(* Title: HOL/UNITY/Client.thy
ID: $Id$
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1998 University of Cambridge
Distributed Resource Management System: the Client
*)
Client = Guar +
consts
Max :: nat (*Maximum number of tokens*)
types
tokbag = nat (*tokbags could be multisets...or any ordered type?*)
record state =
giv :: tokbag list (*input history: tokens granted*)
ask :: tokbag list (*output history: tokens requested*)
rel :: tokbag list (*output history: tokens released*)
tok :: tokbag (*current token request*)
(*Array indexing is translated to list indexing as A[n] == A!(n-1). *)
constdefs
(** Release some tokens **)
rel_act :: "(state*state) set"
"rel_act == {(s,s').
EX nrel. nrel = size (rel s) &
s' = s (| rel := rel s @ [giv s!nrel] |) &
nrel < size (giv s) &
ask s!nrel <= giv s!nrel}"
(** Choose a new token requirement **)
(** Including s'=s suppresses fairness, allowing the non-trivial part
of the action to be ignored **)
tok_act :: "(state*state) set"
"tok_act == {(s,s'). s'=s | (EX t: atMost Max. s' = s (|tok := t|))}"
ask_act :: "(state*state) set"
"ask_act == {(s,s'). s'=s |
(s' = s (|ask := ask s @ [tok s]|) &
size (ask s) = size (rel s))}"
Cli_prg :: state program
"Cli_prg == mk_program ({s. tok s : atMost Max &
giv s = [] &
ask s = [] &
rel s = []},
{rel_act, tok_act, ask_act})"
giv_meets_ask :: state set
"giv_meets_ask ==
{s. size (giv s) <= size (ask s) &
(ALL n: lessThan (size (giv s)). ask s!n <= giv s!n)}"
end