src/HOL/UNITY/Extend.thy
 author nipkow Tue Jan 09 15:32:27 2001 +0100 (2001-01-09) changeset 10834 a7897aebbffc parent 10064 1a77667b21ef child 13790 8d7e9fce8c50 permissions -rw-r--r--
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1 (*  Title:      HOL/UNITY/Extend.thy
2     ID:         \$Id\$
3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
4     Copyright   1998  University of Cambridge
6 Extending of state sets
7   function f (forget)    maps the extended state to the original state
8   function g (forgotten) maps the extended state to the "extending part"
9 *)
11 Extend = Guar +
13 constdefs
15   (*MOVE to Relation.thy?*)
16   Restrict :: "[ 'a set, ('a*'b) set] => ('a*'b) set"
17     "Restrict A r == r Int (A <*> UNIV)"
19   good_map :: "['a*'b => 'c] => bool"
20     "good_map h == surj h & (ALL x y. fst (inv h (h (x,y))) = x)"
21      (*Using the locale constant "f", this is  f (h (x,y))) = x*)
23   extend_set :: "['a*'b => 'c, 'a set] => 'c set"
24     "extend_set h A == h ` (A <*> UNIV)"
26   project_set :: "['a*'b => 'c, 'c set] => 'a set"
27     "project_set h C == {x. EX y. h(x,y) : C}"
29   extend_act :: "['a*'b => 'c, ('a*'a) set] => ('c*'c) set"
30     "extend_act h == %act. UN (s,s'): act. UN y. {(h(s,y), h(s',y))}"
32   project_act :: "['a*'b => 'c, ('c*'c) set] => ('a*'a) set"
33     "project_act h act == {(x,x'). EX y y'. (h(x,y), h(x',y')) : act}"
35   extend :: "['a*'b => 'c, 'a program] => 'c program"
36     "extend h F == mk_program (extend_set h (Init F),
37 			       extend_act h ` Acts F,
38 			       project_act h -` AllowedActs F)"
40   (*Argument C allows weak safety laws to be projected*)
41   project :: "['a*'b => 'c, 'c set, 'c program] => 'a program"
42     "project h C F ==
43        mk_program (project_set h (Init F),
44 		   project_act h ` Restrict C ` Acts F,
45 		   {act. Restrict (project_set h C) act :
46 		         project_act h ` Restrict C ` AllowedActs F})"
48 locale Extend =
49   fixes
50     f       :: 'c => 'a
51     g       :: 'c => 'b
52     h       :: "'a*'b => 'c"    (*isomorphism between 'a * 'b and 'c *)
53     slice   :: ['c set, 'b] => 'a set
55   assumes
56     good_h  "good_map h"
57   defines
58     f_def       "f z == fst (inv h z)"
59     g_def       "g z == snd (inv h z)"
60     slice_def   "slice Z y == {x. h(x,y) : Z}"
62 end