include "joint/Joint_paolo.ma".

inductive rtl_argument : Type[0] ≝ 
  | Reg : register → rtl_argument
  | Imm : Byte → rtl_argument.
  
coercion reg_to_rtl_argument : ∀r : register.rtl_argument ≝ Reg
  on _r : register to rtl_argument.

coercion byte_to_rtl_argument : ∀b : Byte.rtl_argument ≝ Imm
  on _b : Byte to rtl_argument.

definition imm_nat : nat → rtl_argument ≝ λn.Imm (nat_to_bv ? n).
  
coercion nat_to_rtl_argument : ∀n : nat.rtl_argument ≝ imm_nat
  on _n : nat to rtl_argument.

inductive rtl_seq : Type[0] ≝
  | rtl_stack_address: register → register → rtl_seq.
 
inductive rtl_call : Type[0] ≝
  | rtl_call_ptr: register → register → list rtl_argument → list register → rtl_call.

inductive rtl_tailcall : Type[0] ≝
  | rtl_tailcall_id: ident → list rtl_argument → rtl_tailcall
  | rtl_tailcall_ptr: register → register → list rtl_argument → rtl_tailcall.

definition rtl_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 ≝ *) (register × rtl_argument)
    (* call_args ≝ *) (list rtl_argument)
    (* call_dest ≝ *) (list register)
    (* ext_seq ≝ *) rtl_seq
    (* ext_call ≝ *) rtl_call
    (* ext_tailcall ≝ *) rtl_tailcall
  )
  (mk_local_params
    (mk_funct_params
      (* resultT ≝ *) (list register)
      (* paramsT ≝ *) (list register))
      (* localsT ≝ *) register).

definition rtl_params ≝ mk_graph_params rtl_uns_params.
definition lin_rtl_params ≝ mk_lin_params rtl_uns_params.
definition rtl_internal_function ≝
  λglobals. joint_internal_function globals rtl_params.
definition rtl_program ≝ joint_program rtl_params.
definition rtl_step ≝ joint_step rtl_params.
definition rtl_seq ≝ joint_seq rtl_params.
definition rtl_statement ≝ joint_statement rtl_params.

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

(* aid unification *)
include "hints_declaration.ma".
unification hint 0 ≔
(*---------------*) ⊢
acc_a_reg rtl_params ≡ register.
unification hint 0 ≔
(*---------------*) ⊢
acc_b_reg rtl_params ≡ register.
unification hint 0 ≔
(*---------------*) ⊢
acc_a_arg rtl_params ≡ rtl_argument.
unification hint 0 ≔
(*---------------*) ⊢
acc_b_arg rtl_params ≡ rtl_argument.
unification hint 0 ≔
(*---------------*) ⊢
dpl_reg rtl_params ≡ register.
unification hint 0 ≔
(*---------------*) ⊢
dph_reg rtl_params ≡ register.
unification hint 0 ≔
(*---------------*) ⊢
dpl_arg rtl_params ≡ rtl_argument.
unification hint 0 ≔
(*---------------*) ⊢
dph_arg rtl_params ≡ rtl_argument.
unification hint 0 ≔
(*---------------*) ⊢
snd_arg rtl_params ≡ rtl_argument.
unification hint 0 ≔
(*---------------*) ⊢
pair_move rtl_params ≡ register × rtl_argument.
unification hint 0 ≔
(*---------------*) ⊢
call_args rtl_params ≡ list rtl_argument.
unification hint 0 ≔
(*---------------*) ⊢
call_dest rtl_params ≡ list register.

unification hint 0 ≔
(*---------------*) ⊢
ext_seq rtl_params ≡ rtl_seq.
unification hint 0 ≔
(*---------------*) ⊢
ext_call rtl_params ≡ rtl_call.
unification hint 0 ≔
(*---------------*) ⊢
ext_tailcall rtl_params ≡ rtl_tailcall.
unification hint 0 ≔ globals
(*---------------*) ⊢
joint_step rtl_params globals ≡ rtl_step globals.

unification hint 0 ≔ globals
(*---------------*) ⊢
joint_seq rtl_params globals ≡ rtl_seq globals.
unification hint 0 ≔ globals
(*---------------*) ⊢
joint_statement (stmt_pars (graph_params_to_params rtl_params)) globals ≡ rtl_statement globals.

coercion reg_to_rtl_snd_argument : ∀r : register.snd_arg rtl_params ≝ Reg
  on _r : register to snd_arg rtl_params.
coercion byte_to_rtl_snd_argument : ∀b : Byte.snd_arg rtl_params ≝ Imm
  on _b : Byte to snd_arg rtl_params.


(************ Same without tail calls ****************)

definition rtlntc_params ≝ mk_graph_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 ≝ *) (register × rtl_argument)
    (* call_args ≝ *) (list rtl_argument)
    (* call_dest ≝ *) (list register)
    (* ext_seq ≝ *) rtl_seq
    (* ext_call ≝ *) rtl_call
    (* ext_tailcall ≝ *) void
  )
  (mk_local_params
    (mk_funct_params
      (* resultT ≝ *) (list register)
      (* paramsT ≝ *) (list register))
      (* localsT ≝ *) register)).

definition rtlntc_statement ≝ joint_statement (rtlntc_params : params).

definition rtlntc_internal_function ≝
  λglobals. joint_internal_function … globals rtlntc_params.

definition rtlntc_program ≝ joint_program rtlntc_params.