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https://github.com/idris-lang/Idris2.git
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108 lines
3.2 KiB
Idris
108 lines
3.2 KiB
Idris
module Data.DPair
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%default total
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namespace DPair
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public export
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curry : {0 p : a -> Type} -> ((x : a ** p x) -> c) -> (x : a) -> p x -> c
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curry f x y = f (x ** y)
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public export
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uncurry : {0 p : a -> Type} -> ((x : a) -> p x -> c) -> (x : a ** p x) -> c
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uncurry f s = f s.fst s.snd
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public export
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bimap : {0 p : a -> Type} -> {0 q : b -> Type} -> (f : a -> b) -> (forall x. p x -> q (f x)) -> (x : a ** p x) -> (y : b ** q y)
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bimap f g (x ** y) = (f x ** g y)
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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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||| @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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record Exists {0 type : Type} this where
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constructor Evidence
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0 fst : type
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snd : this fst
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public export
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curry : {0 p : a -> Type} -> (Exists p -> c) -> ({0 x : a} -> p x -> c)
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curry f = f . Evidence _
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public export
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uncurry : {0 p : a -> Type} -> ({0 x : a} -> p x -> c) -> Exists p -> c
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uncurry f ex = f ex.snd
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export
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evidenceInjectiveFst : Evidence x p = Evidence y q -> x = y
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evidenceInjectiveFst Refl = Refl
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export
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evidenceInjectiveSnd : Evidence x p = Evidence x q -> p = q
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evidenceInjectiveSnd Refl = Refl
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public export
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bimap : (0 f : a -> b) -> (forall x. p x -> q (f x)) -> Exists {type=a} p -> Exists {type=b} q
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bimap f g (Evidence x y) = Evidence (f x) (g y)
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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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||| 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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record Subset type pred where
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constructor Element
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fst : type
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0 snd : pred fst
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public export
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curry : {0 p : a -> Type} -> (Subset a p -> c) -> (x : a) -> (0 _ : p x) -> c
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curry f x y = f $ Element x y
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public export
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uncurry : {0 p : a -> Type} -> ((x : a) -> (0 _ : p x) -> c) -> Subset a p -> c
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uncurry f s = f s.fst s.snd
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export
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elementInjectiveFst : Element x p = Element y q -> x = y
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elementInjectiveFst Refl = Refl
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export
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elementInjectiveSnd : Element x p = Element x q -> p = q
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elementInjectiveSnd Refl = Refl
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public export
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bimap : (f : a -> b) -> (0 _ : forall x. p x -> q (f x)) -> Subset a p -> Subset b q
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bimap f g (Element x y) = Element (f x) (g y)
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public export
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Eq type => Eq (Subset type pred) where
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(==) = (==) `on` fst
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public export
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Ord type => Ord (Subset type pred) where
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compare = compare `on` fst
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||| This Show implementation replaces the (erased) invariant
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||| with an underscore.
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export
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Show type => Show (Subset type pred) where
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showPrec p (Element v _) = showCon p "Element" $ showArg v ++ " _"
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