val push_stack_variables_maintains_variable_among_gvars
      (v: var_id_t)
      (actor: tid_t)
      (writer_pc: pc_t)
      (writer_expression_number: nat)
      (method_id: method_id_t)
      (frame_uniq: root_id_uniquifier_t)
      (initializers: list initializer_t)
      (s: Armada.State.t)
    : Lemma (requires variable_among_gvars s.mem v)
      (ensures
        (match
            push_stack_variables actor
              writer_pc
              writer_expression_number
              method_id
              frame_uniq
              initializers
              s
          with
          | ComputationImpossible | ComputationUndefined -> True
          | ComputationProduces s' -> variable_among_gvars s'.mem v))
      (decreases initializers)
val push_stack_variables_maintains_variable_among_gvars
      (v: var_id_t)
      (actor: tid_t)
      (writer_pc: pc_t)
      (writer_expression_number: nat)
      (method_id: method_id_t)
      (frame_uniq: root_id_uniquifier_t)
      (initializers: list initializer_t)
      (s: Armada.State.t)
    : Lemma (requires variable_among_gvars s.mem v)
      (ensures
        (match
            push_stack_variables actor
              writer_pc
              writer_expression_number
              method_id
              frame_uniq
              initializers
              s
          with
          | ComputationImpossible | ComputationUndefined -> True
          | ComputationProduces s' -> variable_among_gvars s'.mem v))
      (decreases initializers)
let rec push_stack_variables_maintains_variable_among_gvars
  (v: var_id_t)
  (actor: tid_t)
  (writer_pc: pc_t)
  (writer_expression_number: nat)
  (method_id: method_id_t)
  (frame_uniq: root_id_uniquifier_t)
  (initializers: list initializer_t)
  (s: Armada.State.t)
  : Lemma (requires variable_among_gvars s.mem v)
          (ensures  (match push_stack_variables actor writer_pc writer_expression_number method_id
                             frame_uniq initializers s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> variable_among_gvars s'.mem v))
          (decreases initializers) =
  match initializers with
  | [] -> ()
  | first_initializer :: remaining_initializers ->
      push_stack_variable_maintains_variable_among_gvars v actor writer_pc writer_expression_number method_id frame_uniq
        first_initializer s;
      (match push_stack_variable actor writer_pc writer_expression_number method_id frame_uniq first_initializer s with
       | ComputationImpossible | ComputationUndefined -> ()
       | ComputationProduces s' ->
           push_stack_variables_maintains_variable_among_gvars v actor writer_pc (writer_expression_number + 1)
             method_id frame_uniq remaining_initializers s')
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

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

let update_expression_maintains_variable_among_gvars
  (v: var_id_t)
  (exp: expression_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_expression exp 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 s' = update_expression exp actor writer_pc writer_expression_number bypassing_write_buffer
             new_value s in
  if   not (expression_valid exp)
     || not (object_value_valid new_value)
     || neqb (object_value_to_td new_value) (expression_to_td exp) then
    ()
  else (
    match lvalue_computation exp actor s with
    | ComputationImpossible | ComputationUndefined -> ()
    | ComputationProduces p ->
        update_pointed_to_value_maintains_variable_among_gvars v p actor writer_pc writer_expression_number
          bypassing_write_buffer new_value s
  )

let rec update_expressions_maintains_variable_among_gvars
  (v: var_id_t)
  (exps: list expression_t)
  (actor: tid_t)
  (writer_pc: pc_t)
  (writer_expression_number: nat)
  (bypassing_write_buffer: bool)
  (new_values: list object_value_t)
  (s: Armada.State.t)
  : Lemma (requires variable_among_gvars s.mem v)
          (ensures  (match update_expressions exps actor writer_pc writer_expression_number bypassing_write_buffer
                             new_values s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> variable_among_gvars s'.mem v))
          (decreases exps) =
  match exps, new_values with
  | [], [] -> ()
  | first_exp :: remaining_exps, first_new_value :: remaining_new_values ->
      update_expression_maintains_variable_among_gvars v first_exp actor writer_pc writer_expression_number
        bypassing_write_buffer first_new_value s;
      (match update_expression first_exp actor writer_pc writer_expression_number
               bypassing_write_buffer first_new_value s with
       | ComputationImpossible | ComputationUndefined -> ()
       | ComputationProduces s' ->
           update_expressions_maintains_variable_among_gvars v remaining_exps actor writer_pc
             (writer_expression_number + 1) bypassing_write_buffer remaining_new_values s')
  | _ -> ()

