(* Title: HOL/UNITY/Token
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1998 University of Cambridge
The Token Ring.
From Misra, "A Logic for Concurrent Programming" (1994), sections 5.2 and 13.2.
*)
Token = WFair +
(*process states*)
datatype pstate = Hungry | Eating | Thinking
record state =
token :: nat
proc :: nat => pstate
constdefs
HasTok :: nat => state set
"HasTok i == {s. token s = i}"
H :: nat => state set
"H i == {s. proc s i = Hungry}"
E :: nat => state set
"E i == {s. proc s i = Eating}"
T :: nat => state set
"T i == {s. proc s i = Thinking}"
locale Token =
fixes
N :: nat (*number of nodes in the ring*)
F :: state program
nodeOrder :: "nat => (nat*nat)set"
next :: nat => nat
assumes
N_positive "0<N"
TR2 "F : constrains (T i) (T i Un H i)"
TR3 "F : constrains (H i) (H i Un E i)"
TR4 "F : constrains (H i - HasTok i) (H i)"
TR5 "F : constrains (HasTok i) (HasTok i Un -(E i))"
TR6 "F : leadsTo (H i Int HasTok i) (E i)"
TR7 "F : leadsTo (HasTok i) (HasTok (next i))"
defines
nodeOrder_def
"nodeOrder j == (inv_image less_than (%i. ((j+N)-i) mod N)) Int
(lessThan N Times lessThan N)"
next_def
"next i == (Suc i) mod N"
end