import logic namespace algebra inductive mul_struct (A : Type) : Type := mk : (A → A → A) → mul_struct A definition mul {A : Type} {s : mul_struct A} (a b : A) := mul_struct.rec (λ f, f) s a b infixl `*`:75 := mul end algebra namespace nat inductive nat : Type := zero : nat, succ : nat → nat constant mul : nat → nat → nat constant add : nat → nat → nat definition mul_struct [instance] : algebra.mul_struct nat := algebra.mul_struct.mk mul end nat section open algebra nat parameters a b c : nat check a * b * c definition tst1 : nat := a * b * c end section open [notation] algebra open nat -- check mul_struct nat << This is an error, we are open only the notation from algebra parameters a b c : nat check a * b * c definition tst2 : nat := a * b * c end section open nat -- check mul_struct nat << This is an error, we are open only the notation from algebra parameters a b c : nat check #algebra a*b*c definition tst3 : nat := #algebra a*b*c end section open nat set_option pp.implicit true definition add_struct [instance] : algebra.mul_struct nat := algebra.mul_struct.mk add parameters a b c : nat check #algebra a*b*c -- << is open add instead of mul definition tst4 : nat := #algebra a*b*c end