i))) -> 
		    print_string ((string_of_int i) 
				  ^ "is an int, but a float is expected.\n");
		    assert false
		| Some(B(f)) -> 
		    print_string ((string_of_bool f) 
				  ^ "is a bool, not a float is expected.\n");
		    assert false
	    )

	| Ival(i) ->  
	    ( (GneMap.add 
		(NeMap.add "" (I(i)) NeMap.empty) 
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		(Bdd.dtrue (Env_state.bdd_manager ())) 
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		GneMap.empty),
	      false
	    )

	| Fval(f) -> 
	    ( (GneMap.add 
		(NeMap.add "" (F(f)) NeMap.empty) 
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		(Bdd.dtrue (Env_state.bdd_manager ()))
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		GneMap.empty),
	      false
	    )

	| Ite(f, e1, e2) -> 
	    let (add_formula_to_gne_acc : Bdd.t -> n_expr -> Bdd.t -> 
		   Gne.gn_expr -> Gne.gn_expr) = 
	      fun bdd nexpr c acc -> 
		(* Used (by a GneMap.fold) to add the condition [c] to every
		   condition of a garded expression. *)
		let _ = assert (
		  try 
		    let _ = GneMap.find nexpr acc in
		      false
		  with Not_found -> true
		) 
		in
		let new_bdd = (Bdd.dand bdd c) in
		  if Bdd.is_false new_bdd
		  then acc
		  else GneMap.add nexpr new_bdd acc
	    in
	    let (bdd, dep1) = formula_to_bdd input f in
	    let bdd_not = Bdd.dnot bdd
	    and (gne_t, dep2) = (expr_to_gne e1 input)
	    and (gne_e, dep3) = (expr_to_gne e2 input) in
	    let gne1 = GneMap.fold (add_formula_to_gne_acc bdd) gne_t GneMap.empty in
	    let gne  = GneMap.fold (add_formula_to_gne_acc bdd_not) gne_e gne1 in
	      (gne, dep1 || dep2 || dep3)
    in
      (gne, dep)
	
