val log_expressions_computation_maintains_roots_match
      (actor: tid_t)
      (logs_clauses: list expression_t)
      (s: Armada.State.t)
    : Lemma (requires roots_match s.mem)
      (ensures
        (match log_expressions_computation actor logs_clauses s with
          | ComputationImpossible | ComputationUndefined -> True
          | ComputationProduces s' -> roots_match s'.mem))
      (decreases logs_clauses)
val log_expressions_computation_maintains_roots_match
      (actor: tid_t)
      (logs_clauses: list expression_t)
      (s: Armada.State.t)
    : Lemma (requires roots_match s.mem)
      (ensures
        (match log_expressions_computation actor logs_clauses s with
          | ComputationImpossible | ComputationUndefined -> True
          | ComputationProduces s' -> roots_match s'.mem))
      (decreases logs_clauses)
let rec log_expressions_computation_maintains_roots_match
  (actor: tid_t)
  (logs_clauses: list expression_t)
  (s: Armada.State.t)
  : Lemma (requires roots_match s.mem)
          (ensures  (match log_expressions_computation actor logs_clauses s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> roots_match s'.mem))
          (decreases logs_clauses) =
  match logs_clauses with
  | [] -> ()
  | first_logs_clause :: remaining_logs_clauses ->
      (match rvalue_computation first_logs_clause actor s with
       | ComputationImpossible | ComputationUndefined -> ()
       | ComputationProduces event ->
           let trace' = s.trace $:: event in
           let s' = { s with trace = trace' } in
           log_expressions_computation_maintains_roots_match actor remaining_logs_clauses s')
module Strategies.ArmadaInvariant.RootsMatch

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.Tactics

let root_matches_root_id (root: root_t) (root_id: root_id_t) : GTot bool =
  match root with
  | RootGlobal _ -> RootIdGlobal? root_id
  | RootStackVariable _ _ _ -> RootIdStack? root_id
  | RootAllocated _ _ _ -> RootIdAllocation? root_id
  | RootFence storage ->
          RootIdFence? root_id
       && eqb (object_storage_to_td storage) (ObjectTDPrimitive PrimitiveTDBool)
  | RootInvalid -> true

let roots_match (mem: Armada.Memory.t) : ubool =
  forall root_id. root_matches_root_id (mem root_id) root_id

let init_implies_roots_match (program: Armada.Program.t) (s: Armada.State.t)
  : Lemma (requires init_program program s)
          (ensures  roots_match s.mem) =
  let thread = s.threads s.initial_tid in
  let initial_frame_uniq = Cons?.hd s.uniqs_used in
  introduce forall root_id. root_matches_root_id (s.mem root_id) root_id
  with (
    let thread = s.threads s.initial_tid in
    let initial_frame_uniq = Cons?.hd s.uniqs_used in
    assert (root_invalid_outside_initializations s.mem program.global_initializers s.initial_tid
              program.main_method_id initial_frame_uniq thread.top.local_variables root_id)
  )

let rec update_pointer_directly_maintains_roots_match
  (p: Armada.Pointer.t)
  (new_storage: valid_object_storage_t)
  (mem: Armada.Memory.t)
  : Lemma (requires roots_match mem)
          (ensures  (match update_pointer_directly p new_storage mem with
                     | ComputationProduces mem' -> roots_match mem'
                     | _ -> 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_roots_match 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_roots_match array_ptr new_parent mem)
       | PointerRoot root_id -> ()
       | _ -> ())

#push-options "--z3rlimit 10"

let update_pointer_maintains_roots_match
  (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 roots_match mem)
          (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') -> roots_match mem')) =
  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_roots_match 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_roots_match array_ptr new_parent mem)
            | _ -> ()))

