bool.ml 12 KB
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let (<) : int -> int -> bool = (<)
let (>) : int -> int -> bool = (>)
let (=) : int -> int -> bool = (=)

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type 'a bdd =
    False
  | True
  | Split of int * 'a * 'a bdd * 'a bdd * 'a bdd

let empty = False

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module type S =
sig
  type elem
  include Custom.T

  val get: t -> (elem list * elem list) list

  val empty : t
  val full  : t
  val cup   : t -> t -> t
  val cap   : t -> t -> t
  val diff  : t -> t -> t
  val atom  : elem -> t
  val is_empty : t -> bool
  val iter: (elem-> unit) -> t -> unit

  val compute:
    empty:'b -> full:'b ->
    cup:('b -> 'b -> 'b) ->
    cap:('b -> 'b -> 'b) ->
    diff:('b -> 'b -> 'b) ->
    atom:(elem -> 'b) -> t -> 'b

  val trivially_disjoint: t -> t -> bool
end


module Make(X : Custom.T) =
struct
  type elem = X.t
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  type t = elem bdd
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  let rec equal a b =
    (a == b) ||
    match (a,b) with
      | Split (h1,x1, p1,i1,n1), Split (h2,x2, p2,i2,n2) ->
	  (h1 == h2) &&
	  (equal p1 p2) && (equal i1 i2) &&
	  (equal n1 n2) && (X.equal x1 x2)
      | _ -> false

(* Idea: add a mutable "unique" identifier and set it to
   the minimum of the two when egality ... *)

  let rec compare a b =
    if (a == b) then 0
    else match (a,b) with
      | Split (h1,x1, p1,i1,n1), Split (h2,x2, p2,i2,n2) ->
	  if h1 < h2 then -1 else if h1 > h2 then 1
	  else let c = X.compare x1 x2 in if c <> 0 then c
	  else let c = compare p1 p2 in if c <> 0 then c
	  else let c = compare i1 i2 in if c <> 0 then c
	  else compare n1 n2
      | True,_  -> -1
      | _, True -> 1
      | False,_ -> -1
      | _,False -> 1


  let rec hash = function
    | True -> 1
    | False -> 0
    | Split(h, _,_,_,_) -> h

  let compute_hash x p i n =
	(X.hash x) + 17 * (hash p) + 257 * (hash i) + 16637 * (hash n)

  let rec check = function
    | True | False -> ()
    | Split (h,x,p,i,n) ->
	assert (h = compute_hash x p i n);
	(match p with Split (_,y,_,_,_) -> assert (X.compare x y < 0) | _ -> ());
	(match i with Split (_,y,_,_,_) -> assert (X.compare x y < 0) | _ -> ());
	(match n with Split (_,y,_,_,_) -> assert (X.compare x y < 0) | _ -> ());
	X.check x; check p; check i; check n

  let atom x =
    let h = X.hash x + 17 in (* partial evaluation of compute_hash... *)
    Split (h, x,True,False,False)


  let is_empty t = (t == False)

  let rec iter f = function
    | Split (_, x, p,i,n) -> f x; iter f p; iter f i; iter f n
    | _ -> ()

  let rec dump ppf = function
    | False -> Format.fprintf ppf "⊥"
    | True -> Format.fprintf ppf "⊤"
    | Split (_,x, p,i,n) ->
      Format.fprintf ppf "@[@[%a@][@[<hov>%a,@\n%a,@\n%a@]]@]"
	X.dump x dump p dump i dump n

  let rec print f ppf = function
    | True -> Format.fprintf ppf "Any"
    | False -> Format.fprintf ppf "Empty"
    | Split (_, x, p,i, n) ->
	let flag = ref false in
	let b () = if !flag then Format.fprintf ppf " | " else flag := true in
	(match p with
	   | True -> b(); Format.fprintf ppf "%a" f x
	   | False -> ()
	   | _ -> b (); Format.fprintf ppf "%a & @[(%a)@]" f x (print f) p );
	(match i with
	   | True -> assert false;
	   | False -> ()
	   | _ -> b(); print f ppf i);
	(match n with
	   | True -> b (); Format.fprintf ppf "@[~%a@]" f x
	   | False -> ()
	   | _ -> b (); Format.fprintf ppf "@[~%a@] & @[(%a)@]" f x (print f) n)

