(* Title: HOL/UNITY/Counter
ID: $Id$
Author: Sidi O Ehmety, Cambridge University Computer Laboratory
Copyright 2001 University of Cambridge
A family of similar counters, version close to the original.
From Charpentier and Chandy,
Examples of Program Composition Illustrating the Use of Universal Properties
In J. Rolim (editor), Parallel and Distributed Processing,
Spriner LNCS 1586 (1999), pages 1215-1227.
*)
Counter = Comp +
(* Variables are names *)
datatype name = C | c nat
types state = name=>int
consts
sum :: "[nat,state]=>int"
sumj :: "[nat, nat, state]=>int"
primrec (* sum I s = sigma_{i<I}. s (c i) *)
"sum 0 s = #0"
"sum (Suc i) s = s (c i) + sum i s"
primrec
"sumj 0 i s = #0"
"sumj (Suc n) i s = (if n=i then sum n s else s (c n) + sumj n i s)"
types command = "(state*state)set"
constdefs
a :: "nat=>command"
"a i == {(s, s'). s'=s(c i:= s (c i) + #1, C:= s C + #1)}"
Component :: "nat => state program"
"Component i ==
mk_program({s. s C = #0 & s (c i) = #0}, {a i},
UN G: preserves (%s. s (c i)). Acts G)"
end