79 lines
1.8 KiB
Text
79 lines
1.8 KiB
Text
prelude
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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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universe variables u v
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variables {T1 T2 : Type u}
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variable {T3 : Type v}
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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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