77 lines
1.6 KiB
Text
77 lines
1.6 KiB
Text
prelude
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constant A.{l1 l2} : Type.{l1} → Type.{l2}
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check A
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definition tst.{l} (A : Type) (B : Type) (C : Type.{l}) : Type := A → B → C
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check tst
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constant group.{l} : Type.{l+1}
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constant carrier.{l} : group.{l} → Type.{l}
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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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context
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universe l
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universe 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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definition is_proj2 := ∀ x y, f x y = y
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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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definition is_proj2 := ∀ x y, f x y = y
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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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definition is_proj2 := ∀ x y, f x y = y
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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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