include "utilities/lists.ma".
include "common/Globalenvs.ma".
include "Cminor/syntax.ma".
include "RTLabs/syntax.ma".

definition env ≝ identifier_map SymbolTag register.
definition label_env ≝ identifier_map SymbolTag label.
definition populate_env : env → universe RegisterTag → list ident → res (list register × env × (universe RegisterTag)) ≝
λen,gen. foldr ??
 (λid,rsengen.
   do 〈rs,en,gen〉 ← rsengen;
   do 〈r,gen'〉 ← fresh … gen;
   OK ? 〈r::rs, add ?? en id r, gen'〉) (OK ? 〈[ ], en, gen〉).

definition populate_label_env : label_env → universe LabelTag → list ident → res (label_env × (universe LabelTag)) ≝
λen,gen. foldr ??
 (λid,engen.
   do 〈en,gen〉 ← engen;
   do 〈r,gen'〉 ← fresh … gen;
   OK ? 〈add ?? en id r, gen'〉) (OK ? 〈en, gen〉).

(* Add a statement to the graph, *without* updating the entry label. *)
definition fill_in_statement : label → statement → internal_function → internal_function ≝
λl,s,f.
  mk_internal_function (f_labgen f) (f_reggen f) (f_sig f)
                       (f_result f) (f_params f) (f_locals f) (f_ptrs f)
                       (f_stacksize f) (add ?? (f_graph f) l s) (f_entry f) (f_exit f).

(* Add a statement to the graph, making it the entry label. *)
definition add_to_graph : label → statement → internal_function → internal_function ≝
λl,s,f.
  mk_internal_function (f_labgen f) (f_reggen f) (f_sig f)
                       (f_result f) (f_params f) (f_locals f) (f_ptrs f)
                       (f_stacksize f) (add ?? (f_graph f) l s) l (f_exit f).

(* Add a statement with a fresh label to the start of the function.  The
   statement is parametrised by the *next* instruction's label. *)
definition add_fresh_to_graph : (label → statement) → internal_function → res internal_function ≝
λs,f.
  do 〈l,g〉 ← fresh … (f_labgen f);
  let s' ≝ s (f_entry f) in
  OK ? (mk_internal_function g (f_reggen f) (f_sig f)
                       (f_result f) (f_params f) (f_locals f) (f_ptrs f)
                       (f_stacksize f) (add ?? (f_graph f) l s') l (f_exit f)).

(* Generate a fresh label and use it as a dangling entry point, to be filled in
   later with the loop head. *)
definition add_loop_label_to_graph : internal_function → res internal_function ≝
λf.
  do 〈l,g〉 ← fresh … (f_labgen f);
  OK ? (mk_internal_function g (f_reggen f) (f_sig f)
                       (f_result f) (f_params f) (f_locals f) (f_ptrs f)
                       (f_stacksize f) (f_graph f) l (f_exit f)).

definition fresh_reg : internal_function → res (register × internal_function) ≝
λf.
  do 〈r,g〉 ← fresh … (f_reggen f);
  OK ? 〈r, mk_internal_function (f_labgen f) g (f_sig f)
                       (f_result f) (f_params f) (r::(f_locals f)) (f_ptrs f)
                       (f_stacksize f) (f_graph f) (f_entry f) (f_exit f)〉.

definition fresh_ptr_reg : internal_function → res (register × internal_function) ≝
λf.
  do 〈r,g〉 ← fresh … (f_reggen f);
  OK ? 〈r, mk_internal_function (f_labgen f) g (f_sig f)
                       (f_result f) (f_params f) (r::(f_locals f)) (r::(f_ptrs f))
                       (f_stacksize f) (f_graph f) (f_entry f) (f_exit f)〉.

let rec expr_yields_pointer (e:expr) (ptrs:list ident) : bool ≝
match e with
[ Id i ⇒ exists ? (eq_identifier ? i) ptrs
| Cst c ⇒ match c with [ Oaddrsymbol _ _ ⇒ true | Oaddrstack _ ⇒ true | _ ⇒ false ]
| Op1 op e' ⇒
    match op with
    [ Oid ⇒ expr_yields_pointer e' ptrs
    | Optrofint _ ⇒ true
    | _ ⇒ false
    ]
| Op2 op e1 e2 ⇒
    match op with
    [ Oaddp ⇒ true
    | Osubpi ⇒ true
    | _ ⇒ false
    ]
| Mem q e' ⇒
    match q with
    [ Mpointer _ ⇒ true
    | _ ⇒ false
    ]
(* Both branches ought to be the same? *)
| Cond e' e1 e2 ⇒ (expr_yields_pointer e1 ptrs) ∨ (expr_yields_pointer e2 ptrs)
| Ecost _ e' ⇒ expr_yields_pointer e' ptrs
].

