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Diffstat (limited to 'lib/ocaml_rts/linksem/src_lem_library/pset.ml')
| -rwxr-xr-x | lib/ocaml_rts/linksem/src_lem_library/pset.ml | 522 |
1 files changed, 0 insertions, 522 deletions
diff --git a/lib/ocaml_rts/linksem/src_lem_library/pset.ml b/lib/ocaml_rts/linksem/src_lem_library/pset.ml deleted file mode 100755 index 35335e88..00000000 --- a/lib/ocaml_rts/linksem/src_lem_library/pset.ml +++ /dev/null @@ -1,522 +0,0 @@ -(***********************************************************************) -(* *) -(* Objective Caml *) -(* *) -(* Xavier Leroy, projet Cristal, INRIA Rocquencourt *) -(* *) -(* Copyright 1996 Institut National de Recherche en Informatique et *) -(* en Automatique. All rights reserved. This file is distributed *) -(* under the terms of the GNU Library General Public License, with *) -(* the special exception on linking described in file ../LICENSE. *) -(* *) -(***********************************************************************) - -(* Modified by Scott Owens 2010-10-28 *) - -(* $Id: set.ml 6694 2004-11-25 00:06:06Z doligez $ *) - -(* Sets over ordered types *) - -type 'a rep = Empty | Node of 'a rep * 'a * 'a rep * int - -(* Sets are represented by balanced binary trees (the heights of the - children differ by at most 2 *) - -let height = function - Empty -> 0 - | Node(_, _, _, h) -> h - -(* Creates a new node with left son l, value v and right son r. - We must have all elements of l < v < all elements of r. - l and r must be balanced and | height l - height r | <= 2. - Inline expansion of height for better speed. *) - -let create l v r = - let hl = match l with Empty -> 0 | Node(_,_,_,h) -> h in - let hr = match r with Empty -> 0 | Node(_,_,_,h) -> h in - Node(l, v, r, (if hl >= hr then hl + 1 else hr + 1)) - -(* Same as create, but performs one step of rebalancing if necessary. - Assumes l and r balanced and | height l - height r | <= 3. - Inline expansion of create for better speed in the most frequent case - where no rebalancing is required. *) - -let bal l v r = - let hl = match l with Empty -> 0 | Node(_,_,_,h) -> h in - let hr = match r with Empty -> 0 | Node(_,_,_,h) -> h in - if hl > hr + 2 then begin - match l with - Empty -> invalid_arg "Set.bal" - | Node(ll, lv, lr, _) -> - if height ll >= height lr then - create ll lv (create lr v r) - else begin - match lr with - Empty -> invalid_arg "Set.bal" - | Node(lrl, lrv, lrr, _)-> - create (create ll lv lrl) lrv (create lrr v r) - end - end else if hr > hl + 2 then begin - match r with - Empty -> invalid_arg "Set.bal" - | Node(rl, rv, rr, _) -> - if height rr >= height rl then - create (create l v rl) rv rr - else begin - match rl with - Empty -> invalid_arg "Set.bal" - | Node(rll, rlv, rlr, _) -> - create (create l v rll) rlv (create rlr rv rr) - end - end else - Node(l, v, r, (if hl >= hr then hl + 1 else hr + 1)) - -(* Insertion of one element *) - -let rec add cmp x = function - Empty -> Node(Empty, x, Empty, 1) - | Node(l, v, r, _) as t -> - let c = cmp x v in - if c = 0 then t else - if c < 0 then bal (add cmp x l) v r else bal l v (add cmp x r) - -(* Same as create and bal, but no assumptions are