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 (***********************************************************************)
17 Time-stamp: <Last modified on 2013-03-05 01:50:21 CET by Kim Nguyen>
22 include FiniteCofinite_sig
24 module type HConsBuilder =
25 functor (H : Common_sig.HashedType) -> Hcons.S with type data = H.t
27 module Builder (HCB : HConsBuilder) (E : Ptset.S) :
28 S with type elt = E.elt and type set = E.t =
31 type node = Finite of E.t | CoFinite of E.t
33 module Node = HCB(struct
38 | CoFinite s1, CoFinite s2 -> E.equal s1 s2
39 | (Finite _| CoFinite _), _ -> false
42 | Finite s -> HASHINT2 (PRIME1, E.hash s)
43 | CoFinite s -> HASHINT2 (PRIME3, E.hash s)
46 let empty = make (Finite E.empty)
47 let any = make (CoFinite E.empty)
48 let finite x = make (Finite x)
49 let cofinite x = make (CoFinite x)
51 let is_empty t = match t.node with
52 | Finite s -> E.is_empty s
55 let is_any t = match t.node with
56 | CoFinite s -> E.is_empty s
59 let is_finite t = match t.node with
63 let kind t = match t.node with
65 | CoFinite _ -> `Cofinite
67 let mem x t = match t.node with
68 | Finite s -> E.mem x s
69 | CoFinite s -> not (E.mem x s)
71 let singleton x = finite (E.singleton x)
73 let add e t = match t.node with
74 | Finite s -> finite (E.add e s)
75 | CoFinite s -> cofinite (E.remove e s)
77 let remove e t = match t.node with
78 | Finite s -> finite (E.remove e s)
79 | CoFinite s -> cofinite (E.add e s)
81 let union s t = match s.node, t.node with
82 | Finite s, Finite t -> finite (E.union s t)
83 | CoFinite s, CoFinite t -> cofinite ( E.inter s t)
84 | Finite s, CoFinite t -> cofinite (E.diff t s)
85 | CoFinite s, Finite t-> cofinite (E.diff s t)
87 let inter s t = match s.node, t.node with
88 | Finite s, Finite t -> finite (E.inter s t)
89 | CoFinite s, CoFinite t -> cofinite (E.union s t)
90 | Finite s, CoFinite t -> finite (E.diff s t)
91 | CoFinite s, Finite t-> finite (E.diff t s)
93 let diff s t = match s.node, t.node with
94 | Finite s, Finite t -> finite (E.diff s t)
95 | Finite s, CoFinite t -> finite(E.inter s t)
96 | CoFinite s, Finite t -> cofinite(E.union t s)
97 | CoFinite s, CoFinite t -> finite (E.diff t s)
99 let complement t = match t.node with
100 | Finite s -> cofinite s
101 | CoFinite s -> finite s
103 let compare s t = match s.node, t.node with
104 | Finite s , Finite t -> E.compare s t
105 | CoFinite s , CoFinite t -> E.compare t s
106 | Finite _, CoFinite _ -> -1
107 | CoFinite _, Finite _ -> 1
109 let subset s t = match s.node, t.node with
110 | Finite s , Finite t -> E.subset s t
111 | CoFinite s , CoFinite t -> E.subset t s
112 | Finite s, CoFinite t -> E.is_empty (E.inter s t)
113 | CoFinite _, Finite _ -> false
115 (* given a list l of type t list,
116 returns two sets (f,c) where :
117 - f is the union of all the finite sets of l
118 - c is the union of all the cofinite sets of l
119 - f and c are disjoint
120 Invariant : cup f c = List.fold_left cup empty l
121 We treat the CoFinite part explicitely :
126 let rec next_finite_cofinite facc cacc = function
127 | [] -> finite facc, cofinite (E.diff cacc facc)
128 | { node = Finite s; _ } ::r ->
129 next_finite_cofinite (E.union s facc) cacc r
130 | { node = CoFinite _ ; _ } ::r when E.is_empty cacc ->
131 next_finite_cofinite facc cacc r
132 | { node = CoFinite s; _ } ::r ->
133 next_finite_cofinite facc (E.inter cacc s) r
135 let rec first_cofinite facc = function
137 | { node = Finite s ; _ } :: r-> first_cofinite (E.union s facc) r
138 | { node = CoFinite s ; _ } :: r -> next_finite_cofinite facc s r
140 first_cofinite E.empty l
142 let exn = FiniteCofinite_sig.InfiniteSet
144 let fold f t a = match t.node with
145 | Finite s -> E.fold f s a
146 | CoFinite _ -> raise exn
148 let iter f t = match t.node with
149 | Finite t -> E.iter f t
150 | CoFinite _ -> raise exn
152 let for_all f t = match t.node with
153 | Finite s -> E.for_all f s
154 | CoFinite _ -> raise exn
156 let exists f t = match t.node with
157 | Finite s -> E.exists f s
158 | CoFinite _ -> raise exn
160 let filter f t = match t.node with
161 | Finite s -> finite (E.filter f s)
162 | CoFinite _ -> raise exn
164 let partition f t = match t.node with
165 | Finite s -> let a,b = E.partition f s in finite a,finite b
166 | CoFinite _ -> raise exn
168 let cardinal t = match t.node with
169 | Finite s -> E.cardinal s
170 | CoFinite _ -> raise exn
172 let elements t = match t.node with
173 | Finite s -> E.elements s
174 | CoFinite _ -> raise exn
177 finite (List.fold_left (fun x a -> E.add a x ) E.empty l)
179 let choose t = match t.node with
180 Finite s -> E.choose s
181 | CoFinite _ -> raise exn
183 let is_singleton t = match t.node with
184 | Finite s -> E.is_singleton s
185 | CoFinite _ -> false
187 let intersect s t = match s.node, t.node with
188 | Finite s, Finite t -> E.intersect s t
189 | CoFinite s, Finite t -> not (E.subset t s)
190 | Finite s, CoFinite t -> not (E.subset s t)
191 | CoFinite _ , CoFinite _ -> true
193 let split x s = match s.node with
195 let s1, b, s2 = E.split x s in
196 finite s1, b, finite s2
198 | CoFinite _ -> raise exn
200 let min_elt s = match s.node with
201 | Finite s -> E.min_elt s
202 | CoFinite _ -> raise exn
204 let max_elt s = match s.node with
205 | Finite s -> E.min_elt s
206 | CoFinite _ -> raise exn
208 let positive t = match t.node with
210 | CoFinite _ -> E.empty
212 let negative t = match t.node with
214 | Finite _ -> E.empty
216 let inj_positive t = finite t
217 let inj_negative t = cofinite t
220 module Make = Builder(Hcons.Make)
221 module Weak = Builder(Hcons.Weak)