author | paulson |
Thu, 11 Nov 1999 10:25:17 +0100 | |
changeset 8005 | b64d86018785 |
parent 7947 | b999c1ab9327 |
child 8055 | bb15396278fb |
permissions | -rw-r--r-- |
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) |
|
7947 | 11 |
|
12 |
CAN PROBABLY DELETE the "Disjoint" predicate |
|
5252 | 13 |
*) |
14 |
||
15 |
Union = SubstAx + FP + |
|
16 |
||
17 |
constdefs |
|
5648 | 18 |
JOIN :: ['a set, 'a => 'b program] => 'b program |
6295
351b3c2b0d83
removed the infernal States, eqStates, compatible, etc.
paulson
parents:
6012
diff
changeset
|
19 |
"JOIN I F == mk_program (INT i:I. Init (F i), UN i:I. Acts (F i))" |
5252 | 20 |
|
5648 | 21 |
Join :: ['a program, 'a program] => 'a program (infixl 65) |
6295
351b3c2b0d83
removed the infernal States, eqStates, compatible, etc.
paulson
parents:
6012
diff
changeset
|
22 |
"F Join G == mk_program (Init F Int Init G, Acts F Un Acts G)" |
5252 | 23 |
|
6295
351b3c2b0d83
removed the infernal States, eqStates, compatible, etc.
paulson
parents:
6012
diff
changeset
|
24 |
SKIP :: 'a program |
351b3c2b0d83
removed the infernal States, eqStates, compatible, etc.
paulson
parents:
6012
diff
changeset
|
25 |
"SKIP == mk_program (UNIV, {})" |
5259 | 26 |
|
7878
43b03d412b82
working version with localTo[C] instead of localTo
paulson
parents:
7826
diff
changeset
|
27 |
Diff :: "['a set, 'a program, ('a * 'a)set set] => 'a program" |
43b03d412b82
working version with localTo[C] instead of localTo
paulson
parents:
7826
diff
changeset
|
28 |
"Diff C G acts == |
43b03d412b82
working version with localTo[C] instead of localTo
paulson
parents:
7826
diff
changeset
|
29 |
mk_program (Init G, (Restrict C `` Acts G) - (Restrict C `` acts))" |
5648 | 30 |
|
5804
8e0a4c4fd67b
Revising the Client proof as suggested by Michel Charpentier. New lemmas
paulson
parents:
5648
diff
changeset
|
31 |
(*The set of systems that regard "v" as local to F*) |
7878
43b03d412b82
working version with localTo[C] instead of localTo
paulson
parents:
7826
diff
changeset
|
32 |
LOCALTO :: ['a => 'b, 'a set, 'a program] => 'a program set |
43b03d412b82
working version with localTo[C] instead of localTo
paulson
parents:
7826
diff
changeset
|
33 |
("(_/ localTo[_]/ _)" [80,0,80] 80) |
43b03d412b82
working version with localTo[C] instead of localTo
paulson
parents:
7826
diff
changeset
|
34 |
"v localTo[C] F == {G. ALL z. Diff C G (Acts F) : stable {s. v s = z}}" |
43b03d412b82
working version with localTo[C] instead of localTo
paulson
parents:
7826
diff
changeset
|
35 |
|
43b03d412b82
working version with localTo[C] instead of localTo
paulson
parents:
7826
diff
changeset
|
36 |
(*The weak version of localTo, considering only G's reachable states*) |
43b03d412b82
working version with localTo[C] instead of localTo
paulson
parents:
7826
diff
changeset
|
37 |
LocalTo :: ['a => 'b, 'a program] => 'a program set (infixl 80) |
7915
c7fd7eb3b0ef
ALMOST working version: LocalTo results commented out
paulson
parents:
7878
diff
changeset
|
38 |
"v LocalTo F == {G. G : v localTo[reachable (F Join G)] F}" |
5804
8e0a4c4fd67b
Revising the Client proof as suggested by Michel Charpentier. New lemmas
paulson
parents:
5648
diff
changeset
|
39 |
|
7826
c6a8b73b6c2a
working shapshot with "projecting" and "extending"
paulson
parents:
7359
diff
changeset
|
40 |
(*Two programs with disjoint actions, except for identity actions. |
c6a8b73b6c2a
working shapshot with "projecting" and "extending"
paulson
parents:
7359
diff
changeset
|
41 |
It's a weak property but still useful.*) |
7878
43b03d412b82
working version with localTo[C] instead of localTo
paulson
parents:
7826
diff
changeset
|
42 |
Disjoint :: ['a set, 'a program, 'a program] => bool |
43b03d412b82
working version with localTo[C] instead of localTo
paulson
parents:
7826
diff
changeset
|
43 |
"Disjoint C F G == |
43b03d412b82
working version with localTo[C] instead of localTo
paulson
parents:
7826
diff
changeset
|
44 |
(Restrict C `` (Acts F - {Id})) Int (Restrict C `` (Acts G - {Id})) |
43b03d412b82
working version with localTo[C] instead of localTo
paulson
parents:
7826
diff
changeset
|
45 |
<= {}" |
5648 | 46 |
|
5313
1861a564d7e2
Constrains, Stable, Invariant...more of the substitution axiom, but Union
paulson
parents:
5259
diff
changeset
|
47 |
syntax |
7359 | 48 |
"@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
|
49 |
"@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
|
50 |
|
1861a564d7e2
Constrains, Stable, Invariant...more of the substitution axiom, but Union
paulson
parents:
5259
diff
changeset
|
51 |
translations |
1861a564d7e2
Constrains, Stable, Invariant...more of the substitution axiom, but Union
paulson
parents:
5259
diff
changeset
|
52 |
"JN x:A. B" == "JOIN A (%x. B)" |
7359 | 53 |
"JN x y. B" == "JN x. JN y. B" |
54 |
"JN x. B" == "JOIN UNIV (%x. B)" |
|
5313
1861a564d7e2
Constrains, Stable, Invariant...more of the substitution axiom, but Union
paulson
parents:
5259
diff
changeset
|
55 |
|
5252 | 56 |
end |