Theory ProcedureInterface (Isabelle2005: October 2005)

# Theory ProcedureInterface

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theory ProcedureInterface
imports TLA RPCMemoryParams
uses [ProcedureInterface.ML]
begin

    (*
        File:        ProcedureInterface.thy
        ID:          $Id: ProcedureInterface.thy,v 1.6 2005/09/07 18:22:42 wenzelm Exp $
        Author:      Stephan Merz
        Copyright:   1997 University of Munich

       Theory Name: ProcedureInterface
       Logic Image: TLA

       Procedure interface for RPC-Memory components.
    *)

    theory ProcedureInterface
    imports TLA RPCMemoryParams
    begin

    typedecl
      (* type of channels with argument type 'a and return type 'r.
         we model a channel as an array of variables (of type chan)
         rather than a single array-valued variable because the
         notation gets a little simpler.
      *)
      ('a,'r) chan
    types
      ('a,'r) channel =" (PrIds => ('a,'r) chan) stfun"

    consts
      (* data-level functions *)
      cbit          :: "('a,'r) chan => bit"
      rbit          :: "('a,'r) chan => bit"
      arg           :: "('a,'r) chan => 'a"
      res           :: "('a,'r) chan => 'r"

      (* state functions *)
      caller        :: "('a,'r) channel => (PrIds => (bit * 'a)) stfun"
      rtrner        :: "('a,'r) channel => (PrIds => (bit * 'r)) stfun"

      (* state predicates *)
      Calling   :: "('a,'r) channel => PrIds => stpred"

      (* actions *)
      ACall      :: "('a,'r) channel => PrIds => 'a stfun => action"
      AReturn    :: "('a,'r) channel => PrIds => 'r stfun => action"

      (* temporal formulas *)
      PLegalCaller      :: "('a,'r) channel => PrIds => temporal"
      LegalCaller       :: "('a,'r) channel => temporal"
      PLegalReturner    :: "('a,'r) channel => PrIds => temporal"
      LegalReturner     :: "('a,'r) channel => temporal"

      (* slice through array-valued state function *)
      slice        :: "('a => 'b) stfun => 'a => 'b stfun"

    syntax
      "_slice"    :: "[lift, 'a] => lift"      ("(_!_)" [70,70] 70)

      "_Call"     :: "['a, 'b, lift] => lift"    ("(Call _ _ _)" [90,90,90] 90)
      "_Return"   :: "['a, 'b, lift] => lift"    ("(Return _ _ _)" [90,90,90] 90)

    translations
      "_slice"  ==  "slice"

      "_Call"   ==  "ACall"
      "_Return" ==  "AReturn"

    defs
      slice_def:     "(PRED (x!i)) s == x s i"

      caller_def:    "caller ch   == %s p. (cbit (ch s p), arg (ch s p))"
      rtrner_def:    "rtrner ch   == %s p. (rbit (ch s p), res (ch s p))"

      Calling_def:   "Calling ch p  == PRED cbit< ch!p > ~= rbit< ch!p >"
      Call_def:      "(ACT Call ch p v)   == ACT  ~ $Calling ch p
                                         & (cbit<ch!p>$ ~= $rbit<ch!p>)
                                         & (arg<ch!p>$ = $v)"
      Return_def:    "(ACT Return ch p v) == ACT  $Calling ch p
                                         & (rbit<ch!p>$ = $cbit<ch!p>)
                                         & (res<ch!p>$ = $v)"
      PLegalCaller_def:      "PLegalCaller ch p == TEMP
                                 Init(~ Calling ch p)
                                 & [][ ? a. Call ch p a ]_((caller ch)!p)"
      LegalCaller_def:       "LegalCaller ch == TEMP (! p. PLegalCaller ch p)"
      PLegalReturner_def:    "PLegalReturner ch p == TEMP
                                    [][ ? v. Return ch p v ]_((rtrner ch)!p)"
      LegalReturner_def:     "LegalReturner ch == TEMP (! p. PLegalReturner ch p)"

    ML {* use_legacy_bindings (the_context ()) *}

    end

theorem Call_changed:

      |- Call ch p v --> <Call ch p v>_(caller ch!p)

theorem Return_changed:

      |- Return ch p v --> <Return ch p v>_(rtrner ch!p)