made on the - relative heights of l and r. *) - -let rec join cmp l v r = - match (l, r) with - (Empty, _) -> add cmp v r - | (_, Empty) -> add cmp v l - | (Node(ll, lv, lr, lh), Node(rl, rv, rr, rh)) -> - if lh > rh + 2 then bal ll lv (join cmp lr v r) else - if rh > lh + 2 then bal (join cmp l v rl) rv rr else - create l v r - -(* Smallest and greatest element of a set *) - -let rec min_elt = function - Empty -> raise Not_found - | Node(Empty, v, r, _) -> v - | Node(l, v, r, _) -> min_elt l - -let rec max_elt = function - Empty -> raise Not_found - | Node(l, v, Empty, _) -> v - | Node(l, v, r, _) -> max_elt r - -(* Remove the smallest element of the given set *) - -let rec remove_min_elt = function - Empty -> invalid_arg "Set.remove_min_elt" - | Node(Empty, v, r, _) -> r - | Node(l, v, r, _) -> bal (remove_min_elt l) v r - -(* Merge two trees l and r into one. - All elements of l must precede the elements of r. - Assume | height l - height r | <= 2. *) - -let merge t1 t2 = - match (t1, t2) with - (Empty, t) -> t - | (t, Empty) -> t - | (_, _) -> bal t1 (min_elt t2) (remove_min_elt t2) - -(* Merge two trees l and r into one. - All elements of l must precede the elements of r. - No assumption on the heights of l and r. *) - -let concat cmp t1 t2 = - match (t1, t2) with - (Empty, t) -> t - | (t, Empty) -> t - | (_, _) -> join cmp t1 (min_elt t2) (remove_min_elt t2) - -(* Splitting. split x s returns a triple (l, present, r) where - - l is the set of elements of s that are < x - - r is the set of elements of s that are > x - - present is false if s contains no element equal to x, - or true if s contains an element equal to x. *) - -let rec split cmp x = function - Empty -> - (Empty, false, Empty) - | Node(l, v, r, _) -> - let c = cmp x v in - if c = 0 then (l, true, r) - else if c < 0 then - let (ll, pres, rl) = split cmp x l in (ll, pres, join cmp rl v r) - else - let (lr, pres, rr) = split cmp x r in (join cmp l v lr, pres, rr) - -(* Implementation of the set operations *) - -let empty = Empty - -let is_empty = function Empty -> true | _ -> false - -let rec mem cmp x = function - Empty -> false - | Node(l, v, r, _) -> - let c = cmp x v in - c = 0 || mem cmp x (if c < 0 then l else r) - -let singleton x = Node(Empty, x, Empty, 1) - -let rec remove cmp x = function - Empty -> Empty - | Node(l, v, r, _) -> - let c = cmp x v in - if c = 0 then merge l r else - if c < 0 then bal (remove cmp x l) v r else bal l v (remove cmp x r) - -let rec union cmp s1 s2 = - match (s1, s2) with - (Empty, t2) -> t2 - | (t1, Empty) -> t1 - | (Node(l1, v1, r1, h1), Node(l2, v2, r2, h2)) -> - if h1 >= h2 then - if h2 = 1 then add cmp v2 s1 else begin - let (l2, _, r2) = split cmp v1 s2 in - join cmp (union cmp l1 l2) v1 (union cmp r1 r2) - end - else - if h1 = 1 then add cmp v1 s2 else begin - let (l1, _, r1) = split cmp v2 s1 in - join cmp (union cmp l1 l2) v2 (union cmp r1 r2) - end - -let rec inter cmp s1 s2 = - match (s1, s2) with - (Empty, t2) -> Empty - | (t1, Empty) -> Empty - | (Node(l1, v1, r1, _), t2) -> - match split cmp v1 t2 with - (l2, false, r2) -> - concat cmp (inter cmp l1 l2) (inter cmp r1 r2) - | (l2, true, r2) -> - join cmp (inter cmp l1 