Module LTLtyping

Typing rules for LTL.

Require Import Coqlib.
Require Import Maps.
Require Import AST.
Require Import Integers.
Require Import Memdata.
Require Import Op.
Require Import RTL.
Require Import Locations.
Require Import LTL.
Require Import Conventions.

The following predicates define a type system for LTL similar to that of RTL (see file RTLtyping): it statically guarantees that operations and addressing modes are applied to the right number of arguments and that the arguments are of the correct types. Moreover, it also guarantees that the locations of arguments and results are "acceptable", i.e. either non-temporary registers or Local stack locations.

Section WT_INSTR.

Variable funct: function.

Definition valid_successor (s: node) : Prop :=
  exists i, funct.(fn_code)!s = Some i.

Definition call_loc_acceptable (sig: signature) (los: loc + ident) : Prop :=
  match los with
  | inl l => Loc.type l = Tint /\ loc_acceptable l /\ ~In l (loc_arguments sig)
  | inr s => True

Inductive wt_instr : instruction -> Prop :=
  | wt_Lnop:
      forall s,
      valid_successor s ->
      wt_instr (Lnop s)
  | wt_Lopmove:
      forall r1 r s,
      Loc.type r1 = Loc.type r -> loc_acceptable r1 -> loc_acceptable r ->
      valid_successor s ->
      wt_instr (Lop Omove (r1 :: nil) r s)
  | wt_Lop:
      forall op args res s,
      op <> Omove ->
      ( Loc.type args, Loc.type res) = type_of_operation op ->
      locs_acceptable args -> loc_acceptable res ->
      valid_successor s ->
      wt_instr (Lop op args res s)
  | wt_Lload:
      forall chunk addr args dst s, Loc.type args = type_of_addressing addr ->
      Loc.type dst = type_of_chunk chunk ->
      locs_acceptable args -> loc_acceptable dst ->
      valid_successor s ->
      wt_instr (Lload chunk addr args dst s)
  | wt_Lstore:
      forall chunk addr args src s, Loc.type args = type_of_addressing addr ->
      Loc.type src = type_of_chunk chunk ->
      locs_acceptable args -> loc_acceptable src ->
      valid_successor s ->
      wt_instr (Lstore chunk addr args src s)
  | wt_Lcall:
      forall sig ros args res s, Loc.type args = sig.(sig_args) ->
      Loc.type res = proj_sig_res sig ->
      call_loc_acceptable sig ros ->
      locs_acceptable args -> loc_acceptable res ->
      valid_successor s ->
      wt_instr (Lcall sig ros args res s)
  | wt_Ltailcall:
      forall sig ros args, Loc.type args = sig.(sig_args) ->
      call_loc_acceptable sig ros ->
      locs_acceptable args ->
      sig.(sig_res) = funct.(fn_sig).(sig_res) ->
      tailcall_possible sig ->
      wt_instr (Ltailcall sig ros args)
  | wt_Lbuiltin:
      forall ef args res s, Loc.type args = (ef_sig ef).(sig_args) ->
      Loc.type res = proj_sig_res (ef_sig ef) ->
      arity_ok (ef_sig ef).(sig_args) = true \/ ef_reloads ef = false ->
      locs_acceptable args -> loc_acceptable res ->
      valid_successor s ->
      wt_instr (Lbuiltin ef args res s)
  | wt_Lcond:
      forall cond args s1 s2, Loc.type args = type_of_condition cond ->
      locs_acceptable args ->
      valid_successor s1 -> valid_successor s2 ->
      wt_instr (Lcond cond args s1 s2)
  | wt_Ljumptable:
      forall arg tbl,
      Loc.type arg = Tint ->
      loc_acceptable arg ->
      (forall lbl, In lbl tbl -> valid_successor lbl) ->
      list_length_z tbl * 4 <= Int.max_unsigned ->
      wt_instr (Ljumptable arg tbl)
  | wt_Lreturn:
      forall optres,
      option_map Loc.type optres = funct.(fn_sig).(sig_res) ->
      match optres with None => True | Some r => loc_acceptable r end ->
      wt_instr (Lreturn optres).


Record wt_function (f: function): Prop :=
  mk_wt_function {
    wt_params: Loc.type f.(fn_params) = f.(fn_sig).(sig_args);
      locs_acceptable f.(fn_params);
      Loc.norepet f.(fn_params);
      forall pc instr,
      f.(fn_code)!pc = Some instr -> wt_instr f instr;
      valid_successor f f.(fn_entrypoint)

Inductive wt_fundef: fundef -> Prop :=
  | wt_fundef_external: forall ef,
      wt_fundef (External ef)
  | wt_function_internal: forall f,
      wt_function f ->
      wt_fundef (Internal f).

Definition wt_program (p: program): Prop :=
  forall i f, In (i, f) (prog_funct p) -> wt_fundef f.