    module Agda.Utils.Function where

    -- | Repeat a state transition @f :: a -> (b, a)@ with output @b@
    --   while condition @cond@ on the output is true.
    --   Return all intermediate results and the final result
    --   where @cond@ is @False@.
    --
    --   Postconditions (when it terminates):
    --   @fst (last (iterWhile cond f a)) == False@.
    --   @all fst (init (interWhile cond f a))@.

    iterWhile :: (b -> Bool) -> (a -> (b, a)) -> a -> [(b,a)]
    iterWhile :: forall b a. (b -> Bool) -> (a -> (b, a)) -> a -> [(b, a)]
    iterWhile b -> Bool
    cond a -> (b, a)
    f = a -> [(b, a)]
    loop where
      loop :: a -> [(b, a)]
    loop a
    a = (b, a)
    r (b, a) -> [(b, a)] -> [(b, a)]
    forall a. a -> [a] -> [a]
    : if b -> Bool
    cond b
    b then a -> [(b, a)]
    loop a
    a' else []
        where r :: (b, a)
    r@(b
    b, a
    a') = a -> (b, a)
    f a
    a

    -- | Repeat something while a condition on some state is true.
    --   Return the last state (including the changes of the last
    --   transition, even if the condition became false then).

    repeatWhile :: (a -> (Bool, a)) -> a -> a
    repeatWhile :: forall a. (a -> (Bool, a)) -> a -> a
    repeatWhile a -> (Bool, a)
    f = a -> a
    loop where
      loop :: a -> a
    loop a
    a = if Bool
    again then a -> a
    loop a
    a' else a
    a'
        where (Bool
    again, a
    a') = a -> (Bool, a)
    f a
    a

    -- | Monadic version of 'repeatWhile'.
    repeatWhileM :: (Monad m) => (a -> m (Bool, a)) -> a -> m a
    repeatWhileM :: forall (m :: * -> *) a. Monad m => (a -> m (Bool, a)) -> a -> m a
    repeatWhileM a -> m (Bool, a)
    f = a -> m a
    loop where
      loop :: a -> m a
    loop a
    a = do
        (Bool
    again, a
    a') <- a -> m (Bool, a)
    f a
    a
        if Bool
    again then a -> m a
    loop a
    a' else a -> m a
    forall (m :: * -> *) a. Monad m => a -> m a
    return a
    a'

    -- | A version of the trampoline function.
    --
    --   The usual function iterates @f :: a -> Maybe a@ as long
    --   as @Just{}@ is returned, and returns the last value of @a@
    --   upon @Nothing@.
    --
    --   @usualTrampoline f = trampolineWhile $ \ a -> maybe (False,a) (True,) (f a)@.
    --
    --   @trampolineWhile@ is very similar to @repeatWhile@, only that
    --   it discards the state on which the condition went @False@,
    --   and returns the last state on which the condition was @True@.
    trampolineWhile :: (a -> (Bool, a)) -> a -> a
    trampolineWhile :: forall a. (a -> (Bool, a)) -> a -> a
    trampolineWhile a -> (Bool, a)
    f = (a -> (Bool, a)) -> a -> a
    forall a. (a -> (Bool, a)) -> a -> a
    repeatWhile ((a -> (Bool, a)) -> a -> a) -> (a -> (Bool, a)) -> a -> a
    forall a b. (a -> b) -> a -> b
    $ \ a
    a ->
      let (Bool
    again, a
    a') = a -> (Bool, a)
    f a
    a
      in (Bool
    again,) (a -> (Bool, a)) -> a -> (Bool, a)
    forall a b. (a -> b) -> a -> b
    $ if Bool
    again then a
    a' else a
    a

    -- | Monadic version of 'trampolineWhile'.
    trampolineWhileM :: (Monad m) => (a -> m (Bool, a)) -> a -> m a
    trampolineWhileM :: forall (m :: * -> *) a. Monad m => (a -> m (Bool, a)) -> a -> m a
    trampolineWhileM a -> m (Bool, a)
    f = (a -> m (Bool, a)) -> a -> m a
    forall (m :: * -> *) a. Monad m => (a -> m (Bool, a)) -> a -> m a
    repeatWhileM ((a -> m (Bool, a)) -> a -> m a) -> (a -> m (Bool, a)) -> a -> m a
    forall a b. (a -> b) -> a -> b
    $ \ a
    a -> do
      (Bool
    again, a
    a') <- a -> m (Bool, a)
    f a
    a
      (Bool, a) -> m (Bool, a)
    forall (m :: * -> *) a. Monad m => a -> m a
    return ((Bool, a) -> m (Bool, a)) -> (Bool, a) -> m (Bool, a)
    forall a b. (a -> b) -> a -> b
    $ (Bool
    again,) (a -> (Bool, a)) -> a -> (Bool, a)
    forall a b. (a -> b) -> a -> b
    $ if Bool
    again then a
    a' else a
    a