  let print a f = function
    | True -> [ fun ppf -> Format.fprintf ppf "%s" a ]
    | False -> []
    | c -> [ fun ppf -> print f ppf c ]


  let rec get_aux rev accu pos neg = function
    | True ->
      let x =
        if rev then (List.rev pos, List.rev neg)
        else (pos,neg)
      in x :: accu
    | False -> accu
    | Split (_,x, p,i,n) ->
	(*OPT: can avoid creating this list cell when pos or neg =False *)
	let accu = get_aux rev accu (x::pos) neg p in
	let accu = get_aux rev accu pos (x::neg) n in
	let accu = get_aux rev accu pos neg i in
	accu

  let get x = get_aux false [] [] [] x

  let rec get' accu pos neg = function
    | True -> (pos,neg) :: accu
    | False -> accu
    | Split (_,x,p,i,n) ->
	let accu = get' accu (x::pos) neg p in
	let rec aux l = function
	  | Split (_,x,False,i,n') when equal n n' ->
	      aux (x :: l) i
	  | i ->
(*	      if (List.length l > 1) then (print_int (List.length l); flush stdout); *)
	      let accu = get' accu pos (l :: neg) n in
	      get' accu pos neg i
	in
	aux [x] i

  let get' x = get' [] [] [] x

  let compute ~empty ~full ~cup ~cap ~diff ~atom b =
    let rec aux = function
      | True -> full
      | False -> empty
      | Split(_,x, p,i,n) ->
          let x1 = atom x in
          let p = cap x1 (aux p)
          and i = aux i
          and n = diff (aux n) x1 in
          cup (cup p i) n
    in
    aux b

(* Invariant: correct hash value *)

  let split0 x pos ign neg =
    Split (compute_hash x pos ign neg, x, pos, ign, neg)

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  let empty = empty
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  let full = True

(* Invariants:
     Split (x, pos,ign,neg) ==>  (ign <> True), (pos <> neg)
*)

  let rec has_true = function
    | [] -> false
    | True :: _ -> true
    | _ :: l -> has_true l

  let rec has_same a = function
    | [] -> false
    | b :: l -> (equal a b) || (has_same a l)

  module type LeafOpts =
    sig
      val split0 : elem -> t -> t -> t ->t
      val merge_leaves : elem -> elem -> bool
      val cup : elem -> elem -> t
      val cap : elem -> elem -> t
      val diff : elem -> elem -> t
    end


  let make_ops (module LO : LeafOpts) =

    let rec split x p i n =
      if i == True then True
      else if equal p n then p ++ i
    else let p = simplify p [i] and n = simplify n [i] in
    if equal p n then p ++ i
    else
      LO.split0 x p i n

  and simplify a l =
    match a with
      | False -> False
      | True -> if has_true l then False else True
      | Split (_,x,p,i,n) ->
	  if (has_true l) || (has_same a l) then False
	  else s_aux2 a x p i n [] [] [] l
  and s_aux2 a x p i n ap ai an = function
    | [] ->
	let p = simplify p ap
	and n = simplify n an
	and i = simplify i ai in
	if equal p n then p ++ i else split0 x p i n
    | b :: l -> s_aux3 a x p i n ap ai an l b
  and s_aux3 a x p i n ap ai an l = function
    | False -> s_aux2 a x p i n ap ai an l
    | True -> assert false
    | Split (_,x2,p2,i2,n2) as b ->
	if equal a b then False
	else let c = X.compare x2 x in
	if c < 0 then s_aux3 a x p i n ap ai an l i2
	else if c > 0 then s_aux2 a x p i n (b :: ap) (b :: ai) (b :: an) l
	else s_aux2 a x p i n (p2 :: i2 :: ap) (i2 :: ai) (n2 :: i2 :: an) l

