Require Coq.Strings.Ascii.
Require Coq.Strings.String.
Require Import Coq.Strings.String.
Require Import Coq.Program.Wf.
Require Import Coq.PArith.BinPos.
Require Import Coq.ZArith.ZArith.
Require Import ExtLib.Structures.Monoid.
Require Import ExtLib.Structures.Reducible.
Require Import ExtLib.Programming.Injection.
Require Import ExtLib.Data.Char.
Require Import ExtLib.Data.String.
Require Import ExtLib.Data.Fun.
Require Import ExtLib.Core.RelDec.

Set Implicit Arguments.
Set Strict Implicit.

Set Printing Universes.

Universe Ushow.

Polymorphic Definition showM@{T} : Type@{Ushow} :=
  forall m : Type@{T}, Injection ascii m -> Monoid m -> m.

Polymorphic Class ShowScheme@{t} (T : Type@{t}) : Type :=
{ show_mon : Monoid@{t} T
; show_inj : Injection ascii T
}.

Global Instance ShowScheme_string : ShowScheme string :=
{ show_mon := Monoid_string_append
; show_inj := fun x => String x EmptyString
}.

Global Instance ShowScheme_string_compose : ShowScheme (string -> string) :=
{ show_mon := Monoid_compose string
; show_inj := String
}.

Polymorphic Definition runShow {T} {M : ShowScheme T} (m : showM) : T :=
  m _ show_inj show_mon.

Polymorphic Class Show@{t m} (T : Type@{t}) : Type :=
  show : T -> showM@{m}.

Polymorphic Definition to_string {T} {M : Show T} (v : T) : string :=
  runShow (show v) ""%string.

Polymorphic Definition empty : showM :=
  fun _ _ m => monoid_unit m.
Polymorphic Definition cat (a b : showM) : showM :=
  fun _ i m => monoid_plus m (a _ i m) (b _ i m).
Global Polymorphic Instance Injection_ascii_showM : Injection ascii showM :=
  fun v => fun _ i _ => i v.

Polymorphic Fixpoint show_exact (s : string) : showM :=
  match s with
    | EmptyString => empty
    | String a s' => cat (inject a) (show_exact s')
  end.

Module ShowNotation.
  Delimit Scope show_scope with show.

  Notation "x << y" := (cat x%show y%show) (at level 100) : show_scope.
  Coercion show_exact : string >-> showM.
  Definition _inject_char : ascii -> showM := inject.
  Coercion _inject_char : ascii >-> showM.
End ShowNotation.

Polymorphic Definition indent (indent : showM) (v : showM) : showM :=
  let nl := Ascii.ascii_of_nat 10 in
    fun _ inj mon =>
      v _ (fun a => if eq_dec a nl
         then monoid_plus mon (inj a) (indent _ inj mon)
         else inj a) mon.

Section sepBy.
  Import ShowNotation.
  Local Open Scope show_scope.

  Polymorphic Definition sepBy {T : Type}
              {F : Foldable T showM} (sep : showM) (ls : T) : showM :=
    match
      fold (fun s acc =>
        match acc with
          | None => Some s
          | Some x => Some (x << sep << s)
        end) None ls
      with
      | None => empty
      | Some s => s
    end.
End sepBy.

Section sepBy_f.
  Import ShowNotation.
  Local Open Scope show_scope.
  Polymorphic Variables (T : Type) (E : Type).
  Polymorphic Context {F : Foldable T E}.
  Polymorphic Variable (f : E -> showM).

  Polymorphic Definition sepBy_f (sep : showM) (ls : T) : showM :=
    match
      fold (fun s acc =>
        match acc with
          | None => Some (f s)
          | Some x => Some (x << sep << f s)
        end) None ls
      with
      | None => empty
      | Some s => s
    end.
End sepBy_f.

Polymorphic Definition wrap (before after : showM) (x : showM) : showM :=
  cat before (cat x after).

Section sum_Show.
  Import ShowNotation.
  Local Open Scope show_scope.

  Polymorphic Definition sum_Show@{a m}
              {A : Type@{a}} {B : Type@{a}} {AS:Show@{a m} A} {BS:Show@{a m} B}
  : Show@{a m} (A+B) :=
    fun s =>
        let (tag, payload) :=
          match s with
          | inl a => (show_exact "inl"%string, show a)
          | inr b => (show_exact "inr"%string, show b)
          end
        in
        "("%char <<
        tag <<
        " "%char <<
        payload <<
        ")"%char.

End sum_Show.

Section foldable_Show.
  Polymorphic Context {A:Type} {B:Type} {F : Foldable B A} {BS : Show A}.

  Global Polymorphic  Instance foldable_Show : Show B :=
    { show s := sepBy_f show (show_exact ", "%string) s }.

End foldable_Show.

Polymorphic Fixpoint iter_show (ss : list showM) : showM :=
  match ss with
    | nil => empty
    | cons s ss => cat s (iter_show ss)
  end.

Section hiding_notation.
  Import ShowNotation.
  Local Open Scope show_scope.
  Import Ascii.
  Import String.

  Global Instance unit_Show : Show unit :=
  { show u := "tt"%string }.
  Global Instance bool_Show : Show bool :=
  { show b := if b then "true"%string else "false"%string }.
  Global Instance ascii_Show : Show ascii :=
    fun a =>  "'"%char << a << "'"%char.
  Global Instance string_Show : Show string :=
  { show s := """"%char << s << """"%char }.

  Program Fixpoint nat_show (n:nat) {measure n} : showM :=
    if Compare_dec.le_gt_dec n 9 then
      inject (Char.digit2ascii n)
    else
      let n' := NPeano.Nat.div n 10 in
      (@nat_show n' _) << (inject (Char.digit2ascii (n - 10 * n'))).
  Next Obligation.
(* Goal: lt (@fst nat nat (NPeano.Nat.divmod n (S (S (S (S (S (S (S (S (S O))))))))) O (S (S (S (S (S (S (S (S (S O))))))))))) n *)
    assert (NPeano.Nat.div n 10 < n) ; eauto.
(* Goal: lt (NPeano.Nat.div n (S (S (S (S (S (S (S (S (S (S O))))))))))) n *)
    eapply NPeano.Nat.div_lt.
(* Goal: lt O n *)
(* Goal: lt (S O) (S (S (S (S (S (S (S (S (S (S O)))))))))) *)
    inversion H; apply Lt.lt_O_Sn.
(* Goal: lt (S O) (S (S (S (S (S (S (S (S (S (S O)))))))))) *)
    repeat constructor.
  Defined.
  Global Instance nat_Show : Show nat := { show := nat_show }.

  Global Instance Show_positive : Show positive :=
    fun x => nat_show (Pos.to_nat x).

  Global Instance Show_Z : Show Z :=
    fun x =>
      match x with
      | Z0 => "0"%char
      | Zpos p => show p
      | Zneg p => "-"%char << show p
      end.

  Section pair_Show.
    Polymorphic Definition pair_Show@{a m}
                {A : Type@{a}} {B : Type@{a}} {AS:Show A} {BS:Show B}
    : Show (A*B) :=
      fun p =>
        let (a,b) := p in
        "("%char << show a << ","%char << show b << ")"%char.
  End pair_Show.
End hiding_notation.



(*
Examples:
Eval compute in (runShow (show (42,"foo"%string)) : string).
Eval compute in (runShow (show (inl true : bool+string))).
*)
