```------------------------------------------------------------------------
------------------------------------------------------------------------

{-# OPTIONS --universe-polymorphism #-}

-- Note that currently the monad laws are not included here.

open import Category.Applicative.Indexed
open import Function
open import Level

record RawIMonad {i f} {I : Set i} (M : IFun I f) :
Set (i ⊔ suc f) where
infixl 1 _>>=_ _>>_
infixr 1 _=<<_

field
return : ∀ {i A} → A → M i i A
_>>=_  : ∀ {i j k A B} → M i j A → (A → M j k B) → M i k B

_>>_ : ∀ {i j k A B} → M i j A → M j k B → M i k B
m₁ >> m₂ = m₁ >>= λ _ → m₂

_=<<_ : ∀ {i j k A B} → (A → M j k B) → M i j A → M i k B
f =<< c = c >>= f

join : ∀ {i j k A} → M i j (M j k A) → M i k A
join m = m >>= id

rawIApplicative : RawIApplicative M
rawIApplicative = record
{ pure = return
; _⊛_  = λ f x → f >>= λ f' → x >>= λ x' → return (f' x')
}

open RawIApplicative rawIApplicative public

record RawIMonadZero {i f} {I : Set i} (M : IFun I f) :
Set (i ⊔ suc f) where
field
∅     : ∀ {i j A} → M i j A

record RawIMonadPlus {i f} {I : Set i} (M : IFun I f) :
Set (i ⊔ suc f) where
infixr 3 _∣_
field
_∣_       : ∀ {i j A} → M i j A → M i j A → M i j A