(* This file checks the compatibility of naming strategy *)
(* This does not mean that the given naming strategy is good *)

Parameter x2:nat.
Definition foo y := forall x x3 x4 S, x + S = x3 + x4 + y.
Section A.
Variable x3:nat.
Goal forall x x1 x2 x3:nat,
  (forall x x3:nat, x+x1 = x2+x3) -> x+x1 = x2+x3.
Show.
intros.
Show.

(* Remark: in V8.2, this used to be printed

  x3 : nat
  ============================
   forall x x1 x4 x5 : nat,
   (forall x0 x6 : nat, x0 + x1 = x4 + x6) -> x + x1 = x4 + x5

before intro and

  x3 : nat
  x : nat
  x1 : nat
  x4 : nat
  x0 : nat
  H : forall x x3 : nat, x + x1 = x4 + x3
  ============================
   x + x1 = x4 + x0

after. From V8.3, the quantified hypotheses are printed the sames as
they would be intro. However the hypothesis H remains printed
differently to avoid using the same name in autonomous but nested
subterms *)

Abort.

Goal forall x x1 x2 x3:nat,
  (forall x x3:nat, x+x1 = x2+x3 -> foo (S x + x1)) ->
   x+x1 = x2+x3 -> foo (S x).
Show.
unfold foo.
Show.
do 4 intro. (* --> x, x1, x4, x0, ... *)
Show.
do 2 intro.
Show.
do 4 intro.
Show.

(* Remark: in V8.2, this used to be printed

  x3 : nat
  ============================
   forall x x1 x4 x5 : nat,
   (forall x0 x6 : nat,
    x0 + x1 = x4 + x6 ->
    forall x7 x8 x9 S0 : nat, x7 + S0 = x8 + x9 + (S x0 + x1)) ->
   x + x1 = x4 + x5 -> forall x0 x6 x7 S0 : nat, x0 + S0 = x6 + x7 + S x

before the intros and

  x3 : nat
  x : nat
  x1 : nat
  x4 : nat
  x0 : nat
  H : forall x x3 : nat,
      x + x1 = x4 + x3 ->
      forall x0 x4 x5 S0 : nat, x0 + S0 = x4 + x5 + (S x + x1)
  H0 : x + x1 = x4 + x0
  x5 : nat
  x6 : nat
  x7 : nat
  S : nat
  ============================
   x5 + S = x6 + x7 + Datatypes.S x

after (note the x5/x0 and the S0/S) *)

Abort.

(* Check naming in hypotheses *)

Goal forall a, (a = 0 -> forall a, a = 0) -> a = 0.
intros.
Show.
apply H with (a:=a). (* test compliance with printing *)
Abort.

End A.

Module B.

(* Check valid/invalid implicit arguments *)
Definition f1 {x} (y:forall {x}, x=0) := x+0.
Definition f2 := (((fun x => 0):forall {x:nat}, nat), 0).
Definition f3 := fun {x} (y:forall {x}, x=0) => x+0.

Definition g1 {x} := match x with true => fun {x:bool} => x | false => fun x:bool => x end.
(* TODO: do not ignore the implicit here *)
Definition g2 '(x,y) {z} := x+y+z.

Definition h1 := fun x:nat => (fun {x} => x) 0.
Definition h2 := let g := forall {y}, y=0 in g.

Notation "∀ x .. y , P" := (forall x, .. (forall y, P) ..)
  (at level 200, x binder, y binder, right associativity,
  format "'[  ' '[  ' ∀  x  ..  y ']' ,  '/' P ']'") : type_scope.

Definition l1 := ∀ {x:nat} {y:nat}, x=0.

End B.