and
  (gne_to_bdd : Gne.gn_expr -> comp -> Bdd.t) =
  fun gne cmp -> 
    (** Use [cmp] to compare [gne] with 0 and returns the
       corresponding formula.  E.g., if [gne] is bounded to
       [e1 -> c1; e2 -> c2], then [gne_to_bdd gne SupZero] returns
       (the bdd corresponding to) the formula [(c1 and (e1 > 0)) or
       (c2 and (e2 > 0))] *)
    match cmp with
	SupZero ->
	  ( GneMap.fold 
	      (fun nexpr c acc -> 
		 let bdd = 
		   if is_n_expr_a_constant nexpr
		   then 
		     let cst = NeMap.find "" nexpr in
		       match cst with
			   I(i) -> 
			     if i > 0 
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			     then (Bdd.dtrue (Env_state.bdd_manager ()))
			     else (Bdd.dfalse (Env_state.bdd_manager ()))
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			 | F(f) -> 
			     if f > 0. 
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			     then (Bdd.dtrue (Env_state.bdd_manager ()))
			     else (Bdd.dfalse (Env_state.bdd_manager ()))
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		   else 
		     Bdd.ithvar 
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		       (Env_state.bdd_manager ()) 
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		       (Env_state.atomic_formula_to_index (GZ(nexpr))) 
		 in
		   Bdd.dor (Bdd.dand c bdd) acc
	      )
	      gne 
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	      (Bdd.dfalse (Env_state.bdd_manager ()))
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	  )
      | SupEqZero ->
	  ( GneMap.fold 
	      (fun nexpr c acc -> 
		 let bdd = 
		   if is_n_expr_a_constant nexpr
		   then 
		     let cst = NeMap.find "" nexpr in
		       match cst with
			   I(i) -> 
			     if i >= 0 
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			     then (Bdd.dtrue (Env_state.bdd_manager ()))
			     else (Bdd.dfalse (Env_state.bdd_manager ()))
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			 | F(f) -> 
			     if f >= 0. 
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			     then (Bdd.dtrue (Env_state.bdd_manager ()))
			     else (Bdd.dfalse (Env_state.bdd_manager ()))
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		   else 
		     Bdd.ithvar 
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		       (Env_state.bdd_manager ()) 
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		       (Env_state.atomic_formula_to_index (GeqZ(nexpr))) 
		 in
		   Bdd.dor (Bdd.dand c bdd) acc
	      )
	      gne 
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	      (Bdd.dfalse (Env_state.bdd_manager ()))
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	  )
      | EqZero -> 
	  ( GneMap.fold 
	      (fun nexpr c acc -> 
		 let bdd1 = 
		   if is_n_expr_a_constant nexpr
		   then 
		     let cst = NeMap.find "" nexpr in
		       match cst with
			   I(i) -> 
			     if i >= 0 
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			     then (Bdd.dtrue (Env_state.bdd_manager ()))
			     else (Bdd.dfalse (Env_state.bdd_manager ()))
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			 | F(f) -> 
			     if f >= 0. 
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			     then (Bdd.dtrue (Env_state.bdd_manager ()))
			     else (Bdd.dfalse (Env_state.bdd_manager ()))
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		   else 
		     Bdd.ithvar 
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		       (Env_state.bdd_manager ()) 
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		       (Env_state.atomic_formula_to_index (GeqZ(nexpr))) 
		 in
		 let bdd2 = 
		   if is_n_expr_a_constant nexpr
		   then 
		     let cst = NeMap.find "" nexpr in
		       match cst with
			   I(i) -> 
			     if i <= 0 
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			     then (Bdd.dtrue (Env_state.bdd_manager ()))
			     else (Bdd.dfalse (Env_state.bdd_manager ()))
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			 | F(f) -> 
			     if f <= 0. 
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			     then (Bdd.dtrue (Env_state.bdd_manager ()))
			     else (Bdd.dfalse (Env_state.bdd_manager ()))
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		   else 
		     Bdd.ithvar 
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		       (Env_state.bdd_manager ()) 
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		       (Env_state.atomic_formula_to_index (SeqZ(nexpr))) 
		 in
		 let bdd = Bdd.dand bdd1 bdd2 in 
		   (* We transform [e1 = e2] into [e1 <= e2 ^ e1 >= e2] as the 
		      numeric solver can not handle equalities *)
		   Bdd.dor (Bdd.dand c bdd) acc
	      )
	      gne 
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	      (Bdd.dfalse (Env_state.bdd_manager ()))
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	  )
      | NeqZero -> 
	  ( GneMap.fold 
	      (fun nexpr c acc -> 
		 let bdd1 = 
		   if is_n_expr_a_constant nexpr
		   then 
		     let cst = NeMap.find "" nexpr in
		       match cst with
			   I(i) -> 
			     if i > 0 
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			     then (Bdd.dtrue (Env_state.bdd_manager ()))
			     else (Bdd.dfalse (Env_state.bdd_manager ()))
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			 | F(f) -> 
			     if f > 0. 
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			     then (Bdd.dtrue (Env_state.bdd_manager ()))
			     else (Bdd.dfalse (Env_state.bdd_manager ()))
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		   else 
		     Bdd.ithvar 
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		       (Env_state.bdd_manager ()) 
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		       (Env_state.atomic_formula_to_index (GZ(nexpr))) 
		 in
		 let bdd2 = 
		   if is_n_expr_a_constant nexpr
		   then 
		     let cst = NeMap.find "" nexpr in
		       match cst with
			   I(i) -> 
			     if i < 0 
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			     then (Bdd.dtrue (Env_state.bdd_manager ()))
			     else (Bdd.dfalse (Env_state.bdd_manager ()))
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			 | F(f) -> 
			     if f < 0. 
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			     then (Bdd.dtrue (Env_state.bdd_manager ()))
			     else (Bdd.dfalse (Env_state.bdd_manager ()))
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		   else 
		     Bdd.ithvar 
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		       (Env_state.bdd_manager ()) 
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		       (Env_state.atomic_formula_to_index (SZ(nexpr))) 
		 in
		 let bdd = Bdd.dor bdd1 bdd2 in 
		   (* We transform [e1 <> e2] into [e1 < e2 or e1 > e2] as the 
		      numeric solver can not handle disequalities *)
		   Bdd.dor (Bdd.dand c bdd) acc
	      )
	      gne 
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	      (Bdd.dfalse (Env_state.bdd_manager ()))
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	  )
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(****************************************************************************)
(****************************************************************************)


