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70 lines
2.1 KiB
Idris
70 lines
2.1 KiB
Idris
module Dummy
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import Data.Vect
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namespace DList
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||| A list construct for dependent types.
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||| @aTy The type of the value contained within the list element type.
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||| @elemTy The type of the elements within the list
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||| @as The List used to contain the different values within the type.
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public export
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data DList : (aTy : Type)
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-> (elemTy : aTy -> Type)
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-> (as : List aTy)
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-> Type where
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||| Create an empty List
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Nil : DList aTy elemTy Nil
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||| Cons
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||| @elem The element to add
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||| @rest The list for `elem` to be added to.
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(::) : (elem : elemTy x)
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-> (rest : DList aTy elemTy xs)
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-> DList aTy elemTy (x::xs)
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namespace DVect
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||| A list construct for dependent types.
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||| @aTy The type of the value contained within the list element type.
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||| @elemTy The type of the elements within the list
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||| @len The length of the list.
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||| @as The List used to contain the different values within the type.
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public export
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data DVect : (aTy : Type)
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-> (elemTy : aTy -> Type)
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-> (len : Nat)
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-> (as : Vect len aTy)
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-> Type where
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||| Create an empty List
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Nil : DVect aTy elemTy Z Nil
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||| Cons
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||| @ex The element to add
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||| @rest The list for `elem` to be added to.
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(::) : (ex : elemTy x)
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-> (rest : DVect aTy elemTy n xs)
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-> DVect aTy elemTy (S n) (x::xs)
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namespace PList
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public export
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data PList : (aTy : Type)
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-> (elemTy : aTy -> Type)
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-> (predTy : aTy -> Type)
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-> (as : List aTy)
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-> (prf : DList aTy predTy as)
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-> Type
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where
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||| Create an empty List
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Nil : PList aTy elemTy predTy Nil Nil
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||| Cons
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||| @elem The element to add and proof that the element's type satisfies a certain predicate.
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||| @rest The list for `elem` to be added to.
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(::) : (elem : elemTy x)
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-> {prf : predTy x}
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-> (rest : PList aTy elemTy predTy xs prfs)
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-> PList aTy elemTy predTy (x :: xs) (prf :: prfs)
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