  and ( ++ ) a b = if a == b then a
  else match (a,b) with
    | True, _ | _, True -> True
    | False, a | a, False -> a
    | Split (_,x1, True,False,False),
      Split (_,x2, True,False,False) when LO.merge_leaves x1 x2 ->
      LO.cup x1 x2
    | Split (_,x1, p1,i1,n1), Split (_,x2, p2,i2,n2) ->
	let c = X.compare x1 x2 in
	if c = 0 then split x1 (p1 ++ p2) (i1 ++ i2) (n1 ++ n2)
	else if c < 0 then split x1 p1 (i1 ++ b) n1
	else split x2 p2 (i2 ++ a) n2

    (* seems better not to make ++ and this split mutually recursive;
   is the invariant still inforced ? *)
    in
    let rec ( ** ) a b =
      if a == b then a else
	match (a,b) with
	| True, a | a, True -> a
	| False, _ | _, False -> False
	| Split (_,x1, True,False,False),
	  Split (_,x2, True,False,False) when LO.merge_leaves x1 x2 ->
	   LO.cap x1 x2
	| Split (_,x1, p1,i1,n1), Split (_,x2, p2,i2,n2) ->
	   let c = X.compare x1 x2 in
	   if c = 0 then
	     split x1
		   (p1 ** (p2 ++ i2) ++ (p2 ** i1))
		   (i1 ** i2)
		   (n1 ** (n2 ++ i2) ++ (n2 ** i1))
	   else if c < 0 then split x1 (p1 ** b) (i1 ** b) (n1 ** b)
	   else split x2 (p2 ** a) (i2 ** a) (n2 ** a)
    in
    let rec neg = function
      | True -> False
      | False -> True
      | Split (_,x, p,i,False) -> split x False (neg (i ++ p)) (neg i)
      | Split (_,x, False,i,n) -> split x (neg i) (neg (i ++ n)) False
      | Split (_,x, p,False,n) -> split x (neg p) (neg (p ++ n)) (neg n)
      | Split (_,x, p,i,n) -> split x (neg (i ++ p)) False (neg (i ++ n))
    in
    let rec ( // ) a b =
      (*    if equal a b then False  *)
      if a == b then False
      else match (a,b) with
	   | False,_ | _, True -> False
	   | a, False -> a
	   | True, b -> neg b
	   | Split (_,x1, True,False,False),
	     Split (_,x2, True,False,False) when LO.merge_leaves x1 x2 ->
	      LO.diff x1 x2
	   | Split (_,x1, p1,i1,n1), Split (_,x2, p2,i2,n2) ->
	      let c = X.compare x1 x2 in
	      if c = 0 then
		if (i2 == False) && (n2 == False) then
		  split x1 (p1 // p2) (i1 // p2) (n1 ++ i1)
		else
		  split x1 ((p1++i1) // (p2++i2)) False ((n1++i1) // (n2++i2))
	      else if c < 0 then
		split x1 (p1 // b) (i1 // b) (n1 // b)
	      else
		split x2 (a // (i2 ++ p2)) False (a // (i2 ++ n2))
    in
    let rec trivially_disjoint a b =
      if a == b then a == False
      else match (a,b) with
	   | True, a | a, True -> a == False
	   | False, _ | _, False -> true
	   | Split (_,x1, p1,i1,n1), Split (_,x2, p2,i2,n2) ->
	      let c = X.compare x1 x2 in
	      if c = 0 then
		(* try expanding -> p1 p2; p1 i2; i1 p2; i1 i2 ... *)
		trivially_disjoint  (p1 ++ i1) (p2 ++ i2) &&
		  trivially_disjoint (n1 ++ i1) (n2 ++ i2)
	    else if c < 0 then
		trivially_disjoint p1 b &&
		  trivially_disjoint i1 b &&
		    trivially_disjoint n1 b
	      else
		trivially_disjoint p2 a &&
		  trivially_disjoint i2 a &&
		    trivially_disjoint n2 a
    in
    ( ++ ), ( ** ), ( // ),trivially_disjoint