(* Exported *)
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let rec (is_satisfiable: env_in -> formula list -> bool) = 
  fun input fl -> 
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    let f = formula_list_to_conj fl in
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    let (bdd, _) = formula_to_bdd input f in
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      not (Bdd.is_false bdd) &&
      ( 
	try 
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	  let (n, m) = Env_state.sol_number bdd in 
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	    not ((zero_sol, zero_sol) = (n, m))
	with Not_found -> true
      )
      


(****************************************************************************)
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(****************************************************************************)

type var = int

(** In the following, we call a comb the bdd of a conjunction of
 litterals (var). They provide the ordering in which litterals
 appear in the bdds we manipulate.
*)

let rec (count_missing_vars: Bdd.t -> var -> int -> Bdd.t * int) =
  fun comb var cpt -> 
    (* Returns [cpt] + the number of variables occurring in [comb]
       before reaching [var] ([var] excluded). Also returns the comb
       which topvar is [var]. *)
    let _ = assert (not (Bdd.is_cst comb)) in
    let combvar = Bdd.topvar comb in
      if var = combvar
      then (comb, cpt)
      else count_missing_vars (Bdd.dthen comb) var (cpt+1)


let rec (build_sol_nb_table: Bdd.t -> Bdd.t -> sol_nb * sol_nb) =
  fun bdd comb -> 
    (** Returns the relative (to which bbd points to it) number of
      solutions of [bdd] and the one of its negation. Also udpates
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      the solution number table for [bdd] and its negation, and 
      recursively for all its sub-bdds. 
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    *)
    let bdd_not = (Bdd.dnot bdd) in
    let (sol_nb, sol_nb_not) =
      try
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	let (nt, ne) = Env_state.sol_number bdd 
	and (not_nt, not_ne) = Env_state.sol_number bdd_not in
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	  (* solutions numbers in the table are absolute *)
	  ((add_sol_nb nt ne), (add_sol_nb not_nt not_ne))
      with Not_found ->  	
	let _ = assert (not (Bdd.is_cst bdd)) in
	let (nt, not_nt) = compute_absolute_sol_nb (Bdd.dthen bdd) comb in
	let (ne, not_ne) = compute_absolute_sol_nb (Bdd.delse bdd) comb in
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	  Env_state.set_sol_number bdd (nt, ne) ;
	  Env_state.set_sol_number bdd_not (not_nt, not_ne) ;
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	  ((add_sol_nb nt ne), (add_sol_nb not_nt not_ne))
    in
      (sol_nb, sol_nb_not)
and 
  (compute_absolute_sol_nb: Bdd.t -> Bdd.t -> sol_nb * sol_nb) =
  fun sub_bdd comb -> 
    (* returns the absolute number of solutions of [sub_bdd] (and its
       negation) w.r.t. [comb], where [comb] is the comb of the
       father of [sub_bdd]. *)
    if Bdd.is_cst sub_bdd 
    then 
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      let sol_nb = 
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	if Bdd.is_true comb (* iff no bool are to be gen *)
	then one_sol
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	else (two_power_of (List.length (Bdd.list_of_support (Bdd.dthen comb)))) 
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      in
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	if Bdd.is_true sub_bdd
	then (sol_nb, zero_sol) 
	else (zero_sol, sol_nb)
    else 
      let topvar = Bdd.topvar sub_bdd in
      let (sub_comb, missing_vars_nb) = 
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	if Bdd.is_true comb (* iff no bool are to be gen *)
	then (comb, 0)
	else count_missing_vars (Bdd.dthen comb) topvar 0 
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      in
      let (n0, not_n0) = build_sol_nb_table sub_bdd sub_comb in
      let factor = (two_power_of missing_vars_nb) in
	(mult_sol_nb n0 factor, mult_sol_nb not_n0 factor)
	
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(****************************************************************************)
(****************************************************************************)