definition choose_reg : env → expr → list ident → internal_function → res (register × internal_function) ≝
λenv,e,ptrs,f.
  match e with
  [ Id i ⇒
      do r ← opt_to_res … (lookup … env i);
      OK ? 〈r, f〉
  | _ ⇒
      if expr_yields_pointer e ptrs then fresh_ptr_reg f else fresh_reg f
  ].

definition choose_regs : env → list expr → list ident → internal_function → res (list register × internal_function) ≝
λenv,es,ptrs,f.
  foldr ?? (λe,acc. do 〈rs,f〉 ← acc;
                    do 〈r,f'〉 ← choose_reg env e ptrs f;
                    OK ? 〈r::rs,f'〉) (OK ? 〈[ ], f〉) es.

let rec add_expr (env:env) (e:expr) (dst:register) (ptrs:list ident) (f:internal_function) on e: res internal_function ≝
match e with
[ Id i ⇒
    do r ← opt_to_res … (lookup ?? env i);
    match register_eq r dst with
    [ inl _ ⇒ OK ? f
    | inr _ ⇒ add_fresh_to_graph (St_op1 Oid dst r) f
    ]
| Cst c ⇒ add_fresh_to_graph (St_const dst c) f
| Op1 op e' ⇒
    do 〈r,f〉 ← choose_reg env e' ptrs f;
    do f ← add_fresh_to_graph (St_op1 op dst r) f;
    add_expr env e' r ptrs f
| Op2 op e1 e2 ⇒
    do 〈r1,f〉 ← choose_reg env e1 ptrs f;
    do 〈r2,f〉 ← choose_reg env e2 ptrs f;
    do f ← add_fresh_to_graph (St_op2 op dst r1 r2) f;
    do f ← add_expr env e2 r2 ptrs f;
    add_expr env e1 r1 ptrs f
| Mem q e' ⇒ 
    add_with_addressing_internal env e' (λm,rs. St_load q m rs dst) ptrs f (add_expr env e')
| Cond e' e1 e2 ⇒
    let resume_at ≝ f_entry f in
    do f ← add_expr env e2 dst ptrs f;
    let lfalse ≝ f_entry f in
    do f ← add_fresh_to_graph (λ_.St_skip resume_at) f;
    do f ← add_expr env e1 dst ptrs f;
    add_branch_internal env e' (f_entry f) lfalse ptrs f (add_expr env e')
| Ecost l e' ⇒
    do f ← add_expr env e' dst ptrs f;
    add_fresh_to_graph (St_cost l) f
    
(* Ugh, the termination checker isn't smart enough to notice that calling
   add_expr with e is OK, so we take it partially applied and define a proper
   add_<whatever> afterwards. *)
]
and add_with_addressing_internal (env:env) (e:expr)
                          (s:∀m:addressing. addr m → label → statement)
                          (ptrs:list ident)
                          (f:internal_function)
                          (termination_hack:register → list ident → internal_function → res internal_function)
                          on e : res internal_function ≝
let add_default : unit → res internal_function ≝ λ_.
    do 〈r, f〉 ← choose_reg env e ptrs f;
    do f ← add_fresh_to_graph (s (Aindexed zero) [[ r ]]) f;
    termination_hack r ptrs f
in
match e with
[ Cst c ⇒
    match c with
    [ Oaddrsymbol id i ⇒ add_fresh_to_graph (s (Aglobal id i) [[ ]]) f
    | Oaddrstack i ⇒ add_fresh_to_graph (s (Ainstack i) [[ ]]) f
    | _ ⇒ Error ? (* int and float constants are nonsense here *)
    ]
| Op2 op e1 e2 ⇒
    match op with
    [ Oaddp ⇒
        let add_generic_addp : unit → res internal_function ≝ λ_.
          do 〈r1, f〉 ← choose_reg env e1 ptrs f;
          do 〈r2, f〉 ← choose_reg env e2 ptrs f;
          do f ← add_fresh_to_graph (s Aindexed2 [[ r1 ; r2 ]]) f;
          do f ← add_expr env e2 r2 ptrs f;
          add_expr env e1 r1 ptrs f
        in
        match e1 with
        [ Cst c ⇒
            match c with
            [ Oaddrsymbol id i ⇒
                do 〈r, f〉 ← choose_reg env e ptrs f;
                do f ← add_fresh_to_graph (s (Abased id i) [[ r ]]) f;
                add_expr env e2 r ptrs f
            | _ ⇒ add_generic_addp it
            ]
        | _ ⇒ add_generic_addp it
        ]
    | _ ⇒ add_default it
    ]
| _ ⇒ add_default it
]
(* and again *)
and add_branch_internal (env:env) (e:expr) (ltrue:label) (lfalse:label) (ptrs:list ident) (f:internal_function)
        (termination_hack_add_expr : register → list ident → internal_function → res internal_function) on e : res internal_function ≝
match e with
[ Id i ⇒
    do r ← opt_to_res … (lookup ?? env i);
    add_fresh_to_graph (λ_. St_cond1 Oid r ltrue lfalse) f
| Cst c ⇒
    add_fresh_to_graph (λ_. St_condcst c ltrue lfalse) f
| Op1 op e' ⇒
    do 〈r,f〉 ← choose_reg env e' ptrs f;
    do f ← add_fresh_to_graph (λ_. St_cond1 op r ltrue lfalse) f;
    add_expr env e' r ptrs f
| Op2 op e1 e2 ⇒
    do 〈r1,f〉 ← choose_reg env e1 ptrs f;
    do 〈r2,f〉 ← choose_reg env e2 ptrs f;
    do f ← add_fresh_to_graph (λ_. St_cond2 op r1 r2 ltrue lfalse) f;
    do f ← add_expr env e2 r2 ptrs f;
    add_expr env e1 r1 ptrs f
| _ ⇒
    do 〈r,f〉 ← choose_reg env e ptrs f;
    do f ← add_fresh_to_graph (λ_. St_cond1 Oid r ltrue lfalse) f;
    termination_hack_add_expr r ptrs f
].

