38 lines
862 B
Text
38 lines
862 B
Text
inductive nat : Type :=
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zero : nat,
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succ : nat → nat
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namespace nat end nat open nat
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inductive list (A : Type) : Type :=
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nil {} : list A,
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cons : A → list A → list A
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abbreviation nil := @list.nil
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abbreviation cons := @list.cons
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check nil
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check nil.{1}
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check @nil.{1} nat
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check @nil nat
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check cons nat.zero nil
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inductive vector (A : Type) : nat → Type :=
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vnil {} : vector A zero,
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vcons : forall {n : nat}, A → vector A n → vector A (succ n)
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namespace vector end vector open vector
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check vcons zero vnil
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variable n : nat
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check vcons n vnil
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check vector.rec
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definition vector_to_list {A : Type} {n : nat} (v : vector A n) : list A
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:= vector.rec (@nil A) (fun (n : nat) (a : A) (v : vector A n) (l : list A), cons a l) v
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coercion vector_to_list
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variable f : forall {A : Type}, list A → nat
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check f (cons zero nil)
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check f (vcons zero vnil)
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