val update_pointed_to_value_maintains_variable_among_gvars
      (v: var_id_t)
      (p: Armada.Pointer.t)
      (actor: tid_t)
      (writer_pc: pc_t)
      (writer_expression_number: nat)
      (bypassing_write_buffer: bool)
      (new_value: object_value_t)
      (s: Armada.State.t)
    : Lemma (requires variable_among_gvars s.mem v)
      (ensures
        (match
            update_pointed_to_value p
              actor
              writer_pc
              writer_expression_number
              bypassing_write_buffer
              new_value
              s
          with
          | ComputationImpossible | ComputationUndefined -> True
          | ComputationProduces s' -> variable_among_gvars s'.mem v))
val update_pointed_to_value_maintains_variable_among_gvars
      (v: var_id_t)
      (p: Armada.Pointer.t)
      (actor: tid_t)
      (writer_pc: pc_t)
      (writer_expression_number: nat)
      (bypassing_write_buffer: bool)
      (new_value: object_value_t)
      (s: Armada.State.t)
    : Lemma (requires variable_among_gvars s.mem v)
      (ensures
        (match
            update_pointed_to_value p
              actor
              writer_pc
              writer_expression_number
              bypassing_write_buffer
              new_value
              s
          with
          | ComputationImpossible | ComputationUndefined -> True
          | ComputationProduces s' -> variable_among_gvars s'.mem v))
let update_pointed_to_value_maintains_variable_among_gvars
  (v: var_id_t)
  (p: Armada.Pointer.t)
  (actor: tid_t)
  (writer_pc: pc_t)
  (writer_expression_number: nat)
  (bypassing_write_buffer: bool)
  (new_value: object_value_t)
  (s: Armada.State.t)
  : Lemma (requires variable_among_gvars s.mem v)
          (ensures  (match update_pointed_to_value p actor writer_pc writer_expression_number bypassing_write_buffer
                             new_value s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> variable_among_gvars s'.mem v)) =
  update_pointer_maintains_variable_among_gvars v p actor writer_pc writer_expression_number bypassing_write_buffer
    new_value s.mem
module Strategies.GlobalVars.Permanent

open Armada.Action
open Armada.Base
open Armada.Computation
open Armada.Expression
open Armada.Init
open Armada.Memory
open Armada.Pointer
open Armada.Program
open Armada.State
open Armada.Statement
open Armada.Thread
open Armada.Transition
open Armada.Type
open FStar.Sequence.Base
open FStar.Tactics.V2
open Spec.List
open Spec.Map
open Spec.Ubool
open Strategies.ArmadaStatement
open Util.List
open Util.Tactics

let variable_among_gvars (mem: Armada.Memory.t) (v: var_id_t) : GTot bool =
  let root_id = RootIdGlobal v in
  let root = mem root_id in
  RootGlobal? root

let all_variables_among_gvars (mem: Armada.Memory.t) (vs: list var_id_t) : GTot bool =
  for_all_ghost (variable_among_gvars mem) vs

let rec update_pointer_directly_maintains_variable_among_gvars
  (v: var_id_t)
  (p: Armada.Pointer.t)
  (new_storage: valid_object_storage_t)
  (mem: Armada.Memory.t)
  : Lemma (requires variable_among_gvars mem v)
          (ensures  (match update_pointer_directly p new_storage mem with
                     | ComputationProduces mem' -> variable_among_gvars mem' v
                     | _ -> True)) =
  match update_pointer_directly p new_storage mem with
  | ComputationImpossible | ComputationUndefined -> ()
  | ComputationProduces mem' ->
      (match p with
       | PointerField struct_ptr field_id ->
           let parent = ComputationProduces?.result (dereference_computation struct_ptr mem) in
           (match parent with
            | ObjectStorageStruct fields ->
                let new_parent = update_storage_child parent field_id new_storage in
                update_pointer_directly_maintains_variable_among_gvars v struct_ptr new_parent mem)
       | PointerIndex array_ptr idx ->
           let parent = ComputationProduces?.result (dereference_computation array_ptr mem) in
           (match parent with
            | ObjectStorageArray element_td elements ->
                let new_parent = update_storage_child parent idx new_storage in
                update_pointer_directly_maintains_variable_among_gvars v array_ptr new_parent mem)
       | PointerRoot root_id -> ()
       | _ -> ())

#push-options "--z3rlimit 10"

