val update_statement_computation_maintains_positions_valid_in_state
      (actor: tid_t)
      (nd: nondeterminism_t)
      (start_pc: pc_t)
      (bypassing_write_buffer: bool)
      (dst src: expression_t)
      (s: Armada.State.t)
    : Lemma (requires positions_valid_in_state s)
      (ensures
        (match update_statement_computation actor nd start_pc bypassing_write_buffer dst src s with
          | ComputationImpossible | ComputationUndefined -> True
          | ComputationProduces s' -> positions_valid_in_state s'))
val update_statement_computation_maintains_positions_valid_in_state
      (actor: tid_t)
      (nd: nondeterminism_t)
      (start_pc: pc_t)
      (bypassing_write_buffer: bool)
      (dst src: expression_t)
      (s: Armada.State.t)
    : Lemma (requires positions_valid_in_state s)
      (ensures
        (match update_statement_computation actor nd start_pc bypassing_write_buffer dst src s with
          | ComputationImpossible | ComputationUndefined -> True
          | ComputationProduces s' -> positions_valid_in_state s'))
let update_statement_computation_maintains_positions_valid_in_state
  (actor: tid_t)
  (nd: nondeterminism_t)
  (start_pc: pc_t)
  (bypassing_write_buffer: bool)
  (dst: expression_t)
  (src: expression_t)
  (s: Armada.State.t)
  : Lemma (requires positions_valid_in_state s)
          (ensures  (match update_statement_computation actor nd start_pc bypassing_write_buffer dst src s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> positions_valid_in_state s')) =
  let cs' = update_statement_computation actor nd start_pc bypassing_write_buffer dst src s in
  if   Cons? nd
     || neqb (expression_to_td dst) (expression_to_td src) then
    ()
  else (
    match rvalue_computation src actor s with
    | ComputationImpossible | ComputationUndefined -> ()
    | ComputationProduces src_value ->
        update_expression_maintains_positions_valid_in_state dst actor start_pc 0 bypassing_write_buffer src_value s
  )
module Strategies.ArmadaInvariant.PositionsValid

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.Threads
open Armada.Transition
open Armada.Type
open FStar.Sequence.Ambient
open FStar.Sequence.Base
open FStar.Tactics.V2
open Spec.List
open Spec.Ubool
open Strategies.ArmadaStatement
open Util.Tactics

let init_implies_positions_valid_in_state (program: Armada.Program.t) (s: Armada.State.t)
  : Lemma (requires init_program program s)
          (ensures  positions_valid_in_state s) =
  ()

let rec push_stack_variables_maintains_positions_valid_in_state
  (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 positions_valid_in_state s)
          (ensures  (match push_stack_variables actor writer_pc writer_expression_number method_id
                             frame_uniq initializers s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> positions_valid_in_state s'))
          (decreases initializers) =
  match initializers with
  | [] -> ()
  | first_initializer :: remaining_initializers ->
      (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_positions_valid_in_state actor writer_pc (writer_expression_number + 1)
             method_id frame_uniq remaining_initializers s')

let rec push_stack_parameters_maintains_positions_valid_in_state
  (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 positions_valid_in_state s)
          (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' -> positions_valid_in_state s'))
          (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
      (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_positions_valid_in_state actor writer_pc (writer_expression_number + 1)
             method_id frame_uniq remaining_var_ids remaining_parameters s')
  | _ -> ()

#push-options "--z3rlimit 10"

let update_pointed_to_value_maintains_positions_valid_in_state
  (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 positions_valid_in_state s)
          (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' -> positions_valid_in_state s')) =
  ()

let update_expression_maintains_positions_valid_in_state
  (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 positions_valid_in_state s)
          (ensures  (match update_expression exp actor writer_pc writer_expression_number bypassing_write_buffer
                             new_value s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> positions_valid_in_state s')) =
  ()

#pop-options

let rec update_expressions_maintains_positions_valid_in_state
  (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 positions_valid_in_state s)
          (ensures  (match update_expressions exps actor writer_pc writer_expression_number bypassing_write_buffer
                             new_values s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> positions_valid_in_state s'))
          (decreases exps) =
  match exps, new_values with
  | [], [] -> ()
  | first_exp :: remaining_exps, first_new_value :: remaining_new_values ->
      update_expression_maintains_positions_valid_in_state 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_positions_valid_in_state remaining_exps actor writer_pc
             (writer_expression_number + 1) bypassing_write_buffer remaining_new_values s')
  | _ -> ()

let rec external_method_take_snapshot_of_reads_clauses_computation_maintains_positions_valid_in_state
  (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 positions_valid_in_state s)
          (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' -> positions_valid_in_state s'))
          (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_positions_valid_in_state 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_positions_valid_in_state
                  actor writer_pc (writer_expression_number + 1) bypassing_write_buffer remaining_reads_clauses s'))
  | _ -> ()

let rec log_expressions_computation_maintains_positions_valid_in_state
  (actor: tid_t)
  (logs_clauses: list expression_t)
  (s: Armada.State.t)
  : Lemma (requires positions_valid_in_state s)
          (ensures  (match log_expressions_computation actor logs_clauses s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> positions_valid_in_state s'))
          (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_positions_valid_in_state actor remaining_logs_clauses s')

