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type 'a obj = { id : int; mutable v : 'a }
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type 'a t =
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| True
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| False
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| Split of 'a obj * 'a t * 'a t * 'a t
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let rec equal a b =
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(a == b) ||
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match (a,b) with
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| Split (x1, p1,i1,n1), Split (x2, p2,i2,n2) ->
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(x1.id = x2.id) && (equal p1 p2) & (equal i1 i2) &&
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(equal n1 n2)
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| _ -> false
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let rec compare a b =
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if (a == b) then 0
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else match (a,b) with
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| Split (x1, p1,i1,n1), Split (x2, p2,i2,n2) ->
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if x1.id < x2.id then -1
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else if x1.id > x2.id then 1
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else let c = compare p1 p2 in if c <> 0 then c
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else let c = compare i1 i2 in if c <> 0 then c
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else compare n1 n2
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| True,_ -> -1
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| _, True -> 1
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| False,_ -> -1
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| _,False -> 1
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let rec hash = function
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| True -> 1
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| False -> 2
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| Split (x, p,i,n) ->
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x.id + 17 * (hash p) + 257 * (hash i) + 16637 * (hash n)
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let rec iter f = function
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| Split (x, p,i,n) -> f x.v; iter f p; iter f i; iter f n
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| _ -> ()
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(* TODO: precompute hash value for Split node to have fast equality... *)
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(*
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let rec print f ppf = function
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| True -> Format.fprintf ppf "True"
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| False -> Format.fprintf ppf "False"
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| Split (x, p,i,n) ->
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Format.fprintf ppf "%a(@[%a,%a,%a@])"
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f x.v (print f) p (print f) i (print f) n
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*)
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let rec print f ppf = function
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| True -> Format.fprintf ppf "Any"
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| False -> Format.fprintf ppf "Empty"
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| Split (x, p,i, n) ->
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(* Format.fprintf ppf "{%i}" x.id; *)
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let flag = ref false in
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let b () = if !flag then Format.fprintf ppf " | " else flag := true in
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(match p with
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| True -> b(); Format.fprintf ppf "%a" f x.v
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| False -> ()
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| _ -> b (); Format.fprintf ppf "%a & @[(%a)@]" f x.v (print f) p );
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(match i with
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| True -> assert false;
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| False -> ()
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| _ -> b(); print f ppf i);
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(match n with
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| True -> b (); Format.fprintf ppf "@[~%a@]" f x.v
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| False -> ()
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| _ -> b (); Format.fprintf ppf "@[~%a@] & @[(%a)@]" f x.v (print f) n)
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let rec dump ppf = function
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| True -> Format.fprintf ppf "True"
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| False -> Format.fprintf ppf "False"
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| Split (x, p,i,n) ->
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Format.fprintf ppf "%i(@[%a,%a,%a@])"
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x.id dump p dump i dump n
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let rec dnf accu pos neg = function
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| True -> (pos,neg) :: accu
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| False -> accu
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| Split (x, p,i,n) ->
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let accu = dnf accu (x.v::pos) neg p in
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let accu = dnf accu pos (x.v::neg) n in
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let accu = dnf accu pos neg i in
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accu
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let dnf x = dnf [] [] [] x
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let compute ~empty ~any ~cup ~cap ~diff ~atom b =
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let rec aux = function
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| True -> any
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| False -> empty
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| Split(x, p,i,n) ->
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let p = cap (atom x.v) (aux p)
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and i = aux i
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and n = diff (aux p) (atom x.v) in
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cup (cup p i) n
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in
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aux b
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(* Invariants:
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Split (x, pos,ign,neg) ==> (ign <> True);
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(pos <> False or neg <> False)
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Other meaningful invariant that could be enforced:
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- pos <> neg
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- no ``subsumption'' --> DONE (cf below)
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*)
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let split x pos ign neg =