l2) v1 (inter cmp r1 r2) - -let rec diff cmp s1 s2 = - match (s1, s2) with - (Empty, t2) -> Empty - | (t1, Empty) -> t1 - | (Node(l1, v1, r1, _), t2) -> - match split cmp v1 t2 with - (l2, false, r2) -> - join cmp (diff cmp l1 l2) v1 (diff cmp r1 r2) - | (l2, true, r2) -> - concat cmp (diff cmp l1 l2) (diff cmp r1 r2) - -type 'a enumeration = End | More of 'a * 'a rep * 'a enumeration - -let rec cons_enum s e = - match s with - Empty -> e - | Node(l, v, r, _) -> cons_enum l (More(v, r, e)) - -let rec compare_aux cmp e1 e2 = - match (e1, e2) with - (End, End) -> 0 - | (End, _) -> -1 - | (_, End) -> 1 - | (More(v1, r1, e1), More(v2, r2, e2)) -> - let c = cmp v1 v2 in - if c <> 0 - then c - else compare_aux cmp (cons_enum r1 e1) (cons_enum r2 e2) - -let compare cmp s1 s2 = - compare_aux cmp (cons_enum s1 End) (cons_enum s2 End) - -let equal cmp s1 s2 = - compare cmp s1 s2 = 0 - -let rec subset cmp s1 s2 = - match (s1, s2) with - Empty, _ -> - true - | _, Empty -> - false - | Node (l1, v1, r1, _), (Node (l2, v2, r2, _) as t2) -> - let c = cmp v1 v2 in - if c = 0 then - subset cmp l1 l2 && subset cmp r1 r2 - else if c < 0 then - subset cmp (Node (l1, v1, Empty, 0)) l2 && subset cmp r1 t2 - else - subset cmp (Node (Empty, v1, r1, 0)) r2 && subset cmp l1 t2 - -let rec iter f = function - Empty -> () - | Node(l, v, r, _) -> iter f l; f v; iter f r - -let rec fold f s accu = - match s with - Empty -> accu - | Node(l, v, r, _) -> fold f r (f v (fold f l accu)) - -let map cmp f s = fold (fun e s -> add cmp (f e) s) s empty - -let map_union cmp f s = fold (fun e s -> union cmp (f e) s) s empty - - -let rec for_all p = function - Empty -> true - | Node(l, v, r, _) -> p v && for_all p l && for_all p r - -let rec exists p = function - Empty -> false - | Node(l, v, r, _) -> p v || exists p l || exists p r - -let filter cmp p s = - let rec filt accu = function - | Empty -> accu - | Node(l, v, r, _) -> - filt (filt (if p v then add cmp v accu else accu) l) r in - filt Empty s - -let partition cmp p s = - let rec part (t, f as accu) = function - | Empty -> accu - | Node(l, v, r, _) -> - part (part (if p v then (add cmp v t, f) else (t, add cmp v f)) l) r in - part (Empty, Empty) s - -let rec cardinal = function - Empty -> 0 - | Node(l, v, r, _) -> cardinal l + 1 + cardinal r - -let rec elements_aux accu = function - Empty -> accu - | Node(l, v, r, _) -> elements_aux (v :: elements_aux accu r) l - -let elements s = - elements_aux [] s - -let choose = min_elt - -type 'a set = { cmp : 'a -> 'a -> int; s : 'a rep } - -let empty c = { cmp = c; s = Empty; } - -let is_empty s = is_empty s.s - -let mem x s = mem s.cmp x s.s - -let add x s = { s with s = add s.cmp x s.s } - -let singleton c x = { cmp = c; s = singleton x } - -let remove x s = { s with s = remove s.cmp x s.s } - -let union s1 s2 = { s1 with s = union s1.cmp s1.s s2.s } - -let map_union c f s1 = { cmp = c; s = map_union c (fun x -> (f x).s) s1.s} - -let inter s1 s2 = { s1 with s = inter s1.cmp s1.s s2.s } - -let diff s1 s2 = { s1 with s = diff s1.cmp s1.s s2.s } - -let compare_by cmp s1 s2 = compare cmp s1.s s2.s - -let compare s1 s2 = compare s1.cmp s1.s s2.s - -let equal s1 s2 = equal s1.cmp