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let (toss_up_one_var: var -> subst) =
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  fun var -> 
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    (* [var] is a index that ougth to correspond to a boolean
       variable. This fonction performs a toss and returns a
       substitution for the corresponding boolean variable. *)
    let af = Env_state.index_to_atomic_formula var in
    let vn = (
      match af with 
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        Bv(vn0) -> vn0
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      | _  -> 
	  (* Only bool index ougth to appear in the comb. *)
	  assert false
    ) in
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    let ran = Random.float 1. in
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      if (ran < 0.5) 
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      then (vn, Formula.B(true)) 
      else (vn, Formula.B(false))

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let (is_a_numeric_constraint : atomic_formula -> bool) =
  fun af -> 
    match af with
	Bv(_) -> false
      | GZ(_)   -> true 
      | GeqZ(_) -> true
      | SZ(_)   -> true
      | SeqZ(_) -> true
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(* exported *)
exception No_numeric_solution

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let rec (draw_in_bdd: subst list * store -> Bdd.t -> Bdd.t -> 
	   subst list * store) = 
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  fun (sl, store) bdd comb ->
    (** Returns [sl] appended to a draw of all the boolean variables
      bigger than the topvar of [bdd] according to the ordering
      induced by the comb [comb]. Also returns the (non empty) store
      obtained by adding to [store] all the numeric constraints that
      were encountered during this draw.
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      Raises the [No_numeric_solution] exception whenever no valid
      path in [bdd] leads to a satisfiable set of numeric
      constraints.  
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    *)
    let _ = assert (not (Bdd.is_cst bdd)) in
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    let _ = assert (Env_state.sol_number_exists bdd) in
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    let bddvar  = Bdd.topvar bdd in
    let af = (Env_state.index_to_atomic_formula bddvar) in 
    let top_var_is_numeric = is_a_numeric_constraint af in
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      if
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	not(Bdd.is_true comb) && (* iff no bool are to be gen *)
	bddvar <> (Bdd.topvar comb) &&
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	not top_var_is_numeric
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      then
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	let new_sl = (toss_up_one_var (Bdd.topvar comb))::sl in
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	  draw_in_bdd (new_sl, store) bdd (Bdd.dthen comb)
      else 
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	(* bddvar = combvar xor top_var_is_numeric *) 
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	(* nb: I handle those two cases alltogether to avoid code
	   duplication (i.e., retrieving sol numbers, performing the
	   toss, the recursive call, handling the base case where a
	   dtrue bdd is reached, etc).  It makes the code a little
	   bit more obscur, but ...  *)
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	let (n, m) = Env_state.sol_number bdd in
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	let _ =
	  if ((eq_sol_nb n zero_sol) && (eq_sol_nb m zero_sol))
	  then raise No_numeric_solution ;
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	in
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	let (store_plus_af, store_plus_not_af) = 
	  (* A first trick to avoid code dup (cf nb above) *)
	  if top_var_is_numeric
	  then 
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	    split_store store af
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	  else 
	    (store, store)
	in
	let (swap, store1, bdd1, bool1, sol_nb1, store2, bdd2, bool2, sol_nb2) =
	  (* Depending on the result of a toss (based on the number
	     of solution in each branch), we try the [else] or the
	     [then] branch first. [swap] indicates whether or not the
	     [else] part is put before the [then] one. *)
	  let ran = Random.float 1. in
	    if ran < ((float_of_sol_nb n) /. (float_of_sol_nb (add_sol_nb n m)))
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	    then
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	      (false, store_plus_af, (Bdd.dthen bdd), true, n,
	       store_plus_not_af, (Bdd.delse bdd), false, m )
	    else 
	      (true, store_plus_not_af, (Bdd.delse bdd), false, m,
	       store_plus_af, (Bdd.dthen bdd), true, n )
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	in
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	let (sl1, sl2, new_comb) = (
	  (* A second trick to avoid code dup (cf nb above) *)
	  match af with 
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	    Bv(vn) -> 
	      (((vn, Formula.B(bool1))::sl), 
	       ((vn, Formula.B(bool2))::sl), 
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	       (if Bdd.is_true comb then comb else Bdd.dthen comb) )
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	  | _ -> 
	      (* top_var_is_numeric *)
	      (sl, sl, comb)
	  )
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	in
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	let res_opt =
	  (* A solution will be found in this branch iff there exists
	     at least one path in the bdd that leads to a satisfiable
	     set of numeric constraints. If it is not the case,
	     [res_opt] is bound to [None]. *)
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	  if not (is_empty store1)
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	  then 
	    try 
	      let tail_draw1 = 
		if Bdd.is_true bdd1
		then
		  (* Toss the remaining bool vars. *)
		  ( (List.append 
		       sl1 
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		       (map toss_up_one_var (Bdd.list_of_support new_comb))),
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		    store1
		  )
		else
		  draw_in_bdd (sl1, store1) bdd1 new_comb
	      in
		Some(tail_draw1)
	    with No_numeric_solution -> 
	      None
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	  else
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	    None
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	in
	  match res_opt with 
	      Some(res) -> res
	    | None -> 
		(* The second branch is now tried because no path in
		   the first bdd leaded to a satisfiable set of
		   numeric constraints. *)
		if not (eq_sol_nb sol_nb2 zero_sol)
		then
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		  if not (is_empty store2)
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		  then    
		    if Bdd.is_true bdd2
		    then 
		      ( (List.append 
			   sl2 
			   (List.map toss_up_one_var 
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			      (Bdd.list_of_support new_comb))),
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			store2
		      )
		    else
		      draw_in_bdd (sl2, store2) bdd2 new_comb 
		  else
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		    raise No_numeric_solution
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		else
		  raise No_numeric_solution
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let (draw : vn list -> vnt list -> Bdd.t -> Bdd.t -> subst list * subst list) =
  fun bool_vars_to_gen num_vnt_to_gen comb bdd ->
    (** Draw the output and local vars to be generated by the environnent. *)
    let (bool_subst_l, store) = 
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      draw_in_bdd ([], (new_store num_vnt_to_gen)) bdd comb 
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    in
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    let num_subst_l = draw_inside store in
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    let subst_l = append bool_subst_l num_subst_l in
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    let (out_vars, _) = List.split (Env_state.output_var_names ()) 
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    in
      assert ( 
	(*  Checks that we generated all variables. *)
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	let (gen_vars, _) = List.split subst_l in
	let (num_vars_to_gen, _) = List.split num_vnt_to_gen in
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	let vars_to_gen = append bool_vars_to_gen num_vars_to_gen in
          (sort (compare) gen_vars) = (sort (compare) vars_to_gen) 
      );
      (* Splits output and local vars. *)
      List.partition 
	(fun (vn, _) -> List.mem vn out_vars) 
	subst_l
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723
  
