mirror of
https://github.com/idris-lang/Idris2.git
synced 2024-12-21 02:31:50 +03:00
108 lines
3.2 KiB
Idris
108 lines
3.2 KiB
Idris
module Data.DPair
|
|
|
|
%default total
|
|
|
|
namespace DPair
|
|
|
|
public export
|
|
curry : {0 p : a -> Type} -> ((x : a ** p x) -> c) -> (x : a) -> p x -> c
|
|
curry f x y = f (x ** y)
|
|
|
|
public export
|
|
uncurry : {0 p : a -> Type} -> ((x : a) -> p x -> c) -> (x : a ** p x) -> c
|
|
uncurry f s = f s.fst s.snd
|
|
|
|
public export
|
|
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)
|
|
bimap f g (x ** y) = (f x ** g y)
|
|
|
|
namespace Exists
|
|
|
|
||| A dependent pair in which the first field (witness) should be
|
|
||| erased at runtime.
|
|
|||
|
|
||| We can use `Exists` to construct dependent types in which the
|
|
||| type-level value is erased at runtime but used at compile time.
|
|
||| This type-level value could represent, for instance, a value
|
|
||| required for an intrinsic invariant required as part of the
|
|
||| dependent type's representation.
|
|
|||
|
|
||| @type The type of the type-level value in the proof.
|
|
||| @this The dependent type that requires an instance of `type`.
|
|
public export
|
|
record Exists {0 type : Type} this where
|
|
constructor Evidence
|
|
0 fst : type
|
|
snd : this fst
|
|
|
|
public export
|
|
curry : {0 p : a -> Type} -> (Exists p -> c) -> ({0 x : a} -> p x -> c)
|
|
curry f = f . Evidence _
|
|
|
|
public export
|
|
uncurry : {0 p : a -> Type} -> ({0 x : a} -> p x -> c) -> Exists p -> c
|
|
uncurry f ex = f ex.snd
|
|
|
|
export
|
|
evidenceInjectiveFst : Evidence x p = Evidence y q -> x = y
|
|
evidenceInjectiveFst Refl = Refl
|
|
|
|
export
|
|
evidenceInjectiveSnd : Evidence x p = Evidence x q -> p = q
|
|
evidenceInjectiveSnd Refl = Refl
|
|
|
|
public export
|
|
bimap : (0 f : a -> b) -> (forall x. p x -> q (f x)) -> Exists {type=a} p -> Exists {type=b} q
|
|
bimap f g (Evidence x y) = Evidence (f x) (g y)
|
|
|
|
namespace Subset
|
|
|
|
||| A dependent pair in which the second field (evidence) should not
|
|
||| be required at runtime.
|
|
|||
|
|
||| We can use `Subset` to provide extrinsic invariants about a
|
|
||| value and know that these invariants are erased at
|
|
||| runtime but used at compile time.
|
|
|||
|
|
||| @type The type-level value's type.
|
|
||| @pred The dependent type that requires an instance of `type`.
|
|
public export
|
|
record Subset type pred where
|
|
constructor Element
|
|
fst : type
|
|
0 snd : pred fst
|
|
|
|
public export
|
|
curry : {0 p : a -> Type} -> (Subset a p -> c) -> (x : a) -> (0 _ : p x) -> c
|
|
curry f x y = f $ Element x y
|
|
|
|
public export
|
|
uncurry : {0 p : a -> Type} -> ((x : a) -> (0 _ : p x) -> c) -> Subset a p -> c
|
|
uncurry f s = f s.fst s.snd
|
|
|
|
export
|
|
elementInjectiveFst : Element x p = Element y q -> x = y
|
|
elementInjectiveFst Refl = Refl
|
|
|
|
export
|
|
elementInjectiveSnd : Element x p = Element x q -> p = q
|
|
elementInjectiveSnd Refl = Refl
|
|
|
|
public export
|
|
bimap : (f : a -> b) -> (0 _ : forall x. p x -> q (f x)) -> Subset a p -> Subset b q
|
|
bimap f g (Element x y) = Element (f x) (g y)
|
|
|
|
public export
|
|
Eq type => Eq (Subset type pred) where
|
|
(==) = (==) `on` fst
|
|
|
|
public export
|
|
Ord type => Ord (Subset type pred) where
|
|
compare = compare `on` fst
|
|
|
|
||| This Show implementation replaces the (erased) invariant
|
|
||| with an underscore.
|
|
export
|
|
Show type => Show (Subset type pred) where
|
|
showPrec p (Element v _) = showCon p "Element" $ showArg v ++ " _"
|