s1.s s2.s - -let subset s1 s2 = subset s1.cmp s1.s s2.s -let subset_proper s1 s2 = (subset s1 s2) && not (equal s1 s2) - -let iter f s = iter f s.s - -let fold f s a = fold f s.s a - -let map c f s = {cmp = c; s = map c f s.s} - -let for_all p s = for_all p s.s - -let exists p s = exists p s.s - -let filter p s = { s with s = filter s.cmp p s.s } - -let partition p s = - let (r1,r2) = partition s.cmp p s.s in - ({s with s = r1}, {s with s = r2}) - -let cardinal s = cardinal s.s - -let elements s = elements s.s - -let min_elt s = min_elt s.s - -let min_elt_opt s = try Some (min_elt s) with Not_found -> None - -let max_elt s = max_elt s.s - -let max_elt_opt s = try Some (max_elt s) with Not_found -> None - -let choose s = choose s.s - -let set_case s c_emp c_sing c_else = match s.s with - Empty -> c_emp - | Node(Empty, v, Empty, _) -> c_sing v - | _ -> c_else - -let split x s = - let (l,present,r) = split s.cmp x s.s in - ({ s with s = l }, present, { s with s = r }) - -let from_list c l = - List.fold_left (fun s x -> add x s) (empty c) l - -let comprehension1 cmp f p s = - fold (fun x s -> if p x then add (f x) s else s) s (empty cmp) - -let comprehension2 cmp f p s1 s2 = - fold - (fun x1 s -> - fold - (fun x2 s -> - if p x1 x2 then add (f x1 x2) s else s) - s2 - s) - s1 - (empty cmp) - -let comprehension3 cmp f p s1 s2 s3 = - fold - (fun x1 s -> - fold - (fun x2 s -> - fold - (fun x3 s -> - if p x1 x2 x3 then add (f x1 x2 x3) s else s) - s3 - s) - s2 - s) - s1 - (empty cmp) - -let comprehension4 cmp f p s1 s2 s3 s4 = - fold - (fun x1 s -> - fold - (fun x2 s -> - fold - (fun x3 s -> - fold - (fun x4 s -> - if p x1 x2 x3 x4 then add (f x1 x2 x3 x4) s else s) - s4 - s) - s3 - s) - s2 - s) - s1 - (empty cmp) - -let comprehension5 cmp f p s1 s2 s3 s4 s5 = - fold - (fun x1 s -> - fold - (fun x2 s -> - fold - (fun x3 s -> - fold - (fun x4 s -> - fold - (fun x5 s -> - if p x1 x2 x3 x4 x5 then add (f x1 x2 x3 x4 x5) s else s) - s5 - s) - s4 - s) - s3 - s) - s2 - s) - s1 - (empty cmp) - -let comprehension6 cmp f p s1 s2 s3 s4 s5 s6 = - fold - (fun x1 s -> - fold - (fun x2 s -> - fold - (fun x3 s -> - fold - (fun x4 s -> - fold - (fun x5 s -> - fold - (fun x6 s -> - if p x1 x2 x3 x4 x5 x6 then add (f x1 x2 x3 x4 x5 x6) s else s) - s6 - s) - s5 - s) - s4 - s) - s3 - s) - s2 - s) - s1 - (empty cmp) - -let comprehension7 cmp f p s1 s2 s3 s4 s5 s6 s7 = - fold - (fun x1 s -> - fold - (fun x2 s -> - fold - (fun x3 s -> - fold - (fun x4 s -> - fold - (fun x5 s -> - fold - (fun x6 s -> - fold - (fun x7 s -> - if p x1 x2 x3 x4 x5 x6 x7 then add (f x1 x2 x3 x4 x5 x6 x7) s else s) - s7 - s) - s6 - s) - s5 - s) - s4 - s) - s3 - s) - s2 - s) - s1 - (empty cmp) - -let bigunion c xss = - fold union xss (empty c) - -let sigma c xs ys = - fold (fun x xys -> fold (fun y xys -> add (x,y) xys) (ys x) xys) xs (empty c) - -let cross c xs ys = sigma c xs (fun _ -> ys) - -let rec lfp s f = - let s' = f s in - if subset s' s then - s - else - lfp (union s' s) f - -let tc c r = - let one_step r = fold (fun (x,y) xs -> fold (fun (y',z) xs -> - if c (y,y) (y',y') = 0 then add (x,z) xs else xs) r xs) r (empty c) in - lfp r one_step - - -let get_elem_compare s = s.cmp - |