724
(* Exported *)
725
let (solve_formula: env_in -> int -> formula list -> vn list -> vnt list ->
726
       (subst list * subst list) list) =
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  fun input p fl bool_vars_to_gen num_vars_to_gen ->
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    let f = formula_list_to_conj fl in
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    let bdd = 
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      try Env_state.bdd f
      with Not_found -> Env_state.bdd_global f
732
    in
733
    let bool_vars_to_gen_f = 
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      List.fold_left
	(fun acc vn -> (And(Bvar(vn), acc)))
	True
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	bool_vars_to_gen
738
    in
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    let (comb, _) = formula_to_bdd input bool_vars_to_gen_f in

741
    let _ =
742
      if not (Env_state.sol_number_exists bdd)
743
      then
744
	let rec skip_var comb v =
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	  if Bdd.is_true comb (* iff no bool are to be gen *)
	  then comb
	  else 
	    let topvar = (Bdd.topvar comb) in
	      if v = topvar then comb else skip_var (Bdd.dthen comb) v
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	in
	let comb2 = skip_var comb (Bdd.topvar bdd) in
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	let _ = build_sol_nb_table bdd comb2 in
	  ()
754
    in
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      try 	
	Util.unfold (draw bool_vars_to_gen num_vars_to_gen comb) bdd p
757
      with No_numeric_solution -> 
758
	Env_state.set_sol_number bdd (zero_sol, zero_sol);
759
	[]
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