Theory MemoryParameters

Up to index of Isabelle/HOL/TLA/Memory

theory MemoryParameters
imports RPCMemoryParams
begin

(*
    File:        MemoryParameters.thy
    ID:          $Id: MemoryParameters.thy,v 1.6 2006/12/02 01:52:05 wenzelm Exp $
    Author:      Stephan Merz
    Copyright:   1997 University of Munich
*)

header {* RPC-Memory example: Memory parameters *}

theory MemoryParameters
imports RPCMemoryParams
begin

(* the memory operations *)
datatype memOp = read Locs | write Locs Vals

consts
  (* memory locations and contents *)
  MemLoc         :: "Locs set"
  MemVal         :: "Vals set"

  (* some particular values *)
  OK             :: "Vals"
  BadArg         :: "Vals"
  MemFailure     :: "Vals"
  NotAResult     :: "Vals"  (* defined here for simplicity *)

  (* the initial value stored in each memory cell *)
  InitVal        :: "Vals"

axioms
  (* basic assumptions about the above constants and predicates *)
  BadArgNoMemVal:    "BadArg ~: MemVal"
  MemFailNoMemVal:   "MemFailure ~: MemVal"
  InitValMemVal:     "InitVal : MemVal"
  NotAResultNotVal:  "NotAResult ~: MemVal"
  NotAResultNotOK:   "NotAResult ~= OK"
  NotAResultNotBA:   "NotAResult ~= BadArg"
  NotAResultNotMF:   "NotAResult ~= MemFailure"

lemmas [simp] =
  BadArgNoMemVal MemFailNoMemVal InitValMemVal NotAResultNotVal
  NotAResultNotOK NotAResultNotBA NotAResultNotMF
  NotAResultNotOK [symmetric] NotAResultNotBA [symmetric] NotAResultNotMF [symmetric]

lemma MemValNotAResultE: "[| x : MemVal; (x ~= NotAResult ==> P) |] ==> P"
  using NotAResultNotVal by blast

end

lemma

  BadArg  MemVal
  MemFailure  MemVal
  InitVal ∈ MemVal
  NotAResult  MemVal
  NotAResult  OK
  NotAResult  BadArg
  NotAResult  MemFailure
  OK  NotAResult
  BadArg  NotAResult
  MemFailure  NotAResult

lemma MemValNotAResultE:

  [| x ∈ MemVal; x  NotAResult ==> P |] ==> P