    ------------------------------------------------------------------------
    -- The Agda standard library
    --
    -- Right-biased universe-sensitive functor and monad instances for These.
    ------------------------------------------------------------------------

    -- To minimize the universe level of the RawFunctor, we require that
    -- elements of B are "lifted" to a copy of B at a higher universe level
    -- (a ⊔ b).
    -- See the Data.Product.Effectful.Examples for how this is done in a
    -- Product-based similar setting.

    -- This functor can be understood as a notion of computation which can
    -- either fail (that), succeed (this) or accumulate warnings whilst
    -- delivering a successful computation (these).

    -- It is a good alternative to Data.Product.Effectful when the notion
    -- of warnings does not have a neutral element (e.g. List⁺).

    {-# OPTIONS --cubical-compatible --safe #-}

    open import Level using (Level; _⊔_)
    open import Algebra.Bundles using (Semigroup)

    module Data.These.Effectful.Right (a : Level) {c ℓ} (W : Semigroup c ℓ) where

    open import Data.These.Base using (These; this; that; these; map₁; map₂; map)
    open import Effect.Applicative using (RawApplicative)
    open import Effect.Monad using (RawMonad)

    open Semigroup W
    open import Data.These.Effectful.Right.Base a Carrier public

    module _ {a b} {A : Set a} {B : Set b} where

    applicative : RawApplicative Theseᵣ
    applicative = record
      { rawFunctor = functor
      ; pure = this
      ; _<*>_  = ap
      } where

      ap : ∀ {A B}→ Theseᵣ (A → B) → Theseᵣ A → Theseᵣ B
      ap (this f)    t = map₁ f t
      ap (that w)    t = that w
      ap (these f w) t = map f (w ∙_) t

    monad : RawMonad Theseᵣ
    monad = record
      { rawApplicative = applicative
      ; _>>=_  = bind
      } where

      bind : ∀ {A B} → Theseᵣ A → (A → Theseᵣ B) → Theseᵣ B
      bind (this t)    f = f t
      bind (that w)    f = that w
      bind (these t w) f = map₂ (w ∙_) (f t)