include "joint/Joint_paolo.ma".
include "RTL/RTL_paolo.ma".

inductive move_dst: Type[0] ≝
  | PSD: register → move_dst
  | HDW: Register → move_dst.

inductive move_src: Type[0] ≝
  | INT: Byte → move_src
  | REG: move_dst → move_src.

coercion move_dst_to_src : ∀r : move_dst.move_src ≝ REG on _r : move_dst to move_src.

definition rtl_argument_move_src : rtl_argument → move_src ≝
  λarg.match arg with
  [ Imm b ⇒ INT b
  | Reg r ⇒ REG (PSD r)
  ].

coercion rtl_argument_to_move_src : ∀a:rtl_argument.move_src ≝
  rtl_argument_move_src on _a : rtl_argument to move_src.

inductive ertl_seq : Type[0] ≝
  | ertl_new_frame: ertl_seq
  | ertl_del_frame: ertl_seq
  | ertl_frame_size: register → ertl_seq.

definition ertl_uns_params ≝ mk_unserialized_params
  (mk_step_params
    (* acc_a_reg ≝ *) register
    (* acc_b_reg ≝ *) register
    (* acc_a_arg ≝ *) rtl_argument
    (* acc_b_arg ≝ *) rtl_argument
    (* dpl_reg   ≝ *) register
    (* dph_reg   ≝ *) register
    (* dpl_arg   ≝ *) rtl_argument
    (* dph_arg   ≝ *) rtl_argument
    (* snd_arg   ≝ *) rtl_argument
    (* pair_move ≝ *) (move_dst × move_src)
    (* call_args ≝ *) ℕ
    (* call_dest ≝ *) unit
    (* ext_seq ≝ *) ertl_seq
    (* ext_call ≝ *) void
    (* ext_tailcall ≝ *) void
  )
  (mk_local_params
    (mk_funct_params
      (* resultT ≝ *) unit
      (* paramsT ≝ *) ℕ)
      (* localsT ≝ *) register).

  definition ertl_params ≝ mk_graph_params ertl_uns_params.
  definition ertl_internal_function ≝
  λglobals. joint_internal_function globals ertl_params.
definition ertl_program ≝ joint_program ertl_params.

interpretation "move" 'mov r a = (MOVE ?? (mk_Prod move_dst move_src r a)).

(* aid unification *)
unification hint 0 ≔
(*---------------*) ⊢
pair_move ertl_params ≡ move_dst × move_src.
unification hint 0 ≔
(*---------------*) ⊢
acc_a_reg ertl_params ≡ register.
unification hint 0 ≔
(*---------------*) ⊢
acc_b_reg ertl_params ≡ register.
unification hint 0 ≔
(*---------------*) ⊢
acc_a_arg ertl_params ≡ rtl_argument.
unification hint 0 ≔
(*---------------*) ⊢
acc_b_arg ertl_params ≡ rtl_argument.
unification hint 0 ≔
(*---------------*) ⊢
dpl_reg ertl_params ≡ register.
unification hint 0 ≔
(*---------------*) ⊢
dph_reg ertl_params ≡ register.
unification hint 0 ≔
(*---------------*) ⊢
dpl_arg ertl_params ≡ rtl_argument.
unification hint 0 ≔
(*---------------*) ⊢
dph_arg ertl_params ≡ rtl_argument.
unification hint 0 ≔
(*---------------*) ⊢
snd_arg ertl_params ≡ rtl_argument.
unification hint 0 ≔
(*---------------*) ⊢
call_args ertl_params ≡ ℕ.
unification hint 0 ≔
(*---------------*) ⊢
call_dest ertl_params ≡ unit.

unification hint 0 ≔
(*---------------*) ⊢
ext_seq ertl_params ≡ ertl_seq.
unification hint 0 ≔
(*---------------*) ⊢
ext_call ertl_params ≡ void.
unification hint 0 ≔
(*---------------*) ⊢
ext_tailcall ertl_params ≡ void.

coercion reg_to_ertl_snd_argument : ∀r : register.snd_arg ertl_params ≝ Reg
  on _r : register to snd_arg ertl_params.
coercion byte_to_ertl_snd_argument : ∀b : Byte.snd_arg ertl_params ≝ Imm
  on _b : Byte to snd_arg ertl_params.
  
definition ertl_seq_joint ≝ extension_seq ertl_params.
coercion ertl_seq_to_joint_seq : ∀globals.∀s : ertl_seq.joint_seq ertl_params globals ≝ ertl_seq_joint
  on _s : ertl_seq to joint_seq ertl_params.