|
3807
|
1 |
(*
|
|
|
2 |
File: TLA/ex/inc/Inc.thy
|
|
|
3 |
Author: Stephan Merz
|
|
|
4 |
Copyright: 1997 University of Munich
|
|
|
5 |
|
|
|
6 |
Theory Name: Inc
|
|
|
7 |
Logic Image: TLA
|
|
|
8 |
|
|
|
9 |
Lamport's "increment" example.
|
|
|
10 |
*)
|
|
|
11 |
|
|
|
12 |
Inc = TLA + Nat + Pcount +
|
|
|
13 |
|
|
|
14 |
consts
|
|
|
15 |
(* program variables *)
|
|
|
16 |
x,y,sem :: "nat stfun"
|
|
|
17 |
pc1,pc2 :: "pcount stfun"
|
|
|
18 |
|
|
|
19 |
(* names of actions and predicates *)
|
|
|
20 |
M1,M2,N1,N2 :: "action"
|
|
|
21 |
alpha1,alpha2,beta1,beta2,gamma1,gamma2 :: "action"
|
|
|
22 |
InitPhi, InitPsi :: "action"
|
|
|
23 |
PsiInv,PsiInv1,PsiInv2,PsiInv3 :: "action"
|
|
|
24 |
|
|
|
25 |
(* temporal formulas *)
|
|
|
26 |
Phi, Psi :: "temporal"
|
|
|
27 |
|
|
|
28 |
rules
|
|
|
29 |
(* the "base" variables, required to compute enabledness predicates *)
|
|
|
30 |
Inc_base "base_var <x, y, sem, pc1, pc2>"
|
|
|
31 |
|
|
|
32 |
(* definitions for high-level program *)
|
|
|
33 |
InitPhi_def "InitPhi == ($x .= # 0) .& ($y .= # 0)"
|
|
|
34 |
M1_def "M1 == (x$ .= Suc[$x]) .& (y$ .= $y)"
|
|
|
35 |
M2_def "M2 == (y$ .= Suc[$y]) .& (x$ .= $x)"
|
|
|
36 |
Phi_def "Phi == Init(InitPhi) .& [][M1 .| M2]_<x,y> .& \
|
|
|
37 |
\ WF(M1)_<x,y> .& WF(M2)_<x,y>"
|
|
|
38 |
|
|
|
39 |
(* definitions for low-level program *)
|
|
|
40 |
InitPsi_def "InitPsi == ($pc1 .= #a) .& ($pc2 .= #a) .& \
|
|
|
41 |
\ ($x .= # 0) .& ($y .= # 0) .& ($sem .= Suc[# 0])"
|
|
|
42 |
alpha1_def "alpha1 == ($pc1 .= #a) .& (pc1$ .= #b) .& ($sem .= Suc[sem$]) .& \
|
|
|
43 |
\ unchanged(<x,y,pc2>)"
|
|
|
44 |
alpha2_def "alpha2 == ($pc2 .= #a) .& (pc2$ .= #b) .& ($sem .= Suc[sem$]) .& \
|
|
|
45 |
\ unchanged(<x,y,pc1>)"
|
|
|
46 |
beta1_def "beta1 == ($pc1 .= #b) .& (pc1$ .= #g) .& (x$ .= Suc[$x]) .& \
|
|
|
47 |
\ unchanged(<y,sem,pc2>)"
|
|
|
48 |
beta2_def "beta2 == ($pc2 .= #b) .& (pc2$ .= #g) .& (y$ .= Suc[$y]) .& \
|
|
|
49 |
\ unchanged(<x,sem,pc1>)"
|
|
|
50 |
gamma1_def "gamma1 == ($pc1 .= #g) .& (pc1$ .= #a) .& (sem$ .= Suc[$sem]) .& \
|
|
|
51 |
\ unchanged(<x,y,pc2>)"
|
|
|
52 |
gamma2_def "gamma2 == ($pc2 .= #g) .& (pc2$ .= #a) .& (sem$ .= Suc[$sem]) .& \
|
|
|
53 |
\ unchanged(<x,y,pc1>)"
|
|
|
54 |
N1_def "N1 == alpha1 .| beta1 .| gamma1"
|
|
|
55 |
N2_def "N2 == alpha2 .| beta2 .| gamma2"
|
|
|
56 |
Psi_def "Psi == Init(InitPsi) \
|
|
|
57 |
\ .& [][N1 .| N2]_<x,y,sem,pc1,pc2> \
|
|
|
58 |
\ .& SF(N1)_<x,y,sem,pc1,pc2> \
|
|
|
59 |
\ .& SF(N2)_<x,y,sem,pc1,pc2>"
|
|
|
60 |
|
|
|
61 |
PsiInv1_def "PsiInv1 == ($sem .= Suc[# 0]) .& ($pc1 .= #a) .& ($pc2 .= #a)"
|
|
|
62 |
PsiInv2_def "PsiInv2 == ($sem .= # 0) .& ($pc1 .= #a) .& ($pc2 .= #b .| $pc2 .= #g)"
|
|
|
63 |
PsiInv3_def "PsiInv3 == ($sem .= # 0) .& ($pc2 .= #a) .& ($pc1 .= #b .| $pc1 .= #g)"
|
|
|
64 |
PsiInv_def "PsiInv == PsiInv1 .| PsiInv2 .| PsiInv3"
|
|
|
65 |
|
|
|
66 |
end
|
|
|
67 |
|
|
|
68 |
ML
|