#pop-options

let update_pointed_to_value_maintains_roots_match
  (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 roots_match s.mem)
          (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' -> roots_match s'.mem)) =
  update_pointer_maintains_roots_match p actor writer_pc writer_expression_number bypassing_write_buffer
    new_value s.mem

let update_expression_maintains_roots_match
  (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 roots_match s.mem)
          (ensures  (match update_expression exp actor writer_pc writer_expression_number bypassing_write_buffer
                             new_value s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> roots_match s'.mem)) =
  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_roots_match p actor writer_pc writer_expression_number
          bypassing_write_buffer new_value s
  )

let rec update_expressions_maintains_roots_match
  (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 roots_match s.mem)
          (ensures  (match update_expressions exps actor writer_pc writer_expression_number bypassing_write_buffer
                             new_values s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> roots_match s'.mem))
          (decreases exps) =
  match exps, new_values with
  | [], [] -> ()
  | first_exp :: remaining_exps, first_new_value :: remaining_new_values ->
      update_expression_maintains_roots_match 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_roots_match remaining_exps actor writer_pc
             (writer_expression_number + 1) bypassing_write_buffer remaining_new_values s')
  | _ -> ()

let push_stack_variable_maintains_roots_match
  (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 roots_match s.mem)
          (ensures  (match push_stack_variable actor writer_pc writer_expression_number method_id frame_uniq
                             initializer s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> roots_match s'.mem)) =
  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_roots_match (ExpressionLocalVariable td var_id) actor writer_pc
             writer_expression_number false value s')

let rec push_stack_variables_maintains_roots_match
  (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 roots_match s.mem)
          (ensures  (match push_stack_variables actor writer_pc writer_expression_number method_id
                             frame_uniq initializers s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> roots_match s'.mem))
          (decreases initializers) =
  match initializers with
  | [] -> ()
  | first_initializer :: remaining_initializers ->
      push_stack_variable_maintains_roots_match 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_roots_match actor writer_pc (writer_expression_number + 1)
             method_id frame_uniq remaining_initializers s')

let rec push_stack_parameters_maintains_roots_match
  (actor: tid_t)
  (writer_pc: pc_t)
  (writer_expression_number: nat)
  (method_id: method_id_t)
  (frame_uniq: root_id_uniquifier_t)
  (var_ids: list var_id_t)
  (parameters: list object_value_t)
  (s: Armada.State.t)
  : Lemma (requires roots_match s.mem)
          (ensures  (match push_stack_parameters actor writer_pc writer_expression_number method_id frame_uniq
                             var_ids parameters s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> roots_match s'.mem))
          (decreases parameters) =
  match parameters, var_ids with
  | [], [] -> ()
  | first_parameter :: remaining_parameters, first_var_id :: remaining_var_ids ->
      let first_initializer =
        { var_id = first_var_id; iv = InitializerSpecific first_parameter; weakly_consistent = false } in
      push_stack_variable_maintains_roots_match 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_parameters_maintains_roots_match actor writer_pc (writer_expression_number + 1)
             method_id frame_uniq remaining_var_ids remaining_parameters s')
  | _ -> ()

let rec pop_stack_variables_maintains_roots_match
  (actor: tid_t)
  (method_id: method_id_t)
  (frame_uniq: root_id_uniquifier_t)
  (var_ids: list var_id_t)
  (mem: Armada.Memory.t)
  : Lemma (requires roots_match mem)
          (ensures  (match pop_stack_variables actor method_id frame_uniq var_ids mem with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces mem' -> roots_match mem')) =
  match var_ids with
  | [] -> ()
  | first_var_id :: remaining_var_ids ->
      (match pop_stack_variable actor method_id frame_uniq first_var_id mem with
       | ComputationImpossible | ComputationUndefined -> ()
       | ComputationProduces mem' ->
           pop_stack_variables_maintains_roots_match actor method_id frame_uniq remaining_var_ids mem')