(* See comment above. *)
definition add_with_addressing ≝
λenv,e,s,ptrs,f. add_with_addressing_internal env e s ptrs f (add_expr env e).
definition add_branch ≝
λenv,e,ltrue,lfalse,ptrs,f. add_branch_internal env e ltrue lfalse ptrs f (add_expr env e).

let rec add_exprs (env:env) (es:list expr) (dsts:list register) (ptrs:list ident) (f:internal_function) on es: res internal_function ≝
match es with
[ nil ⇒ match dsts with [ nil ⇒ OK ? f | cons _ _ ⇒ Error ? ]
| cons e et ⇒
    match dsts with
    [ nil ⇒ Error ?
    | cons r rt ⇒
        do f ← add_exprs env et rt ptrs f;
        add_expr env e r ptrs f
    ]
].

let rec add_stmt (env:env) (label_env:label_env) (s:stmt) (exits:list label) (ptrs:list ident) (f:internal_function) on s : res internal_function ≝
match s with
[ St_skip ⇒ OK ? f
| St_assign x e ⇒
    do dst ← opt_to_res … (lookup ?? env x);
    add_expr env e dst ptrs f
| St_store q e1 e2 ⇒
    do 〈val_reg, f〉 ← choose_reg env e2 ptrs f;
    do f ← add_with_addressing env e1 (λm,rs. St_store q m rs val_reg) ptrs f;
    add_expr env e2 val_reg ptrs f
| St_call return_opt_id e args sig ⇒
    do return_opt_reg ←
      match return_opt_id with
      [ None ⇒ OK ? (None ?)
      | Some id ⇒ do r ← opt_to_res … (lookup ?? env id); OK ? (Some ? r)
      ];
    do 〈args_regs, f〉 ← choose_regs env args ptrs f;
    do f ←
      match e with
      [ Id id ⇒ add_fresh_to_graph (St_call_id id args_regs return_opt_reg sig) f
      | _ ⇒ 
        do 〈fnr, f〉 ← choose_reg env e ptrs f;
        do f ← add_fresh_to_graph (St_call_ptr fnr args_regs return_opt_reg sig) f;
        add_expr env e fnr ptrs f
      ];
    add_exprs env args args_regs ptrs f
| St_tailcall e args sig ⇒
    do 〈args_regs, f〉 ← choose_regs env args ptrs f;
    do f ←
      match e with
      [ Id id ⇒ add_fresh_to_graph (λ_. St_tailcall_id id args_regs sig) f
      | _ ⇒ 
        do 〈fnr, f〉 ← choose_reg env e ptrs f;
        do f ← add_fresh_to_graph (λ_. St_tailcall_ptr fnr args_regs sig) f;
        add_expr env e fnr ptrs f
      ];
    add_exprs env args args_regs ptrs f
| St_seq s1 s2 ⇒
    do f ← add_stmt env label_env s2 exits ptrs f;
    add_stmt env label_env s1 exits ptrs f
| St_ifthenelse e s1 s2 ⇒ 
    let l_next ≝ f_entry f in
    do f ← add_stmt env label_env s2 exits ptrs f;
    let l2 ≝ f_entry f in
    do f ← add_fresh_to_graph ? (* XXX: fails, but works if applied afterwards: λ_. St_skip l_next*) f;
    do f ← add_stmt env label_env s1 exits ptrs f;
    add_branch env e (f_entry f) l2 ptrs f
| St_loop s ⇒
    do f ← add_loop_label_to_graph f;
    let l_loop ≝ f_entry f in
    do f ← add_stmt env label_env s exits ptrs f;
    OK ? (fill_in_statement l_loop (* XXX another odd failure: St_skip (f_entry f)*)? f)
| St_block s ⇒
    add_stmt env label_env s ((f_entry f)::exits) ptrs f
| St_exit n ⇒
    do l ← opt_to_res … (nth_opt ? n exits);
    add_fresh_to_graph (* XXX another: λ_. St_skip l*)? f
| St_switch e tab n ⇒
    do 〈r,f〉 ← choose_reg env e ptrs f;
    do l_default ← opt_to_res … (nth_opt ? n exits);
    do f ← add_fresh_to_graph (* XXX grrrr: λ_. St_skip l_default*)? f;
    do f ← foldr ?? (λcs,f.
      do f ← f;
      let 〈i,n〉 ≝ cs in
      do 〈cr,f〉 ← fresh_reg … f;
      do l_case ← opt_to_res … (nth_opt ? n exits);
      do f ← add_fresh_to_graph (St_cond2 (Ocmpu Ceq) (* signed? *) r cr l_case) f;
      add_fresh_to_graph (St_const cr (Ointconst i)) f) (OK ? f) tab;
    add_expr env e r ptrs f
| St_return opt_e ⇒
    do f ← add_fresh_to_graph (λ_. St_return) f;
    match opt_e with
    [ None ⇒ OK ? f
    | Some e ⇒
        match f_result f with
        [ None ⇒ Error ?
        | Some r ⇒ add_expr env e r ptrs f
        ]
    ]
| St_label l s' ⇒
    do f ← add_stmt env label_env s' exits ptrs f;
    do l' ← opt_to_res … (lookup ?? label_env l);
    OK ? (add_to_graph l' (* XXX again: St_skip (f_entry f)*)? f)
| St_goto l ⇒
    do l' ← opt_to_res … (lookup ?? label_env l);
    add_fresh_to_graph (* XXX again: λ_.St_skip l'*)? f
| St_cost l s' ⇒
    do f ← add_stmt env label_env s' exits ptrs f;
    add_fresh_to_graph (St_cost l) f
| _ ⇒ Error ? (* XXX implement *)
].
[ @(λ_. St_skip l_next)
| @(St_skip (f_entry f))
| @(λ_. St_skip l)
| @(λ_. St_skip l_default)
| @(St_skip (f_entry f))
| @(λ_.St_skip l')
] qed. 

