include "joint/Joint.ma".

inductive rtl_seq : Type[0] ≝
  | rtl_stack_address: register → register → rtl_seq.
 
definition RTL_uns ≝ mk_unserialized_params
    (* acc_a_reg ≝ *) register
    (* acc_b_reg ≝ *) register
    (* acc_a_arg ≝ *) psd_argument
    (* acc_b_arg ≝ *) psd_argument
    (* dpl_reg   ≝ *) register
    (* dph_reg   ≝ *) register
    (* dpl_arg   ≝ *) psd_argument
    (* dph_arg   ≝ *) psd_argument
    (* snd_arg   ≝ *) psd_argument
    (* pair_move ≝ *) (register × psd_argument)
    (* call_args ≝ *) (list psd_argument)
    (* call_dest ≝ *) (list register)
    (* ext_seq ≝ *) rtl_seq
    (* ext_seq_labels ≝ *) (λ_.[])
    (* has_tailcalls ≝ *) false
    (* paramsT ≝ *) (list register).

definition RTL_functs ≝ mk_get_pseudo_reg_functs RTL_uns 
(* acc_a_regs *) (λr.[r])
(* acc_b_regs *) (λr.[r])
(* acc_a_args *) (λa. match a with [Reg r ⇒ [r] |Imm _ ⇒ [ ]])
(* acc_b_args *) (λa. match a with [Reg r ⇒ [r] |Imm _ ⇒ [ ]])
(* dpl_regs *) (λr.[r])
(* dph_regs *) (λr.[r])
(* dpl_args *) (λa. match a with [Reg r ⇒ [r] |Imm _ ⇒ [ ]])
(* dph_args *) (λa. match a with [Reg r ⇒ [r] |Imm _ ⇒ [ ]])
(* snd_args *) (λa. match a with [Reg r ⇒ [r] |Imm _ ⇒ [ ]])
(* pair_move_regs *) (λx.[\fst x] @ (match \snd x with [Reg r ⇒ [r] |Imm _ ⇒ [ ]]))
(* f_call_args *) (λl.foldl ?? (λl1.λa.l1@(match a with [Reg r ⇒ [r] |Imm _ ⇒ [ ]])) [ ] l)
(* f_call_dest *) (λx.x)
(* ext_seq_regs *) (λext.match ext with [rtl_stack_address r1 r2 ⇒ [r1;r2]])
(* params_regs *) (λx.x).

definition RTL ≝ mk_graph_params (mk_uns_params RTL_uns RTL_functs).
definition rtl_program ≝ joint_program RTL.
unification hint 0 ≔ ⊢ rtl_program ≡ joint_program RTL.

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

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

unification hint 0 ≔
(*---------------*) ⊢
ext_seq RTL ≡ rtl_seq.

coercion reg_to_rtl_snd_argument : ∀r : register.snd_arg RTL ≝ psd_argument_from_reg
  on _r : register to snd_arg RTL.
coercion byte_to_rtl_snd_argument : ∀b : Byte.snd_arg RTL ≝ psd_argument_from_byte
  on _b : Byte to snd_arg RTL.

(* parameters for main need to be passed to the premain *)
definition RTL_premain : ∀p : rtl_program.
  joint_closed_internal_function RTL (prog_names … p) ≝
λp.
let l1 : label ≝ an_identifier … one in
let l2 : label ≝ an_identifier … (p0 one) in
let l3 : label ≝ an_identifier … (p1 one) in
let rs : list register ≝
  [ an_identifier … one ;
    an_identifier … (p0 one) ;
    an_identifier … (p1 one) ;
    an_identifier … (p0 (p0 one)) ] in
let res ≝
  mk_joint_internal_function RTL (prog_names … p)
  (mk_universe … (p0 (p0 one)))
  (mk_universe … (p1 (p0 one)))
  [ ] rs 0 0 (empty_map …) l1 in
(* todo: args for main? *)
let res ≝ add_graph … l1
  (sequential … (COST_LABEL … (init_cost_label … p)) l2)
  res in
let res ≝ add_graph … l2
  (sequential … (CALL RTL ? (inl … (prog_main … p)) [ ] rs) l3)
  res in
let res ≝ add_graph … l3
  (GOTO ? l3)
  res in
res.
%
[ ** [2,3: * [2,3,5,6: #p ]] #s whd in ⊢ (??%?→?); #EQ destruct
  %
  [1,3,5: %{I} % whd in ⊢ (??%(??%)→?); #EQ destruct
  |2: %
  |4,6: % whd in ⊢ (??%%→?); #EQ destruct
  ]
| ** [2,3: * [2,3,5,6: #p ]] #s whd in ⊢ (??%?→?); #EQ destruct % try @I %{I I}
| ** [2,3: * [2,3,5,6: #p ]] * whd whd in ⊢ (?%%); //
| ** [2,3: * [2,3,5,6: #p ]] #s whd in ⊢ (??%%→?); #EQ destruct try @I
  try % try % try % try % try % whd /2 by double_lt3/
| %{l2} %{(init_cost_label … p)} %
]
qed.