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use super::type_app::*;

pub trait Functor : TypeAppGeneric
{
  fn fmap < A, B >
    ( fa: Applied < Self, A >,
      mapper: impl Fn (A) -> B,
    ) ->
      Applied < Self, B >
  where
    A: Send + 'static,
    B: Send + 'static,
  ;
}

pub trait Applicative
  : Functor
{
  fn apply < A, B, Func >
    ( fab : Applied < Self, Func >,
      fa : Applied < Self, A >
    ) ->
      Applied < Self, B >
  where
    Func : Fn (A) -> B,
    A: Send + 'static,
    B: Send + 'static,
  ;
}

pub trait Monad
  : Applicative
{
  fn bind < A, B >
    ( fa : Applied < Self, A >,
      cont : impl Fn (A) -> Applied < Self, B >
    ) ->
      Applied < Self, B >
  where
    A: Send + 'static,
    B: Send + 'static,
  ;
}

pub trait NaturalTransformation < F1, F2 >
where
  F1: TyCon,
  F2: TyCon,
{
  fn lift < A >
    ( fa: Applied < F1, A > )
    -> Applied < F2, A >
  where
    A: Send + 'static,
  ;
}