author  paulson 
Mon, 11 Oct 1999 10:53:39 +0200  
changeset 7826  c6a8b73b6c2a 
parent 7359  98a2afab3f86 
child 7878  43b03d412b82 
permissions  rwrr 
5252  1 
(* Title: HOL/UNITY/Union.thy 
2 
ID: $Id$ 

3 
Author: Lawrence C Paulson, Cambridge University Computer Laboratory 

4 
Copyright 1998 University of Cambridge 

5 

6 
Unions of programs 

7 

5804
8e0a4c4fd67b
Revising the Client proof as suggested by Michel Charpentier. New lemmas
paulson
parents:
5648
diff
changeset

8 
Partly from Misra's Chapter 5: Asynchronous Compositions of Programs 
7359  9 

10 
Do we need a Meet operator? (Aka Intersection) 

5252  11 
*) 
12 

13 
Union = SubstAx + FP + 

14 

15 
constdefs 

5648  16 
JOIN :: ['a set, 'a => 'b program] => 'b program 
6295
351b3c2b0d83
removed the infernal States, eqStates, compatible, etc.
paulson
parents:
6012
diff
changeset

17 
"JOIN I F == mk_program (INT i:I. Init (F i), UN i:I. Acts (F i))" 
5252  18 

5648  19 
Join :: ['a program, 'a program] => 'a program (infixl 65) 
6295
351b3c2b0d83
removed the infernal States, eqStates, compatible, etc.
paulson
parents:
6012
diff
changeset

20 
"F Join G == mk_program (Init F Int Init G, Acts F Un Acts G)" 
5252  21 

6295
351b3c2b0d83
removed the infernal States, eqStates, compatible, etc.
paulson
parents:
6012
diff
changeset

22 
SKIP :: 'a program 
351b3c2b0d83
removed the infernal States, eqStates, compatible, etc.
paulson
parents:
6012
diff
changeset

23 
"SKIP == mk_program (UNIV, {})" 
5259  24 

5648  25 
Diff :: "['a program, ('a * 'a)set set] => 'a program" 
6295
351b3c2b0d83
removed the infernal States, eqStates, compatible, etc.
paulson
parents:
6012
diff
changeset

26 
"Diff F acts == mk_program (Init F, Acts F  acts)" 
5648  27 

5804
8e0a4c4fd67b
Revising the Client proof as suggested by Michel Charpentier. New lemmas
paulson
parents:
5648
diff
changeset

28 
(*The set of systems that regard "v" as local to F*) 
5648  29 
localTo :: ['a => 'b, 'a program] => 'a program set (infixl 80) 
5804
8e0a4c4fd67b
Revising the Client proof as suggested by Michel Charpentier. New lemmas
paulson
parents:
5648
diff
changeset

30 
"v localTo F == {G. ALL z. Diff G (Acts F) : stable {s. v s = z}}" 
8e0a4c4fd67b
Revising the Client proof as suggested by Michel Charpentier. New lemmas
paulson
parents:
5648
diff
changeset

31 

7826
c6a8b73b6c2a
working shapshot with "projecting" and "extending"
paulson
parents:
7359
diff
changeset

32 
(*Two programs with disjoint actions, except for identity actions. 
c6a8b73b6c2a
working shapshot with "projecting" and "extending"
paulson
parents:
7359
diff
changeset

33 
It's a weak property but still useful.*) 
5804
8e0a4c4fd67b
Revising the Client proof as suggested by Michel Charpentier. New lemmas
paulson
parents:
5648
diff
changeset

34 
Disjoint :: ['a program, 'a program] => bool 
6295
351b3c2b0d83
removed the infernal States, eqStates, compatible, etc.
paulson
parents:
6012
diff
changeset

35 
"Disjoint F G == Acts F Int Acts G <= {Id}" 
5648  36 

5313
1861a564d7e2
Constrains, Stable, Invariant...more of the substitution axiom, but Union
paulson
parents:
5259
diff
changeset

37 
syntax 
7359  38 
"@JOIN1" :: [pttrns, 'b set] => 'b set ("(3JN _./ _)" 10) 
5313
1861a564d7e2
Constrains, Stable, Invariant...more of the substitution axiom, but Union
paulson
parents:
5259
diff
changeset

39 
"@JOIN" :: [pttrn, 'a set, 'b set] => 'b set ("(3JN _:_./ _)" 10) 
1861a564d7e2
Constrains, Stable, Invariant...more of the substitution axiom, but Union
paulson
parents:
5259
diff
changeset

40 

1861a564d7e2
Constrains, Stable, Invariant...more of the substitution axiom, but Union
paulson
parents:
5259
diff
changeset

41 
translations 
1861a564d7e2
Constrains, Stable, Invariant...more of the substitution axiom, but Union
paulson
parents:
5259
diff
changeset

42 
"JN x:A. B" == "JOIN A (%x. B)" 
7359  43 
"JN x y. B" == "JN x. JN y. B" 
44 
"JN x. B" == "JOIN UNIV (%x. B)" 

5313
1861a564d7e2
Constrains, Stable, Invariant...more of the substitution axiom, but Union
paulson
parents:
5259
diff
changeset

45 

5252  46 
end 