Special variants of DPair as records (#922)

libs/base/Data/DPair.idr

@@ -16,37 +16,10 @@ namespace Exists
   ||| @type The type of the type-level value in the proof.
   ||| @this The dependent type that requires an instance of `type`.
   public export
-  data Exists : (this : type -> Type) -> Type where
+  record Exists {0 type : _} this where
-    Evidence : (0 value : type)
+    constructor Evidence
-            -> (prf : this value)
+    0 fst : type
-            -> Exists this
+    snd : this fst
-
-  ||| Return the type-level value (evidence) required by the dependent type.
-  |||
-  ||| We need to be in the Erased setting for this to work.
-  |||
-  ||| @type The type-level value's type.
-  ||| @pred The dependent type that requires an instance of `type`.
-  ||| @prf  That there is a value that satisfies `prf`.
-  public export
-  0
-  fst : {0 type : Type}
-     -> {0 pred : type -> Type}
-     -> (1 prf  : Exists pred)
-     -> type
-  fst (Evidence value _) = value
-
-  ||| Return the dependently typed value.
-  |||
-  ||| @type The type-level value's type.
-  ||| @pred The dependent type that requires an instance of `type`.
-  ||| @prf  That there is a value that satisfies `prf`.
-  public export
-  snd : {0 type : Type}
-     -> {0 pred : type -> Type}
-     -> (1 prf  : Exists pred)
-     -> pred (Exists.fst prf)
-  snd (Evidence value prf) = prf
 
 namespace Subset
 
@@ -60,37 +33,7 @@ namespace Subset
   ||| @type The type-level value's type.
   ||| @pred The dependent type that requires an instance of `type`.
   public export
-  data Subset : (type : Type)
+  record Subset type pred where
-             -> (pred : type -> Type)
+    constructor Element
-             -> Type
+    fst : type
-    where
+    0 snd : pred fst
-      Element : (value : type)
-             -> (0 prf : pred value)
-             -> Subset type pred
-
-  ||| Return the type-level value (evidence) required by the dependent type.
-  |||
-  ||| @type The type-level value's type.
-  ||| @pred The dependent type that requires an instance of `type`.
-  ||| @prf  That there is a value that satisfies `prf`.
-  public export
-  fst : {0 type : Type}
-     -> {0 pred : type -> Type}
-     -> (1 prf  : Subset type pred)
-     -> type
-  fst (Element value prf) = value
-
-  ||| Return the dependently typed value.
-  |||
-  ||| We need to be in the erased setting for this to work.
-  |||
-  ||| @type The type-level value's type.
-  ||| @pred The dependent type that requires an instance of `type`.
-  ||| @prf  That there is a value that satisfies `prf`.
-  public export
-  0
-  snd : {0 type : Type}
-     -> {0 pred : type -> Type}
-     -> (1 value : Subset type pred)
-     -> pred (Subset.fst value)
-  snd (Element value prf) = prf