90a79a0b06
Now, `universe` may declare many universes. The goal is to make it consistent with the `variable` command
85 lines
1.6 KiB
Text
85 lines
1.6 KiB
Text
inductive L1.{u} (α : Type u)
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| nil
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| cons : α → L1 α → L1 α
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#check L1
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#check @L1.cons
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inductive L2.{u} (α : Type u)
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| nil
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| cons (head : α) (tail : L2 α)
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#check @L2.cons
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universe u v
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variable (α : Type u)
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inductive A (β : Type v)
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| nil {}
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| protected cons : α → β → A β → A β
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#check @A.cons
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#check A.nil Nat Bool
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mutual
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inductive isEven : Nat → Prop
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| z : isEven 0
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| s (n : Nat) : isOdd n → isEven (n+1)
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inductive isOdd : Nat → Prop
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| s (n : Nat) : isEven n → isOdd (n+1)
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end
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#check isEven
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#check isOdd.s
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#check @isEven.rec
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inductive V (α : Type _) : Nat → Type _
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| nil : V α 0
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| cons {n : Nat} : α → V α n → V α (n+1)
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#check @V.nil
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#check @V.cons
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#check @V.rec
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#check @V.noConfusion
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#check @V.brecOn
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#check @V.binductionOn
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#check @V.casesOn
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#check @V.recOn
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#check @V.below
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class inductive Dec (p : Prop) : Type
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| isTrue (h : p)
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| isFalse (h : Not p)
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instance tst : Dec True :=
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Dec.isTrue True.intro
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#check tst
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variable (β : Type _)
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inductive T1
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| mk : β → β → T1
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#check @T1.mk
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inductive MyEq {α : Type} (a : α) : α → Prop
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| refl : MyEq a a
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#check @MyEq.refl
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inductive ListLast {α : Type u} : List α → Type u
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| empty : ListLast []
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| nonEmpty : (as : List α) → (a : α) → ListLast (as ++ [a])
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-- make sure to instantiate mvars in constructors
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inductive Test : Nat → Type
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| mk : Test ((fun n => n.succ) Nat.zero)
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inductive SortedMap {α : Type u} {β : Type v} [LT α] : List (α × β) → Prop
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| nil : SortedMap []
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| cons : ∀ (k : α) (v : β) (l : List (α × β)),
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SortedMap l →
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SortedMap ((k,v)::l)
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