Notations4.v

(* An example with constr subentries *)

Module A.

Declare Custom Entry myconstr.

Notation "[ x ]" := x (x custom myconstr at level 6).
Notation "x + y" := (Nat.add x y) (in custom myconstr at level 5).
Notation "x * y" := (Nat.mul x y) (in custom myconstr at level 4).
Notation "< x >" := x (in custom myconstr at level 3, x constr at level 10).
Check [ < 0 > + < 1 > * < 2 >].
Print Custom Grammar myconstr.

Axiom a : nat.
Notation b := a.
Check [ < b > + < a > * < 2 >].

Declare Custom Entry anotherconstr.

Notation "[ x ]" := x (x custom myconstr at level 6).
Notation "<< x >>" := x (in custom myconstr at level 3, x custom anotherconstr at level 10).
Notation "# x" := (Some x) (in custom anotherconstr at level 8, x constr at level 9).
Check [ << # 0 >> ].

End A.

Module B.

Inductive Expr :=
 | Mul : Expr -> Expr -> Expr
 | Add : Expr -> Expr -> Expr
 | One : Expr.

Declare Custom Entry expr.
Notation "[ expr ]" := expr (expr custom expr at level 2).
Notation "1" := One (in custom expr at level 0).
Notation "x y" := (Mul x y) (in custom expr at level 1, left associativity).
Notation "x + y" := (Add x y) (in custom expr at level 2, left associativity).
Notation "( x )" := x (in custom expr at level 0, x at level 2).
Notation "{ x }" := x (in custom expr at level 0, x constr).
Notation "x" := x (in custom expr at level 0, x ident).

Axiom f : nat -> Expr.
Check [1 {f 1}].
Check fun x y z => [1 + y z + {f x}].
Check fun e => match e with
| [x y + z] => [x + y z]
| [1 + 1] => [1]
| y => [y + e]
end.

End B.

Module C.

Inductive Expr :=
 | Add : Expr -> Expr -> Expr
 | One : Expr.

Declare Custom Entry expr.
Notation "[ expr ]" := expr (expr custom expr at level 1).
Notation "1" := One (in custom expr at level 0).
Notation "x + y" := (Add x y) (in custom expr at level 2, left associativity).
Notation "( x )" := x (in custom expr at level 0, x at level 2).

(* Check the use of a two-steps coercion from constr to expr 1 then
   from expr 0 to expr 2 (note that camlp5 parsing is more tolerant
   and does not require parentheses to parse from level 2 while at
   level 1) *)

Check [1 + 1].

End C.

(* An example of interaction between coercion and notations from
   Robbert Krebbers. *)

Require Import String.

Module D.

Inductive expr :=
  | Var : string -> expr
  | Lam : string -> expr -> expr
  | App : expr -> expr -> expr.

Notation Let x e1 e2 := (App (Lam x e2) e1).

Parameter e1 e2 : expr.

Check (Let "x" e1 e2).

Coercion App : expr >-> Funclass.

Check (Let "x" e1 e2).

Axiom free_vars :> expr -> list string.

Check (Let "x" e1 e2) : list string.

End D.

(* Fixing bugs reported by G. Gonthier in #9207 *)

Module I.

Definition myAnd A B := A /\ B.
Notation myAnd1 A := (myAnd A).
Check myAnd1 True True.

Set Warnings "-auto-template".

Record Pnat := {inPnat :> nat -> Prop}.
Axiom r : nat -> Pnat.
Check r 2 3.

End I.

Require Import Coq.Numbers.Cyclic.Int63.Int63.
Module NumeralNotations.
  Module Test17.
    (** Test int63 *)
    Declare Scope test17_scope.
    Delimit Scope test17_scope with test17.
    Local Set Primitive Projections.
    Record myint63 := of_int { to_int : int }.
    Numeral Notation myint63 of_int to_int : test17_scope.
    Check let v := 0%test17 in v : myint63.
  End Test17.
End NumeralNotations.

Module K.

Notation "# x |-> t & u" := ((fun x => (x,t)),(fun x => (x,u)))
  (at level 0, x pattern, t, u at level 39).
Check fun y : nat => # (x,z) |-> y & y.
Check fun y : nat => # (x,z) |-> (x + y) & (y + z).

End K.

Module EmptyRecordSyntax.

