(** Derived functions dealing with polymorphic variants *)

val read : r ::: {Unit} -> t ::: Type -> folder r -> $(mapU t r) -> variant (mapU {} r) -> t
val write : r ::: {Unit} -> t ::: Type -> folder r -> $(mapU t r) -> variant (mapU {} r) -> t -> $(mapU t r)

val search : r ::: {Unit} -> t ::: Type -> (variant (mapU {} r) -> option t) -> folder r -> option t
val find : r ::: {Unit} -> (variant (mapU {} r) -> bool) -> folder r -> option (variant (mapU {} r))

val test : nm :: Name -> t ::: Type -> ts ::: {Type} -> [[nm] ~ ts] => folder ([nm = t] ++ ts)
                                                                    -> variant ([nm = t] ++ ts) -> option t
val testLess : nm :: Name -> t ::: Type -> ts ::: {Type} -> [[nm] ~ ts] => folder ts -> variant ([nm = t] ++ ts) -> option t

val weaken : r1 ::: {Type} -> r2 ::: {Type} -> [r1 ~ r2] => folder r1
             -> variant r1 -> variant (r1 ++ r2)

val testEq : K --> f :: (K -> Type) -> nm :: Name -> t ::: K -> ts ::: {K} -> r ::: {K} -> [[nm] ~ ts] =>
    Eq.eq r ([nm = t] ++ ts)
    -> folder r
    -> variant (map f r) -> option (f t)

val eq : r ::: {Unit} -> folder r -> variant (mapU {} r) -> variant (mapU {} r) -> bool

val makeEq : K --> f :: (K -> Type) -> nm :: Name -> t ::: K -> ts ::: {K} -> r ::: {K} -> [[nm] ~ ts] =>
    Eq.eq r ([nm = t] ++ ts)
    -> f t
    -> variant (map f r)

val mp : r ::: {Unit} -> t ::: Type -> folder r -> (variant (mapU {} r) -> t) -> $(mapU t r)

val fold : r ::: {Unit} -> t ::: Type -> folder r -> (variant (mapU {} r) -> t -> t) -> t -> t

val foldR : tr ::: Type -> r ::: {Unit} -> t ::: Type -> folder r -> (variant (mapU {} r) -> tr -> t -> t) -> $(mapU tr r) -> t -> t

val appR : m ::: (Type -> Type) -> monad m
           -> tr ::: Type -> r ::: {Unit} -> folder r -> (variant (mapU {} r) -> tr -> m {}) -> $(mapU tr r) -> m {}

val mapR : tr ::: Type -> t ::: Type -> r ::: {Unit} -> folder r -> (variant (mapU {} r) -> tr -> t) -> $(mapU tr r) -> $(mapU t r)

val destrR : K --> f :: (K -> Type) -> fr :: (K -> Type) -> t ::: Type
             -> (p :: K -> f p -> fr p -> t)
             -> r ::: {K} -> folder r -> variant (map f r) -> $(map fr r) -> t

val destr2R : K --> f1 :: (K -> Type) -> f2 :: (K -> Type) -> fr :: (K -> Type) -> t ::: Type
             -> (p :: K -> f1 p -> f2 p -> fr p -> t)
             -> r ::: {K} -> folder r -> variant (map f1 r) -> variant (map f2 r) -> $(map fr r) -> option t