#push-options "--z3rlimit 10"

let assume_expression_statement_computation_maintains_positions_valid_in_state
  (actor: tid_t)
  (nd: nondeterminism_t)
  (start_pc: pc_t)
  (exp: expression_t)
  (s: Armada.State.t)
  : Lemma (requires positions_valid_in_state s)
          (ensures  (match assume_expression_statement_computation actor nd start_pc exp s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> positions_valid_in_state s')) =
  ()

let assume_predicate_statement_computation_maintains_positions_valid_in_state
  (actor: tid_t)
  (nd: nondeterminism_t)
  (start_pc: pc_t)
  (pred: Armada.State.t -> GTot bool)
  (s: Armada.State.t)
  : Lemma (requires positions_valid_in_state s)
          (ensures  (match assume_predicate_statement_computation actor nd start_pc pred s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> positions_valid_in_state s')) =
  ()

let assert_true_statement_computation_maintains_positions_valid_in_state
  (actor: tid_t)
  (nd: nondeterminism_t)
  (start_pc: pc_t)
  (exp: expression_t)
  (s: Armada.State.t)
  : Lemma (requires positions_valid_in_state s)
          (ensures  (match assert_true_statement_computation actor nd start_pc exp s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> positions_valid_in_state s')) =
  ()

let assert_false_statement_computation_maintains_positions_valid_in_state
  (actor: tid_t)
  (nd: nondeterminism_t)
  (start_pc: pc_t)
  (exp: expression_t)
  (s: Armada.State.t)
  : Lemma (requires positions_valid_in_state s)
          (ensures  (match assert_false_statement_computation actor nd start_pc exp s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> positions_valid_in_state s')) =
  ()

let conditional_jump_statement_computation_maintains_positions_valid_in_state
  (actor: tid_t)
  (nd: nondeterminism_t)
  (start_pc: pc_t)
  (exp: expression_t)
  (s: Armada.State.t)
  : Lemma (requires positions_valid_in_state s)
          (ensures  (match conditional_jump_statement_computation actor nd start_pc exp s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> positions_valid_in_state s')) =
  ()

let unconditional_jump_statement_computation_maintains_positions_valid_in_state
  (actor: tid_t)
  (nd: nondeterminism_t)
  (start_pc: pc_t)
  (s: Armada.State.t)
  : Lemma (requires positions_valid_in_state s)
          (ensures  (match unconditional_jump_statement_computation actor nd start_pc s with
                     | ComputationImpossible | ComputationUndefined -> True
                     | ComputationProduces s' -> positions_valid_in_state s')) =
  ()
/
Util.Tactics.fst.checked Strategies.ArmadaStatement.fst.checked Spec.Ubool.fst.checked Spec.List.fst.checked prims.fst.checked FStar.Tactics.V2.fst.checked FStar.Sequence.Base.fsti.checked FStar.Sequence.Ambient.fst.checked FStar.Pervasives.Native.fst.checked FStar.Pervasives.fsti.checked Armada.Type.fst.checked Armada.Transition.fst.checked Armada.Threads.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.PositionsValid.fst

    actor: Armada.Base.tid_t ->
    nd: Armada.Type.nondeterminism_t ->
    start_pc: Armada.Base.pc_t ->
    bypassing_write_buffer: Prims.bool ->
    dst: Armada.Expression.expression_t ->
    src: Armada.Expression.expression_t ->
    s: Armada.State.t
  -> FStar.Pervasives.Lemma
      (requires Strategies.ArmadaInvariant.PositionsValid.positions_valid_in_state s)
      (ensures
        ((match
              Armada.Statement.update_statement_computation actor
                nd
                start_pc
                bypassing_write_buffer
                dst
                src
                s
            with
            | Armada.Computation.ComputationImpossible #_ -> Prims.l_True
            | Armada.Computation.ComputationUndefined #_ -> Prims.l_True
            | Armada.Computation.ComputationProduces #_ s' ->
              Strategies.ArmadaInvariant.PositionsValid.positions_valid_in_state s')
          <:
          Type0))
Armada.Base.tid_t Armada.Type.nondeterminism_t Armada.Base.pc_t Prims.bool Armada.Expression.expression_t Armada.State.t Prims.op_BarBar Prims.uu___is_Cons Armada.Type.object_value_t Spec.Ubool.neqb Armada.Type.object_td_t Armada.Expression.expression_to_td Armada.Expression.rvalue_computation Armada.Type.valid_object_value_t Strategies.ArmadaInvariant.PositionsValid.update_expression_maintains_positions_valid_in_state Prims.unit Armada.Computation.conditional_computation_t Armada.Statement.update_statement_computation Strategies.ArmadaInvariant.PositionsValid.positions_valid_in_state Prims.squash Prims.l_True Prims.Nil FStar.Pervasives.pattern
let update_statement_computation_maintains_positions_valid_in_state
      (actor: tid_t)
      (nd: nondeterminism_t)
      (start_pc: pc_t)
      (bypassing_write_buffer: bool)
      (dst src: expression_t)
      (s: Armada.State.t)
    : Lemma (requires positions_valid_in_state s)
      (ensures
        (match update_statement_computation actor nd start_pc bypassing_write_buffer dst src s with
          | ComputationImpossible | ComputationUndefined -> True
          | ComputationProduces s' -> positions_valid_in_state s')) =
  
let cs' = update_statement_computation actor nd start_pc bypassing_write_buffer dst src s in
if Cons? nd || neqb (expression_to_td dst) (expression_to_td src)
then ()
else
  (match rvalue_computation src actor s with
    | ComputationImpossible | ComputationUndefined -> ()
    | ComputationProduces src_value ->
      update_expression_maintains_positions_valid_in_state dst
        actor
        start_pc
        0
        bypassing_write_buffer
        src_value
        s)