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--
*** empty log message ***
     1 (*  Title:      HOL/UNITY/Extend.thy
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1998  University of Cambridge
     5 
     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 *)
    10 
    11 Extend = Guar +
    12 
    13 constdefs
    14 
    15   (*MOVE to Relation.thy?*)
    16   Restrict :: "[ 'a set, ('a*'b) set] => ('a*'b) set"
    17     "Restrict A r == r Int (A <*> UNIV)"
    18 
    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*)
    22   
    23   extend_set :: "['a*'b => 'c, 'a set] => 'c set"
    24     "extend_set h A == h ` (A <*> UNIV)"
    25 
    26   project_set :: "['a*'b => 'c, 'c set] => 'a set"
    27     "project_set h C == {x. EX y. h(x,y) : C}"
    28 
    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))}"
    31 
    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}"
    34 
    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)"
    39 
    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})"
    47 
    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
    54 
    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}"
    61 
    62 end