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+(* This file is giving some examples about how implicit arguments and
+   scopes are treated when using abbreviations or notations, in terms
+   or patterns, or when using @ and parentheses in terms and patterns.
+
+The convention is:
+
+Constant foo with implicit arguments and scopes used in a term or a pattern:
+
+       foo      do not deactivate further arguments and scopes
+       @foo     deactivates further arguments and scopes
+       (foo x)  deactivates further arguments and scopes
+       (@foo x) deactivates further arguments and scopes
+
+Notations binding to foo:
+
+#   := foo      do not deactivate further arguments and scopes
+#   := @foo     deactivates further arguments and scopes
+# x := foo x    deactivates further arguments and scopes
+# x := @foo x   deactivates further arguments and scopes
+
+Abbreviations binding to foo:
+
+f   := foo      do not deactivate further arguments and scopes
+f   := @foo     deactivates further arguments and scopes
+f x := foo x    do not deactivate further arguments and scopes
+f x := @foo x   do not deactivate further arguments and scopes
+*)
+
+(* One checks that abbreviations and notations in patterns now behave like in terms *)
+
+Inductive prod' A : Type -> Type :=
+| pair' (a:A) B (b:B) (c:bool) : prod' A B.
+Arguments pair' [A] a%bool_scope [B] b%bool_scope c%bool_scope.
+Notation "0" := true : bool_scope.
+
+(* 1. Abbreviations do not stop implicit arguments to be inserted and scopes to be used *)
+Notation c1 x := (pair' x).
+Check pair' 0 0 0 : prod' bool bool.
+Check (pair' 0) _ 0%bool 0%bool : prod' bool bool. (* parentheses are blocking implicit and scopes *)
+Check c1 0 0 0 : prod' bool bool.
+Check fun x : prod' bool bool => match x with c1 0 y 0 => 2 | _ => 1 end.
+
+(* 2. Abbreviations do not stop implicit arguments to be inserted and scopes to be used *)
+Notation c2 x := (@pair' _ x).
+Check (@pair' _ 0) _ 0%bool 0%bool : prod' bool bool. (* parentheses are blocking implicit and scopes *)
+Check c2 0 0 0 : prod' bool bool.
+Check fun A (x : prod' bool A) => match x with c2 0 y 0 => 2 | _ => 1 end.
+Check fun A (x : prod' bool A) => match x with (@pair' _ 0) _ y 0%bool => 2 | _ => 1 end.
+
+(* 3. Abbreviations do not stop implicit arguments to be inserted and scopes to be used *)
+Notation c3 x := ((@pair') _ x).
+Check (@pair') _ 0%bool _ 0%bool 0%bool : prod' bool bool. (* @ is blocking implicit and scopes *)
+Check ((@pair') _ 0%bool) _ 0%bool 0%bool : prod' bool bool. (* parentheses and @ are blocking implicit and scopes *)
+Check c3 0 0 0 : prod' nat bool. (* First scope is blocked but not the last two scopes *)
+Check fun A (x :prod' nat A) => match x with c3 0 y 0 => 2 | _ => 1 end.
+
+(* 4. Abbreviations do not stop implicit arguments to be inserted and scopes to be used *)
+(* unless an atomic @ is given *)
+Notation c4 := (@pair').
+Check (@pair') _ 0%bool _ 0%bool 0%bool : prod' bool bool.
+Check c4 _ 0%bool _ 0%bool 0%bool : prod' bool bool.
+Check fun A (x :prod' bool A) => match x with c4 _ 0%bool _ y 0%bool => 2 | _ => 1 end.
+Check fun A (x :prod' bool A) => match x with (@pair') _ 0%bool _ y 0%bool => 2 | _ => 1 end.
+
+(* 5. Notations stop further implicit arguments to be inserted and scopes to be used *)
+Notation "# x" := (pair' x) (at level 0, x at level 1).
+Check pair' 0 0 0 : prod' bool bool.
+Check # 0 _ 0%bool 0%bool : prod' bool bool.
+Check fun A (x :prod' bool A) => match x with # 0 _ y 0%bool => 2 | _ => 1 end.
+
+(* 6. Notations stop further implicit arguments to be inserted and scopes to be used *)
+Notation "## x" := ((@pair') _ x) (at level 0, x at level 1).
+Check (@pair') _ 0%bool _ 0%bool 0%bool : prod' bool bool.
+Check ((@pair') _ 0%bool) _ 0%bool 0%bool : prod' bool bool.
+Check ## 0%bool _ 0%bool 0%bool : prod' bool bool.
+Check fun A (x :prod' bool A) => match x with ## 0%bool _ y 0%bool => 2 | _ => 1 end.
+
+(* 7. Notations stop further implicit arguments to be inserted and scopes to be used *)
+Notation "###" := (@pair') (at level 0).
+Check (@pair') _ 0%bool _ 0%bool 0%bool : prod' bool bool.
+Check ### _ 0%bool _ 0%bool 0%bool : prod' bool bool.
+Check fun A (x :prod' bool A) => match x with ### _ 0%bool _ y 0%bool => 2 | _ => 1 end.
+
+(* 8. Notations w/o @ preserves implicit arguments and scopes *)
+Notation "####" := pair' (at level 0).
+Check #### 0 0 0 : prod' bool bool.
+Check fun A (x :prod' bool A) => match x with #### 0 y 0 => 2 | _ => 1 end.
+
+(* 9. Notations w/o @ but arguments do not preserve further implicit arguments and scopes *)
+Notation "##### x" := (pair' x) (at level 0, x at level 1).
+Check ##### 0 _ 0%bool 0%bool : prod' bool bool.
+Check fun A (x :prod' bool A) => match x with ##### 0 _ y 0%bool => 2 | _ => 1 end.