(* 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 = Rename + AllocBase +
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*)
record 'a state_d =
state +
dummy :: 'a (*new variables*)
(*Array indexing is translated to list indexing as A[n] == A!(n-1). *)
constdefs
(** Release some tokens **)
rel_act :: "('a state_d * 'a state_d) 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 :: "('a state_d * 'a state_d) set"
"tok_act == {(s,s'). s'=s | s' = s (|tok := Suc (tok s mod NbT) |)}"
ask_act :: "('a state_d * 'a state_d) set"
"ask_act == {(s,s'). s'=s |
(s' = s (|ask := ask s @ [tok s]|))}"
Client :: 'a state_d program
"Client ==
mk_program ({s. tok s : atMost NbT &
giv s = [] & ask s = [] & rel s = []},
{rel_act, tok_act, ask_act},
UN G: preserves rel Int preserves ask Int preserves tok.
Acts G)"
(*Maybe want a special theory section to declare such maps*)
non_dummy :: 'a state_d => state
"non_dummy s == (|giv = giv s, ask = ask s, rel = rel s, tok = tok s|)"
(*Renaming map to put a Client into the standard form*)
client_map :: "'a state_d => state*'a"
"client_map == funPair non_dummy dummy"
end