{-# OPTIONS --without-K #-}
module Class.Monad.Core where
 
open import Class.Prelude
open import Class.Core
open import Class.Functor
open import Class.Applicative
 
record Monad (M : Type↑) : Typeω where
  infixl  _>>=_ _>>_ _>=>_
  infixr  _=<<_ _<=<_
 
  field
    return : A → M A
    _>>=_  : M A → (A → M B) → M B
 
  _>>_ : M A → M B → M B
  m₁ >> m₂ = m₁ >>= λ _ → m₂
 
  _=<<_ : (A → M B) → M A → M B
  f =<< c = c >>= f
 
  _>=>_ : (A → M B) → (B → M C) → (A → M C)
  f >=> g = _=<<_ g ∘ f
 
  _<=<_ : (B → M C) → (A → M B) → (A → M C)
  g <=< f = f >=> g
 
  join : M (M A) → M A
  join m = m >>= id
 
  Functor-M : Functor M
  Functor-M = λ where ._<$>_ f x → return ∘ f =<< x
 
  instance _ = Functor-M
 
  mapM : (A → M B) → List A → M (List B)
  mapM f []       = return []
  mapM f (x ∷ xs) = do y ← f x; y ∷_ <$> mapM f xs
 
  concatMapM : (A → M (List B)) → List A → M (List B)
  concatMapM f xs = concat <$> mapM f xs
 
  forM : List A → (A → M B) → M (List B)
  forM []       _ = return []
  forM (x ∷ xs) f = do y ← f x; y ∷_ <$> forM xs f
 
  concatForM : List A → (A → M (List B)) → M (List B)
  concatForM xs f = concat <$> forM xs f
 
  return⊤ void : M A → M ⊤
  return⊤ k = k >> return tt
  void = return⊤
 
  filterM : (A → M Bool) → List A → M (List A)
  filterM _ [] = return []
  filterM p (x ∷ xs) = do
    b ← p x
    ((if b then [ x ] else []) ++_) <$> filterM p xs
 
  traverseM : ⦃ Applicative M ⦄ → ⦃ Monad M ⦄ → (A → M B) → List A → M (List B)
  traverseM f = λ where
    [] → return []
    (x ∷ xs) → ⦇ f x ∷ traverseM f xs ⦈
open Monad ⦃...⦄ public