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if ign = True then True
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else if (pos = False) && (neg = False) then ign
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else Split (x, pos, ign, neg)
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let ( !! ) x = Split (x, True, False, False)
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let empty = False
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let any = True
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let rec simplify a l =
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(* Format.fprintf Format.std_formatter "simplify %a <=" dump a;
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List.iter (fun b -> Format.fprintf Format.std_formatter " %a" dump b) l;
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Format.fprintf Format.std_formatter "@\n";
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*)
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if (a = False) then False else simpl_aux1 a [] l
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and simpl_aux1 a accu = function
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| [] ->
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if accu = [] then a else
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(match a with
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| True -> True
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| False -> assert false
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| Split (x,p,i,n) -> simpl_aux2 x p i n [] [] [] accu)
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| False :: l -> simpl_aux1 a accu l
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| True :: l -> False
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| b :: l -> if a == b then False else simpl_aux1 a (b::accu) l
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and simpl_aux2 x p i n ap ai an = function
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| [] -> split x (simplify p ap) (simplify i ai) (simplify n an)
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| (Split (x2,p2,i2,n2) as b) :: l ->
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if x2.id < x.id then
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simpl_aux3 x p i n ap ai an l i2
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else if x.id < x2.id then
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simpl_aux2 x p i n (b :: ap) (b :: ai) (b :: an) l
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else
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simpl_aux2 x p i n (p2 :: i2 :: ap) (i2 :: ai) (n2 :: i2 :: an) l
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| _ -> assert false
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and simpl_aux3 x p i n ap ai an l = function
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| False -> simpl_aux2 x p i n ap ai an l
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| True -> assert false
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| Split (x2,p2,i2,n2) as b ->
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if x2.id < x.id then
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simpl_aux3 x p i n ap ai an l i2
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else if x.id < x2.id then
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simpl_aux2 x p i n (b :: ap) (b :: ai) (b :: an) l
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else
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simpl_aux2 x p i n (p2 :: i2 :: ap) (i2 :: ai) (n2 :: i2 :: an) l
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let split x p i n =
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split x (simplify p [i]) i (simplify n [i])
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let rec ( ++ ) a b =
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if a == b then a
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else match (a,b) with
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| True, _ | _, True -> True
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| False, a | a, False -> a
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| Split (x1, p1,i1,n1), Split (x2, p2,i2,n2) ->
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if x1.id = x2.id then
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split x1 (p1 ++ p2) (i1 ++ i2) (n1 ++ n2)
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else if x1.id < x2.id then
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split x1 p1 (i1 ++ b) n1
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else
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split x2 p2 (i2 ++ a) n2
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(* TODO: optimize the cup with 3 arguments ? *)
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let rec ( ** ) a b =
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if a == b then a
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else match (a,b) with
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| True, a | a, True -> a
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| False, _ | _, False -> False
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| Split (x1, p1,i1,n1), Split (x2, p2,i2,n2) ->
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if x1.id = x2.id then
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split x1
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((p1 ** p2) ++ (p1 ** i2) ++ (p2 ** i1))
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(i1 ** i2)
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((n1 ** n2) ++ (n1 ** i2) ++ (n2 ** i1))
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else if x1.id < x2.id then
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split x1 (p1 ** b) (i1 ** b) (n1 ** b)
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else
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split x2 (p2 ** a) (i2 ** a) (n2 ** a)
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let rec ( // ) a b =
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if a == b then False
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else match (a,b) with
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| False,_ | _, True -> False
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| a, False -> a
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| True, Split (x2, p2,i2,n2) ->
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let i = True // i2 in
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split x2 (i // p2) False (i // n2)
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| Split (x1, p1,i1,n1), Split (x2, p2,i2,n2) ->
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if x1.id = x2.id then
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let i = i1 // i2 in
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split x1
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((p1 // p2 // i2) ++ (i // p2))
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False
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((n1 // n2 // i2) ++ (i // n2))
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else if x1.id < x2.id then
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split x1 (p1 // b) (i1 // b) (n1 // b)
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else
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let i = a // i2 in
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split x2 (i // p2) False (i // n2)
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