(* Get labels from a Cminor statement. *)
let rec labels_of (s:stmt) : list ident ≝
match s with
[ St_seq s1 s2 ⇒ (labels_of s1) @ (labels_of s2)
| St_ifthenelse _ s1 s2 ⇒ (labels_of s1) @ (labels_of s2)
| St_loop s ⇒ labels_of s
| St_block s ⇒ labels_of s
| St_label l s ⇒ l::(labels_of s)
| St_cost _ s ⇒ labels_of s
| _ ⇒ [ ]
].

definition c2ra_function (*: internal_function → internal_function*) ≝
λf.
let labgen0 ≝ new_universe LabelTag in
let reggen0 ≝ new_universe RegisterTag in
let cminor_labels ≝ labels_of (f_body f) in
do 〈params, env1, reggen1〉 ← populate_env (empty_map …) reggen0 (f_params f);
do 〈locals0, env, reggen2〉 ← populate_env env1 reggen1 (f_vars f);
do 〈result, locals, reggen〉 ←
  match sig_res (f_sig f) with
  [ None ⇒ OK ? 〈None ?, locals0, reggen2〉
  | Some _ ⇒
      do 〈r,gen〉 ← fresh … reggen2;
      OK ? 〈Some ? r, r::locals0, gen〉 ];
do ptrs ← mmap ?? (λid. opt_to_res … (lookup ?? env id)) (f_ptrs f);
do 〈label_env, labgen1〉 ← populate_label_env (empty_map …) labgen0 cminor_labels;
do 〈l,labgen〉 ← fresh … labgen1;
let emptyfn ≝
  mk_internal_function
    labgen
    reggen
    (f_sig f)
    result
    params
    locals
    ptrs
    (f_stacksize f)
    (add ?? (empty_map …) l St_return)
    l
    l in
  add_stmt env label_env (f_body f) [ ] (f_ptrs f) emptyfn
.

definition cminor_to_rtlabs : Cminor_program → res RTLabs_program ≝
transform_partial_program ???
  (transf_partial_fundef ?? c2ra_function).

include "Cminor/initialisation.ma".

definition cminor_init_to_rtlabs : Cminor_program → res RTLabs_program ≝
λp. let p' ≝ replace_init p in cminor_to_rtlabs p.