```------------------------------------------------------------------------
-- The Agda standard library
--
------------------------------------------------------------------------

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

{-# OPTIONS --without-K --safe #-}

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

private
variable
a b c i f : Level
A : Set a
B : Set b
C : Set c
I : Set i

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

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

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

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

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

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

join : ∀ {i j k} → 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

RawIMonadT : {I : Set i} (T : IFun I f → IFun I f) → Set (i ⊔ suc f)

record RawIMonadZero {I : Set i} (M : IFun I f) : Set (i ⊔ suc f) where
field
applicativeZero : RawIApplicativeZero M

open RawIApplicativeZero applicativeZero using (∅) public

record RawIMonadPlus {I : Set i} (M : IFun I f) : Set (i ⊔ suc f) where
field