let push_stack_variable_maintains_variable_among_gvars
  (v: var_id_t)
  (actor: tid_t)
  (writer_pc: pc_t)
  (writer_expression_number: nat)
  (method_id: method_id_t)
  (frame_uniq: root_id_uniquifier_t)
  (initializer: initializer_t)
  (s: Armada.State.t)
  : Lemma (requires variable_among_gvars s.mem v)
          (ensures  (match push_stack_variable actor writer_pc writer_expression_number method_id frame_uniq
                             initializer s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> variable_among_gvars s'.mem v)) =
  let root_id = RootIdStack actor method_id frame_uniq initializer.var_id in
  let root = s.mem root_id in
  if not (stack_variable_ready_for_push root initializer) then
    ()
  else
    let thread = s.threads actor in
    let var_id = initializer.var_id in
    if list_contains var_id thread.top.local_variables then
      ()
    else
      let local_variables' = var_id :: thread.top.local_variables in
      let top' = { thread.top with local_variables = local_variables' } in
      let thread' = { thread with top = top' } in
      let threads' = Spec.Map.upd s.threads actor thread' in
      let root' = RootStackVariable true false (RootStackVariable?.storage root) in
      let mem' = upd s.mem root_id root' in
      let s' = { s with mem = mem'; threads = threads' } in
      (match initializer.iv with
       | InitializerArbitrary td -> ()
       | InitializerSpecific value ->
           let td = (object_value_to_td value) in
           update_expression_maintains_variable_among_gvars v (ExpressionLocalVariable td var_id) actor writer_pc
             writer_expression_number false value s')
/
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 ->
    actor: Armada.Base.tid_t ->
    writer_pc: Armada.Base.pc_t ->
    writer_expression_number: Prims.nat ->
    method_id: Armada.Base.method_id_t ->
    frame_uniq: Armada.Base.root_id_uniquifier_t ->
    initializers: Prims.list Armada.Init.initializer_t ->
    s: Armada.State.t
  -> FStar.Pervasives.Lemma
      (requires Strategies.GlobalVars.Permanent.variable_among_gvars (Mkt?.mem s) v)
      (ensures
        ((match
              Armada.Init.push_stack_variables actor
                writer_pc
                writer_expression_number
                method_id
                frame_uniq
                initializers
                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))
      (decreases initializers)
Armada.Base.var_id_t Armada.Base.tid_t Armada.Base.pc_t Prims.nat Armada.Base.method_id_t Armada.Base.root_id_uniquifier_t Prims.list Armada.Init.initializer_t Armada.State.t Armada.Init.push_stack_variable Strategies.GlobalVars.Permanent.push_stack_variables_maintains_variable_among_gvars Prims.op_Addition Prims.unit Strategies.GlobalVars.Permanent.push_stack_variable_maintains_variable_among_gvars Prims.b2t Strategies.GlobalVars.Permanent.variable_among_gvars Armada.State.__proj__Mkt__item__mem Prims.squash Armada.Init.push_stack_variables Prims.l_True Prims.Nil FStar.Pervasives.pattern
let rec push_stack_variables_maintains_variable_among_gvars
      (v: var_id_t)
      (actor: tid_t)
      (writer_pc: pc_t)
      (writer_expression_number: nat)
      (method_id: method_id_t)
      (frame_uniq: root_id_uniquifier_t)
      (initializers: list initializer_t)
      (s: Armada.State.t)
    : Lemma (requires variable_among_gvars s.mem v)
      (ensures
        (match
            push_stack_variables actor
              writer_pc
              writer_expression_number
              method_id
              frame_uniq
              initializers
              s
          with
          | ComputationImpossible | ComputationUndefined -> True
          | ComputationProduces s' -> variable_among_gvars s'.mem v))
      (decreases initializers) =
  
match initializers with
| [] -> ()
| first_initializer :: remaining_initializers ->
  push_stack_variable_maintains_variable_among_gvars v
    actor
    writer_pc
    writer_expression_number
    method_id
    frame_uniq
    first_initializer
    s;
  (match
      push_stack_variable actor
        writer_pc
        writer_expression_number
        method_id
        frame_uniq
        first_initializer
        s
    with
    | ComputationImpossible | ComputationUndefined -> ()
    | ComputationProduces s' ->
      push_stack_variables_maintains_variable_among_gvars v
        actor
        writer_pc
        (writer_expression_number + 1)
        method_id
        frame_uniq
        remaining_initializers
        s')