31 lines
657 B
Text
31 lines
657 B
Text
prelude
|
|
inductive nat : Type
|
|
| zero : nat
|
|
| succ : nat → nat
|
|
namespace nat end nat open nat
|
|
|
|
inductive list (A : Type) : Type
|
|
| nil {} : list
|
|
| cons : A → list → list
|
|
namespace list end list open list
|
|
|
|
check nil
|
|
check nil.{1}
|
|
check @nil.{1} nat
|
|
check @nil nat
|
|
|
|
check cons zero nil
|
|
|
|
inductive vector (A : Type) : nat → Type
|
|
| vnil {} : vector zero
|
|
| vcons : forall {n : nat}, A → vector n → vector (succ n)
|
|
namespace vector end vector open vector
|
|
|
|
check vcons zero vnil
|
|
constant n : nat
|
|
check vcons n vnil
|
|
|
|
check vector.rec
|
|
|
|
definition vector_to_list {A : Type} {n : nat} (v : vector A n) : list A
|
|
:= vector.rec nil (fun n a v l, cons a l) v
|