90bfd84a07
In the standard library, we should use explicit universe variables for universe polymorphic definitions. Users that want to declare universe polymorphic definitions but do not want to provide universe level parameters should use Type _ or Type*
79 lines
1.8 KiB
Text
79 lines
1.8 KiB
Text
prelude
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set_option new_elaborator true
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constant {l1 l2} A : Type l1 → Type l2
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check A
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definition {l} tst (A : Type*) (B : Type*) (C : Type l) : Type* := A → B → C
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check tst
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constant {l} group : Type (l+1)
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constant {l} carrier : group.{l} → Type l
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noncomputable definition to_carrier (g : group) := carrier g
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check to_carrier.{1}
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section
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variable A : Type*
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check A
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definition B := A → A
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end
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constant N : Type 1
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check B N
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constant f : B N
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check f
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constant a : N
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check f a
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section
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variable T1 : Type*
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variable T2 : Type*
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variable f : T1 → T2 → T2
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definition double (a : T1) (b : T2) := f a (f a b)
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end
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check double
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check double.{1 2}
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definition Prop := Type 0
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constant eq : Π {A : Type*}, A → A → Prop
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infix `=`:50 := eq
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check eq.{1}
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section
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universe variable l
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universe variable u
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variable {T1 : Type l}
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variable {T2 : Type l}
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variable {T3 : Type u}
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variable f : T1 → T2 → T2
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noncomputable definition is_proj2 := ∀ x y, f x y = y
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noncomputable definition is_proj3 (f : T1 → T2 → T3 → T3) := ∀ x y z, f x y z = z
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end
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check @is_proj2.{1}
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check @is_proj3.{1 2}
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namespace foo
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section
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variables {T1 T2 : Type*}
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variable {T3 : Type*}
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variable f : T1 → T2 → T2
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noncomputable definition is_proj2 := ∀ x y, f x y = y
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noncomputable definition is_proj3 (f : T1 → T2 → T3 → T3) := ∀ x y z, f x y z = z
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end
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check @foo.is_proj2.{1}
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check @foo.is_proj3.{1 2}
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end foo
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namespace bla
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section
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variable {T1 : Type*}
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variable {T2 : Type*}
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variable {T3 : Type*}
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variable f : T1 → T2 → T2
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noncomputable definition is_proj2 := ∀ x y, f x y = y
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noncomputable definition is_proj3 (f : T1 → T2 → T3 → T3) := ∀ x y z, f x y z = z
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end
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check @bla.is_proj2.{1 2}
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check @bla.is_proj3.{1 2 3}
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end bla
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