let update_pointer_maintains_variable_among_gvars
  (v: var_id_t)
  (p: Armada.Pointer.t)
  (actor: tid_t)
  (writer_pc: pc_t)
  (writer_expression_number: nat)
  (bypassing_write_buffer: bool)
  (new_value: object_value_t)
  (mem: Armada.Memory.t)
  : Lemma (requires variable_among_gvars mem v)
          (ensures  (match update_pointer p actor writer_pc writer_expression_number bypassing_write_buffer
                             new_value mem with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces (optional_write_message, mem') -> variable_among_gvars mem' v)) =
  match p with
  | PointerUninitialized -> ()
  | PointerNull -> ()
  | PointerRoot root_id -> ()
  | PointerField struct_ptr field_id ->
      (match dereference_computation struct_ptr mem with
       | ComputationImpossible | ComputationUndefined -> ()
       | ComputationProduces parent ->
           (match parent with
            | ObjectStorageStruct fields ->
                if field_id >= length fields then
                  ()
                else
                  let field = index fields field_id in
                  if   not (object_storage_valid field)
                     || neqb (object_storage_to_td field) (object_value_to_td new_value) then
                    ()
                  else
                    (match update_storage p actor writer_pc writer_expression_number
                             bypassing_write_buffer field new_value with
                     | ComputationImpossible | ComputationUndefined -> ()
                     | ComputationProduces (write_message, new_field) ->
                         if (not (can_update_storage_child parent field_id new_field)) then
                           ()
                         else
                           let new_parent = update_storage_child parent field_id new_field in
                           update_pointer_directly_maintains_variable_among_gvars v struct_ptr new_parent mem)
            | _ -> ()))
  | PointerIndex array_ptr idx ->
      (match dereference_computation array_ptr mem with
       | ComputationImpossible | ComputationUndefined -> ()
       | ComputationProduces parent ->
           (match parent with
            | ObjectStorageArray element_td elements ->
                if idx < 0 || idx >= length elements then
                  ()
                else
                  let element = index elements idx in
                  if not (object_storage_valid element) then
                    ()
                  else
                    (match update_storage p actor writer_pc writer_expression_number
                             bypassing_write_buffer element new_value with
                     | ComputationImpossible | ComputationUndefined -> ()
                     | ComputationProduces (write_message, new_element) ->
                         if not (can_update_storage_child parent idx new_element) then
                           ()
                         else
                           let new_parent = update_storage_child parent idx new_element in
                           update_pointer_directly_maintains_variable_among_gvars v array_ptr new_parent mem)
            | _ -> ()))

#pop-options
/
Util.Tactics.fst.checked Util.List.fst.checked Strategies.ArmadaStatement.fst.checked Spec.Ubool.fst.checked Spec.Map.fst.checked Spec.List.fst.checked prims.fst.checked FStar.Tactics.V2.fst.checked FStar.Sequence.Base.fsti.checked FStar.Pervasives.Native.fst.checked FStar.Pervasives.fsti.checked FStar.Classical.Sugar.fsti.checked Armada.Type.fst.checked Armada.Transition.fst.checked Armada.Thread.fst.checked Armada.Step.fst.checked Armada.Statement.fst.checked Armada.State.fst.checked Armada.Program.fst.checked Armada.Pointer.fst.checked Armada.Memory.fst.checked Armada.Init.fst.checked Armada.Expression.fst.checked Armada.Computation.fst.checked Armada.Base.fst.checked Armada.Action.fst.checked
Strategies.GlobalVars.Permanent.fst

    v: Armada.Base.var_id_t ->
    p: Armada.Pointer.t ->
    actor: Armada.Base.tid_t ->
    writer_pc: Armada.Base.pc_t ->
    writer_expression_number: Prims.nat ->
    bypassing_write_buffer: Prims.bool ->
    new_value: Armada.Type.object_value_t ->
    s: Armada.State.t
  -> FStar.Pervasives.Lemma
      (requires Strategies.GlobalVars.Permanent.variable_among_gvars (Mkt?.mem s) v)
      (ensures
        ((match
              Armada.Expression.update_pointed_to_value p
                actor
                writer_pc
                writer_expression_number
                bypassing_write_buffer
                new_value
                s
            with
            | Armada.Computation.ComputationImpossible #_ -> Prims.l_True
            | Armada.Computation.ComputationUndefined #_ -> Prims.l_True
            | Armada.Computation.ComputationProduces #_ s' ->
              Strategies.GlobalVars.Permanent.variable_among_gvars (Mkt?.mem s') v)
          <:
          Type0))
Armada.Base.var_id_t Armada.Pointer.t Armada.Base.tid_t Armada.Base.pc_t Prims.nat Prims.bool Armada.Type.object_value_t Armada.State.t Strategies.GlobalVars.Permanent.update_pointer_maintains_variable_among_gvars Armada.State.__proj__Mkt__item__mem Prims.unit Prims.b2t Strategies.GlobalVars.Permanent.variable_among_gvars Prims.squash Armada.Expression.update_pointed_to_value Prims.l_True Prims.Nil FStar.Pervasives.pattern
let update_pointed_to_value_maintains_variable_among_gvars
      (v: var_id_t)
      (p: Armada.Pointer.t)
      (actor: tid_t)
      (writer_pc: pc_t)
      (writer_expression_number: nat)
      (bypassing_write_buffer: bool)
      (new_value: object_value_t)
      (s: Armada.State.t)
    : Lemma (requires variable_among_gvars s.mem v)
      (ensures
        (match
            update_pointed_to_value p
              actor
              writer_pc
              writer_expression_number
              bypassing_write_buffer
              new_value
              s
          with
          | ComputationImpossible | ComputationUndefined -> True
          | ComputationProduces s' -> variable_among_gvars s'.mem v)) =
  
update_pointer_maintains_variable_among_gvars v
  p
  actor
  writer_pc
  writer_expression_number
  bypassing_write_buffer
  new_value
  s.mem