lean2/tests/lean/run/class5.lean

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