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The ports are rather straight forward and I have purposefully written the documentation to be beginner friendly. Note, I have diverged from Idris1 over the naming of the projection functions to make them consistent with `Pair` and `DPair`.
97 lines
3.0 KiB
Idris
97 lines
3.0 KiB
Idris
module Data.DPair
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%default total
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namespace Exists
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||| A dependent pair in which the first field (witness) should be
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||| erased at runtime.
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|||
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||| We can use `Exists` to construct dependent types in which the
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||| type-level value is erased at runtime but used at compile time.
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||| This type-level value could represent, for instance, a value
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||| required for an intrinsic invariant required as part of the
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||| dependent type's representation.
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|||
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||| @type The type of the type-level value in the proof.
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||| @this The dependent type that requires an instance of `type`.
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public export
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data Exists : (this : type -> Type) -> Type where
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Evidence : (0 value : type)
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-> (prf : this value)
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-> Exists this
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||| Return the type-level value (evidence) required by the dependent type.
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|||
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||| We need to be in the Erased setting for this to work.
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|||
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||| @type The type-level value's type.
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||| @pred The dependent type that requires an instance of `type`.
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||| @prf That there is a value that satisfies `prf`.
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public export
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0
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fst : {0 type : Type}
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-> {0 pred : type -> Type}
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-> (1 prf : Exists pred)
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-> type
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fst (Evidence value _) = value
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||| Return the dependently typed value.
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|||
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||| @type The type-level value's type.
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||| @pred The dependent type that requires an instance of `type`.
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||| @prf That there is a value that satisfies `prf`.
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public export
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snd : {0 type : Type}
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-> {0 pred : type -> Type}
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-> (1 prf : Exists pred)
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-> pred (Exists.fst prf)
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snd (Evidence value prf) = prf
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namespace Subset
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||| A dependent pair in which the second field (evidence) should not
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||| be required at runtime.
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|||
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||| We can use `Subset` to provide extrinsic invariants about a
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||| value and know that these invariants are erased at
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||| runtime but used at compile time.
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||| @type The type-level value's type.
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||| @pred The dependent type that requires an instance of `type`.
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public export
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data Subset : (type : Type)
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-> (pred : type -> Type)
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-> Type
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where
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Element : (value : type)
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-> (0 prf : pred value)
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-> Subset type pred
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||| Return the type-level value (evidence) required by the dependent type.
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|||
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||| @type The type-level value's type.
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||| @pred The dependent type that requires an instance of `type`.
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||| @prf That there is a value that satisfies `prf`.
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public export
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fst : {0 type : Type}
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-> {0 pred : type -> Type}
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-> (1 prf : Subset type pred)
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-> type
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fst (Element value prf) = value
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||| Return the dependently typed value.
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||| We need to be in the erased setting for this to work.
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||| @type The type-level value's type.
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||| @pred The dependent type that requires an instance of `type`.
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||| @prf That there is a value that satisfies `prf`.
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public export
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0
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snd : {0 type : Type}
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-> {0 pred : type -> Type}
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-> (1 value : Subset type pred)
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-> pred (Subset.fst value)
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snd (Element value prf) = prf
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