  module SimpleOpts : LeafOpts = struct
      let split0 = split0
      let cup _ _ = assert false
      let cap _ _ = assert false
      let diff _ _ = assert false
      let merge_leaves _ _ = false
    end

  let cup, cap, diff, trivially_disjoint = make_ops (module SimpleOpts)

end

module type V =
sig

  module Atom : S

  include S with type elem = Atom.t Var.var_or_atom
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	     and type t = Atom.t Var.var_or_atom bdd
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  val var : Var.t -> t

  (** returns the union of all leaves in the BDD *)

  val leafconj: t -> Atom.t
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  val get_kind : t -> (Var.t list * Var.t list * Atom.t) list
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  val is_empty : t -> bool
  val extract : t -> [ `Empty | `Full | `Split of (elem * t * t * t) ]

end

module MakeVar (T : S) =
struct
  module Atom = T
  module X = Var.Make(Atom)
  include Make(X)

  let var v =
    let compute_hash x p i n =
        (Var.hash x) + 17 * (hash p) + 257 * (hash i) + 16637 * (hash n)
    in
    let a = atom (`Atm T.full) in
    let h = compute_hash v a False False in
    (Split (h,`Var v, a, False, False) :> t )

  let get x = get_aux true [] [] [] x

  let leafconj x =
    let rec aux accu = function
      | True -> accu
      | False -> accu
      | Split (_,`Atm x, True,False,False) -> T.cup x accu
      | Split (_,`Atm x, _,_,_) -> assert false
      | Split (_,`Var x, p,i,n) ->
        let accu = aux accu p in
        let accu = aux accu n in
        let accu = aux accu i in
        accu
    in
    (aux T.empty x)


  let split0 a p i n =
    match a, p, i, n with
      `Atm x, True, False, False when T.is_empty x -> False
    | `Atm _, True, False, False
    | `Var _, _, _, _ -> split0 a p i n
    | `Atm _, _, _, _ -> assert false

  let full = split0 (`Atm T.full) True False False

  module VarOpts : LeafOpts = struct
      let split0 = split0
      let cup a b =
	match a, b with
	  `Atm x1, `Atm x2 ->
	  split0 (`Atm (T.cup x1 x2)) True False False

	| _ -> assert false
      let cap a b =
	match a, b with
	  `Atm x1, `Atm x2 ->
	  split0 (`Atm (T.cap x1 x2)) True False False

	| _ -> assert false

      let diff a b =
	match a, b with
	  `Atm x1, `Atm x2 ->
	  split0 (`Atm (T.diff x1 x2)) True False False
	| _ -> assert false

      let merge_leaves a b =
	match a, b with
	  `Atm _, `Atm _ -> true
	| _ -> false
    end

  let cup, cap, diff, trivially_disjoint = make_ops (module VarOpts)

  let extract =
    function
    | False -> `Empty
    | True -> `Full
    | Split (_,x,p,i,n) -> `Split (x,p,i,n)

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  (* todo optimize *)
  let get_kind t =
    let rec split_vars l acc =
      match l with
	`Var v :: r -> split_vars r (v :: acc)
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      | [ `Atm a ] -> List.rev acc, a
      | [] -> List.rev acc, Atom.full
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      | _ -> assert false
    in
    List.map (fun (pos, neg) ->
      let pos, atm = split_vars pos [] in
      let neg = List.map (function `Var v -> v | _ -> assert false) neg in
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      (pos, neg, atm)) (get t)
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end