let rec external_method_take_snapshot_of_reads_clauses_computation_maintains_roots_match
  (actor: tid_t)
  (writer_pc: pc_t)
  (writer_expression_number: nat)
  (bypassing_write_buffer: bool)
  (reads_clauses: list (var_id_t * expression_t))
  (s: Armada.State.t)
  : Lemma (requires roots_match s.mem)
          (ensures  (match external_method_take_snapshot_of_reads_clauses_computation actor writer_pc
                             writer_expression_number bypassing_write_buffer reads_clauses s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> roots_match s'.mem))
          (decreases reads_clauses) =
  match reads_clauses with
  | [] -> ()
  | (first_var_id, first_reads_expression) :: remaining_reads_clauses ->
      (match rvalue_computation first_reads_expression actor s with
       | ComputationImpossible | ComputationUndefined -> ()
       | ComputationProduces first_value ->
           let td = expression_to_td first_reads_expression in
           let local_var = ExpressionLocalVariable td first_var_id in
           update_expression_maintains_roots_match local_var actor writer_pc writer_expression_number
             bypassing_write_buffer first_value s;
           (match update_expression local_var actor writer_pc writer_expression_number bypassing_write_buffer
                    first_value s with
            | ComputationImpossible | ComputationUndefined -> ()
            | ComputationProduces s' ->
                external_method_take_snapshot_of_reads_clauses_computation_maintains_roots_match
                  actor writer_pc (writer_expression_number + 1) bypassing_write_buffer remaining_reads_clauses s'))
  | _ -> ()
/
Util.Tactics.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.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.ArmadaInvariant.RootsMatch.fst

    actor: Armada.Base.tid_t ->
    logs_clauses: Prims.list Armada.Expression.expression_t ->
    s: Armada.State.t
  -> FStar.Pervasives.Lemma
      (requires Strategies.ArmadaInvariant.RootsMatch.roots_match (Mkt?.mem s))
      (ensures
        ((match Armada.Statement.log_expressions_computation actor logs_clauses s with
            | Armada.Computation.ComputationImpossible #_ -> Prims.l_True
            | Armada.Computation.ComputationUndefined #_ -> Prims.l_True
            | Armada.Computation.ComputationProduces #_ s' ->
              Strategies.ArmadaInvariant.RootsMatch.roots_match (Mkt?.mem s'))
          <:
          Type0))
      (decreases logs_clauses)
Armada.Base.tid_t Prims.list Armada.Expression.expression_t Armada.State.t Armada.Expression.rvalue_computation Armada.Type.valid_object_value_t Armada.Expression.expression_to_td Strategies.ArmadaInvariant.RootsMatch.log_expressions_computation_maintains_roots_match Armada.State.Mkt Armada.State.__proj__Mkt__item__initial_tid Armada.State.__proj__Mkt__item__uniqs_used Armada.State.__proj__Mkt__item__mem Armada.State.__proj__Mkt__item__threads Armada.State.__proj__Mkt__item__stop_reason FStar.Sequence.Base.seq Armada.State.trace_entry FStar.Sequence.Base.op_Dollar_Colon_Colon Armada.State.__proj__Mkt__item__trace Prims.unit Strategies.ArmadaInvariant.RootsMatch.roots_match Prims.squash Armada.Statement.log_expressions_computation Prims.l_True Prims.Nil FStar.Pervasives.pattern
let rec log_expressions_computation_maintains_roots_match
      (actor: tid_t)
      (logs_clauses: list expression_t)
      (s: Armada.State.t)
    : Lemma (requires roots_match s.mem)
      (ensures
        (match log_expressions_computation actor logs_clauses s with
          | ComputationImpossible | ComputationUndefined -> True
          | ComputationProduces s' -> roots_match s'.mem))
      (decreases logs_clauses) =
  
match logs_clauses with
| [] -> ()
| first_logs_clause :: remaining_logs_clauses ->
  (match rvalue_computation first_logs_clause actor s with
    | ComputationImpossible | ComputationUndefined -> ()
    | ComputationProduces event ->
      let trace' = s.trace $:: event in
      let s' = { s with trace = trace' } in
      log_expressions_computation_maintains_roots_match actor remaining_logs_clauses s')