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(* 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) : nat_scope.
Notation "x * y" := (Nat.mul x y) (in custom myconstr at level 4) : nat_scope.
Notation "< x >" := x (in custom myconstr at level 3, x constr at level 10).
Check [ < 0 > + < 1 > * < 2 >].
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).
End D.
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