Record R := { n : nat }.
Check fun '{|n:=x|} => true.

End EmptyRecordSyntax.

Module L.

(* Testing regression #11053 *)

Section Test.
Variables (A B : Type) (a : A) (b : B).
Variable c : A -> B.
Coercion c : A >-> B.
Notation COERCION := (c).
Check b = a.
End Test.

End L.

Module M.

(* Accept boxes around the end variables of a recursive notation (if equal boxes) *)

Notation " {@ T1 ; T2 ; .. ; Tn } " :=
  (and T1 (and T2 .. (and Tn True)..))
  (format "'[v' {@  '[' T1 ']'  ;  '//' '['  T2  ']'  ;  '//' ..  ;   '//' '['  Tn  ']'  } ']'").

Fail Notation " {@ T1 ; T2 ; .. ; Tn } " :=
  (and T1 (and T2 .. (and Tn True)..))
  (format "'[v' {@  '[' T1 ']'  ;  '//' '['  T2  ']'  ;  '//' ..  ;   '//' '['  Tn   ']'  } ']'").

Fail Notation " {@ T1 ; T2 ; .. ; Tn } " :=
  (and T1 (and T2 .. (and Tn True)..))
  (format "'[v' {@  '[' T1 ']'  ;  '//' '['  T2  ']'  ;  '//' ..  ;   '//' '[v'  Tn  ']'  } ']'").

Fail Notation " {@ T1 ; T2 ; .. ; Tn } " :=
  (and T1 (and T2 .. (and Tn True)..))
  (format "'[v' {@  '[' T1 ']'  ;  '//' '['  T2  ']'  ;  '//' ..  ;   '//' '['   Tn  ']'  } ']'").

Fail Notation " {@ T1 ; T2 ; .. ; Tn } " :=
  (and T1 (and T2 .. (and Tn True)..))
  (format "'[v' {@  '[' T1 ']'  ;  '//' '['  T2  ']'   ;  '//' ..  ;   '//' '['  Tn  ']'  } ']'").

End M.

Module Bug11331.

Declare Custom Entry expr.
Notation "{ p }" := (p) (in custom expr at level 201, p constr).
Print Custom Grammar expr.

End Bug11331.

Module Bug_6082.

Declare Scope foo.
Notation "[ x ]" := (S x) (format "[  x  ]") : foo.
Open Scope foo.
Check fun x => S x.

Declare Scope bar.
Notation "[ x ]" := (S x) (format "[ x ]") : bar.
Open Scope bar.

Check fun x => S x.

End Bug_6082.

Module Bug_7766.

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

Check forall (x : nat), x = x.

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

Check forall (x : nat), x = x.

End Bug_7766.

Module N.

(* Other tests about generic and specific formats *)

Reserved Notation "x %%% y" (format "x  %%%  y", at level 35).
Reserved Notation "x %%% y" (format "x %%% y", at level 35).

(* Not using the reserved format, we warn *)

Notation "x %%% y" := (x+y) (format "x   %%%   y", at level 35).

(* Same scope (here lonely): we warn *)

Notation "x %%%% y" := (x+y) (format "x  %%%%  y", at level 35).
Notation "x %%%% y" := (x+y) (format "x %%%% y", at level 35).

(* Test if the format for a specific notation becomes the default
   generic format or if the generic format, in the absence of a
   Reserved Notation, is the one canonically obtained from the
   notation *)

Declare Scope foo_scope.
Declare Scope bar_scope.
Declare Scope bar'_scope.
Notation "x %% y" := (x+y) (at level 47, format "x   %%   y") : foo_scope.
Open Scope foo_scope.
Check 3 %% 4.

(* No scope, we inherit the initial format *)

Notation "x %% y" := (x*y) : bar_scope. (* Inherit the format *)
Open Scope bar_scope.
Check 3 %% 4.

(* Different scope and no reserved notation, we don't warn *)

Notation "x %% y" := (x*y) (at level 47, format "x    %%    y") : bar'_scope.
Open Scope bar'_scope.
Check 3 %% 4.

(* Warn for combination of "only parsing" and "format" *)

Notation "###" := 0 (at level 0, only parsing, format "###").

(* In reserved notation, warn only for the "only parsing" *)

Reserved Notation "##" (at level 0, only parsing, format "##").

End N.