1 (***********************************************************************)
5 (* Kim Nguyen, LRI UMR8623 *)
6 (* Université Paris-Sud & CNRS *)
8 (* Copyright 2010-2012 Université Paris-Sud and Centre National de la *)
9 (* Recherche Scientifique. All rights reserved. This file is *)
10 (* distributed under the terms of the GNU Lesser General Public *)
11 (* License, with the special exception on linking described in file *)
14 (***********************************************************************)
19 include Sigs.FiniteCofiniteSet
20 include Hcons.S with type t := t
23 module type HConsBuilder =
24 functor (H : Sigs.HashedType) -> Hcons.S with type data = H.t
26 module Builder (HCB : HConsBuilder) (E : Ptset.S) :
27 S with type elt = E.elt and type set = E.t =
30 type node = Finite of E.t | CoFinite of E.t
32 module Node = HCB(struct
36 Finite (s1), Finite (s2)
37 | CoFinite (s1), CoFinite (s2) -> E.equal s1 s2
41 | Finite s -> HASHINT2 (PRIME1, E.hash s)
42 | CoFinite s -> HASHINT2 (PRIME3, E.hash s)
45 let empty = make (Finite E.empty)
46 let any = make (CoFinite E.empty)
47 let finite x = make (Finite x)
48 let cofinite x = make (CoFinite x)
50 let is_empty = function
51 | { node = Finite s } when E.is_empty s -> true
55 | { node = CoFinite s } when E.is_empty s -> true
58 let is_finite t = match t.node with
59 | Finite _ -> true | _ -> false
61 let kind t = match t.node with
65 let mem x t = match t.node with
66 | Finite s -> E.mem x s
67 | CoFinite s -> not (E.mem x s)
69 let singleton x = finite (E.singleton x)
71 let add e t = match t.node with
72 | Finite s -> finite (E.add e s)
73 | CoFinite s -> cofinite (E.remove e s)
75 let remove e t = match t.node with
76 | Finite s -> finite (E.remove e s)
77 | CoFinite s -> cofinite (E.add e s)
79 let union s t = match s.node, t.node with
80 | Finite s, Finite t -> finite (E.union s t)
81 | CoFinite s, CoFinite t -> cofinite ( E.inter s t)
82 | Finite s, CoFinite t -> cofinite (E.diff t s)
83 | CoFinite s, Finite t-> cofinite (E.diff s t)
85 let inter s t = match s.node, t.node with
86 | Finite s, Finite t -> finite (E.inter s t)
87 | CoFinite s, CoFinite t -> cofinite (E.union s t)
88 | Finite s, CoFinite t -> finite (E.diff s t)
89 | CoFinite s, Finite t-> finite (E.diff t s)
91 let diff s t = match s.node, t.node with
92 | Finite s, Finite t -> finite (E.diff s t)
93 | Finite s, CoFinite t -> finite(E.inter s t)
94 | CoFinite s, Finite t -> cofinite(E.union t s)
95 | CoFinite s, CoFinite t -> finite (E.diff t s)
97 let complement t = match t.node with
98 | Finite s -> cofinite s
99 | CoFinite s -> finite s
101 let compare s t = match s.node, t.node with
102 | Finite s , Finite t -> E.compare s t
103 | CoFinite s , CoFinite t -> E.compare t s
104 | Finite _, CoFinite _ -> -1
105 | CoFinite _, Finite _ -> 1
107 let subset s t = match s.node, t.node with
108 | Finite s , Finite t -> E.subset s t
109 | CoFinite s , CoFinite t -> E.subset t s
110 | Finite s, CoFinite t -> E.is_empty (E.inter s t)
111 | CoFinite _, Finite _ -> false
113 (* given a list l of type t list,
114 returns two sets (f,c) where :
115 - f is the union of all the finite sets of l
116 - c is the union of all the cofinite sets of l
117 - f and c are disjoint
118 Invariant : cup f c = List.fold_left cup empty l
119 We treat the CoFinite part explicitely :
124 let rec next_finite_cofinite facc cacc = function
125 | [] -> finite facc, cofinite (E.diff cacc facc)
126 | { node = Finite s } ::r ->
127 next_finite_cofinite (E.union s facc) cacc r
128 | { node = CoFinite _ } ::r when E.is_empty cacc ->
129 next_finite_cofinite facc cacc r
130 | { node = CoFinite s } ::r ->
131 next_finite_cofinite facc (E.inter cacc s) r
133 let rec first_cofinite facc = function
135 | { node = Finite s } :: r-> first_cofinite (E.union s facc) r
136 | { node = CoFinite s } :: r -> next_finite_cofinite facc s r
138 first_cofinite E.empty l
140 let fold f t a = match t.node with
141 | Finite s -> E.fold f s a
142 | CoFinite _ -> raise Sigs.InfiniteSet
144 let iter f t = match t.node with
145 | Finite t -> E.iter f t
146 | CoFinite _ -> raise Sigs.InfiniteSet
148 let for_all f t = match t.node with
149 | Finite s -> E.for_all f s
150 | CoFinite _ -> raise Sigs.InfiniteSet
152 let exists f t = match t.node with
153 | Finite s -> E.exists f s
154 | CoFinite _ -> raise Sigs.InfiniteSet
156 let filter f t = match t.node with
157 | Finite s -> finite (E.filter f s)
158 | CoFinite _ -> raise Sigs.InfiniteSet
160 let partition f t = match t.node with
161 | Finite s -> let a,b = E.partition f s in finite a,finite b
162 | CoFinite _ -> raise Sigs.InfiniteSet
164 let cardinal t = match t.node with
165 | Finite s -> E.cardinal s
166 | CoFinite _ -> raise Sigs.InfiniteSet
168 let elements t = match t.node with
169 | Finite s -> E.elements s
170 | CoFinite _ -> raise Sigs.InfiniteSet
173 finite (List.fold_left (fun x a -> E.add a x ) E.empty l)
175 let choose t = match t.node with
176 Finite s -> E.choose s
177 | _ -> raise Sigs.InfiniteSet
179 let is_singleton t = match t.node with
180 | Finite s -> E.is_singleton s
183 let intersect s t = match s.node, t.node with
184 | Finite s, Finite t -> E.intersect s t
185 | CoFinite s, Finite t -> not (E.subset t s)
186 | Finite s, CoFinite t -> not (E.subset s t)
187 | CoFinite s, CoFinite t -> true
189 let split x s = match s.node with
191 let s1, b, s2 = E.split x s in
192 finite s1, b, finite s2
194 | _ -> raise Sigs.InfiniteSet
196 let min_elt s = match s.node with
197 | Finite s -> E.min_elt s
198 | _ -> raise Sigs.InfiniteSet
200 let max_elt s = match s.node with
201 | Finite s -> E.min_elt s
202 | _ -> raise Sigs.InfiniteSet
214 let inj_positive t = finite t
215 let inj_negative t = cofinite t
218 module Make = Builder(Hcons.Make)
219 module Weak = Builder(Hcons.Weak)