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 2013-01-30 19:09:01 CET by Kim Nguyen>
22 include Sigs.FINITECOFINITE
24 module type HConsBuilder =
25 functor (H : Sigs.AUX.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
37 Finite (s1), Finite (s2)
38 | CoFinite (s1), CoFinite (s2) -> E.equal s1 s2
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 = function
52 | { node = Finite s } when E.is_empty s -> true
56 | { node = CoFinite s } when E.is_empty s -> true
59 let is_finite t = match t.node with
60 | Finite _ -> true | _ -> false
62 let kind t = match t.node with
66 let mem x t = match t.node with
67 | Finite s -> E.mem x s
68 | CoFinite s -> not (E.mem x s)
70 let singleton x = finite (E.singleton x)
72 let add e t = match t.node with
73 | Finite s -> finite (E.add e s)
74 | CoFinite s -> cofinite (E.remove e s)
76 let remove e t = match t.node with
77 | Finite s -> finite (E.remove e s)
78 | CoFinite s -> cofinite (E.add e s)
80 let union s t = match s.node, t.node with
81 | Finite s, Finite t -> finite (E.union s t)
82 | CoFinite s, CoFinite t -> cofinite ( E.inter s t)
83 | Finite s, CoFinite t -> cofinite (E.diff t s)
84 | CoFinite s, Finite t-> cofinite (E.diff s t)
86 let inter s t = match s.node, t.node with
87 | Finite s, Finite t -> finite (E.inter s t)
88 | CoFinite s, CoFinite t -> cofinite (E.union s t)
89 | Finite s, CoFinite t -> finite (E.diff s t)
90 | CoFinite s, Finite t-> finite (E.diff t s)
92 let diff s t = match s.node, t.node with
93 | Finite s, Finite t -> finite (E.diff s t)
94 | Finite s, CoFinite t -> finite(E.inter s t)
95 | CoFinite s, Finite t -> cofinite(E.union t s)
96 | CoFinite s, CoFinite t -> finite (E.diff t s)
98 let complement t = match t.node with
99 | Finite s -> cofinite s
100 | CoFinite s -> finite s
102 let compare s t = match s.node, t.node with
103 | Finite s , Finite t -> E.compare s t
104 | CoFinite s , CoFinite t -> E.compare t s
105 | Finite _, CoFinite _ -> -1
106 | CoFinite _, Finite _ -> 1
108 let subset s t = match s.node, t.node with
109 | Finite s , Finite t -> E.subset s t
110 | CoFinite s , CoFinite t -> E.subset t s
111 | Finite s, CoFinite t -> E.is_empty (E.inter s t)
112 | CoFinite _, Finite _ -> false
114 (* given a list l of type t list,
115 returns two sets (f,c) where :
116 - f is the union of all the finite sets of l
117 - c is the union of all the cofinite sets of l
118 - f and c are disjoint
119 Invariant : cup f c = List.fold_left cup empty l
120 We treat the CoFinite part explicitely :
125 let rec next_finite_cofinite facc cacc = function
126 | [] -> finite facc, cofinite (E.diff cacc facc)
127 | { node = Finite s } ::r ->
128 next_finite_cofinite (E.union s facc) cacc r
129 | { node = CoFinite _ } ::r when E.is_empty cacc ->
130 next_finite_cofinite facc cacc r
131 | { node = CoFinite s } ::r ->
132 next_finite_cofinite facc (E.inter cacc s) r
134 let rec first_cofinite facc = function
136 | { node = Finite s } :: r-> first_cofinite (E.union s facc) r
137 | { node = CoFinite s } :: r -> next_finite_cofinite facc s r
139 first_cofinite E.empty l
141 let exn = Sigs.FINITECOFINITE.InfiniteSet
143 let fold f t a = match t.node with
144 | Finite s -> E.fold f s a
145 | CoFinite _ -> raise exn
147 let iter f t = match t.node with
148 | Finite t -> E.iter f t
149 | CoFinite _ -> raise exn
151 let for_all f t = match t.node with
152 | Finite s -> E.for_all f s
153 | CoFinite _ -> raise exn
155 let exists f t = match t.node with
156 | Finite s -> E.exists f s
157 | CoFinite _ -> raise exn
159 let filter f t = match t.node with
160 | Finite s -> finite (E.filter f s)
161 | CoFinite _ -> raise exn
163 let partition f t = match t.node with
164 | Finite s -> let a,b = E.partition f s in finite a,finite b
165 | CoFinite _ -> raise exn
167 let cardinal t = match t.node with
168 | Finite s -> E.cardinal s
169 | CoFinite _ -> raise exn
171 let elements t = match t.node with
172 | Finite s -> E.elements s
173 | CoFinite _ -> raise exn
176 finite (List.fold_left (fun x a -> E.add a x ) E.empty l)
178 let choose t = match t.node with
179 Finite s -> E.choose s
182 let is_singleton t = match t.node with
183 | Finite s -> E.is_singleton s
186 let intersect s t = match s.node, t.node with
187 | Finite s, Finite t -> E.intersect s t
188 | CoFinite s, Finite t -> not (E.subset t s)
189 | Finite s, CoFinite t -> not (E.subset s t)
190 | CoFinite s, CoFinite t -> true
192 let split x s = match s.node with
194 let s1, b, s2 = E.split x s in
195 finite s1, b, finite s2
199 let min_elt s = match s.node with
200 | Finite s -> E.min_elt s
203 let max_elt s = match s.node with
204 | Finite s -> E.min_elt s
217 let inj_positive t = finite t
218 let inj_negative t = cofinite t
221 module Make = Builder(Hcons.Make)
222 module Weak = Builder(Hcons.Weak)