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(**************************************************************************)
(* *)
(* This file is part of Frama-C. *)
(* *)
(* Copyright (C) 2007-2010 *)
(* CEA (Commissariat l'nergie atomique et aux nergies *)
(* alternatives) *)
(* INRIA (Institut National de Recherche en Informatique et en *)
(* Automatique) *)
(* *)
(* you can redistribute it and/or modify it under the terms of the GNU *)
(* Lesser General Public License as published by the Free Software *)
(* Foundation, version 2.1. *)
(* *)
(* It is distributed in the hope that it will be useful, *)
(* but WITHOUT ANY WARRANTY; without even the implied warranty of *)
(* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *)
(* GNU Lesser General Public License for more details. *)
(* *)
(* See the GNU Lesser General Public License version v2.1 *)
(* for more details (enclosed in the file licenses/LGPLv2.1). *)
(* *)
(**************************************************************************)
(* Decidable Equality *)
type 'a equality
logic is_equal : 'a equality,'a,'a-> prop
axiom is_equal_dec :
forall eq:'a equality. forall a,a':'a.
is_equal(eq,a,a') or (not (is_equal(eq,a,a')))
axiom is_equal_sym:
forall eq:'a equality. forall a,a':'a.
is_equal(eq,a,a') -> is_equal(eq,a',a)
axiom is_equal_trans :
forall eq:'a equality. forall a,b,c:'a.
is_equal(eq,a,b) ->
is_equal(eq,b,c) ->
is_equal(eq,a,c)
axiom is_equal_not_trans:
forall eq:'a equality. forall a,b,c:'a.
is_equal(eq,a,b) ->
not (is_equal(eq,b,c)) ->
not (is_equal(eq,a,c))
(* Map Definition *)
type ('a,'b) map
logic get: ('a,'b) map,'a -> 'b
logic set: ('a,'b) map,'a , 'b -> ('a,'b) map
axiom get_set_same :
forall m:('a,'b) map. forall a:'a. forall b:'b.
get(set(m,a,b),a) = b
axiom get_set_other :
forall m:('a,'b) map. forall a,a':'a. forall b:'b.
a<>a' -> get(set(m,a,b),a') = get(m,a')
axiom get_set_eq :
forall m:('a,'b) map. forall eq:'a equality. forall a,a':'a. forall b:'b.
is_equal(eq,a,a')->get(set(m,a,b),a) = b
axiom get_set_neq :
forall m:('a,'b) map. forall eq:'a equality. forall a,a':'a. forall b:'b.
not (is_equal(eq,a,a')) -> get(set(m,a,b),a') = get(m,a')
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