module Prelude

data Nat : U where
  Z : Nat
  S : Nat -> Nat

data Maybe : U -> U where
  Just : {a : U} -> a -> Maybe a
  Nothing : {a : U} -> Maybe a

data Either : U -> U -> U where
  Left : {a b : U} -> a -> Either a b
  Right : {a b : U} -> b -> Either a b

-- TODO this is special cased in some languages, maybe for easier
-- inference? Figure out why.

infixr 0 _$_

-- Currently very noisy in generated code
_$_ : {a b : U} -> (a -> b) -> a -> b
f $ a = f a


-- Monad

-- TODO stack with Applicative, etc?

data Monad : (U -> U) -> U where
  MkMonad : { M : U -> U } ->
            (bind : {A B : U} -> (M A) -> (A -> M B) -> M B) ->
            (pure : {A : U} -> A -> M A) ->
            Monad M

infixl 1 _>>=_ _>>_
_>>=_ : {a b : U} -> {m : U -> U} -> {{x : Monad m}} -> (m a) -> (a -> m b) -> m b
_>>=_ {a} {b} {m} {{MkMonad bind' _}}  ma amb = bind' {a} {b} ma amb

_>>_ : {a b : U} -> {m : U -> U} -> {{x : Monad m}} -> m a -> m b -> m b
ma >> mb = mb

pure : {a : U} {m : U -> U} {{_ : Monad m}} -> a -> m a
pure {_} {_} {{MkMonad _ pure'}} a = pure' a

-- IO