    -- | More general trampoline, which allows some final computation
    --   from iteration state @a@ into result type @b@.
    trampoline :: (a -> Either b a) -> a -> b
    trampoline :: forall a b. (a -> Either b a) -> a -> b
    trampoline a -> Either b a
    f = a -> b
    loop where
      loop :: a -> b
    loop a
    a = (b -> b) -> (a -> b) -> Either b a -> b
    forall a c b. (a -> c) -> (b -> c) -> Either a b -> c
    either b -> b
    forall a. a -> a
    id a -> b
    loop (Either b a -> b) -> Either b a -> b
    forall a b. (a -> b) -> a -> b
    $ a -> Either b a
    f a
    a

    -- | Monadic version of 'trampoline'.
    trampolineM :: Monad m => (a -> m (Either b a)) -> a -> m b
    trampolineM :: forall (m :: * -> *) a b.
    Monad m =>
    (a -> m (Either b a)) -> a -> m b
    trampolineM a -> m (Either b a)
    f = a -> m b
    loop where
      loop :: a -> m b
    loop a
    a = (b -> m b) -> (a -> m b) -> Either b a -> m b
    forall a c b. (a -> c) -> (b -> c) -> Either a b -> c
    either b -> m b
    forall (m :: * -> *) a. Monad m => a -> m a
    return a -> m b
    loop (Either b a -> m b) -> m (Either b a) -> m b
    forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
    =<< a -> m (Either b a)
    f a
    a

    -- | Iteration to fixed-point.
    --
    --   @iterateUntil r f a0@ iterates endofunction @f@, starting with @a0@,
    --   until @r@ relates its result to its input, i.e., @f a `r` a@.
    --
    --   This is the generic pattern behind saturation algorithms.
    --
    --   If @f@ is monotone with regard to @r@,
    --   meaning @a `r` b@ implies @f a `r` f b@,
    --   and @f@-chains starting with @a0@ are finite
    --   then iteration is guaranteed to terminate.
    --
    --   A typical instance will work on sets, and @r@ could be set inclusion,
    --   and @a0@ the empty set, and @f@ the step function of a saturation algorithm.
    iterateUntil :: (a -> a -> Bool) -> (a -> a) -> a -> a
    iterateUntil :: forall a. (a -> a -> Bool) -> (a -> a) -> a -> a
    iterateUntil a -> a -> Bool
    r a -> a
    f = a -> a
    loop where
      loop :: a -> a
    loop a
    a = if a -> a -> Bool
    r a
    a' a
    a then a
    a' else a -> a
    loop a
    a'
        where a' :: a
    a' = a -> a
    f a
    a

    -- | Monadic version of 'iterateUntil'.
    iterateUntilM :: Monad m => (a -> a -> Bool) -> (a -> m a) -> a -> m a
    iterateUntilM :: forall (m :: * -> *) a.
    Monad m =>
    (a -> a -> Bool) -> (a -> m a) -> a -> m a
    iterateUntilM a -> a -> Bool
    r a -> m a
    f = a -> m a
    loop where
      loop :: a -> m a
    loop a
    a = do
        a
    a' <- a -> m a
    f a
    a
        if a -> a -> Bool
    r a
    a' a
    a then a -> m a
    forall (m :: * -> *) a. Monad m => a -> m a
    return a
    a' else a -> m a
    loop a
    a'

    -- | @'iterate'' n f x@ applies @f@ to @x@ @n@ times and returns the
    -- result.
    --
    -- The applications are calculated strictly.

    iterate' :: Integral i => i -> (a -> a) -> a -> a
    iterate' :: forall i a. Integral i => i -> (a -> a) -> a -> a
    iterate' i
    0 a -> a
    _ a
    x             = a
    x
    iterate' i
    n a -> a
    f a
    x | i
    n i -> i -> Bool
    forall a. Ord a => a -> a -> Bool
    > i
    0     = i -> (a -> a) -> a -> a
    forall i a. Integral i => i -> (a -> a) -> a -> a
    iterate' (i
    n i -> i -> i
    forall a. Num a => a -> a -> a
    - i
    1) a -> a
    f (a -> a) -> a -> a
    forall a b. (a -> b) -> a -> b
    $! a -> a
    f a
    x
                   | Bool
    otherwise = [Char] -> a
    forall a. HasCallStack => [Char] -> a
    error [Char]
    "iterate': Negative input."

    -- * Iteration over Booleans.

    -- | @applyWhen b f a@ applies @f@ to @a@ when @b@.
    applyWhen :: Bool -> (a -> a) -> a -> a
    applyWhen :: forall a. Bool -> (a -> a) -> a -> a
    applyWhen Bool
    b a -> a
    f = if Bool
    b then a -> a
    f else a -> a
    forall a. a -> a
    id

    -- | @applyUnless b f a@ applies @f@ to @a@ unless @b@.
    applyUnless :: Bool -> (a -> a) -> a -> a
    applyUnless :: forall a. Bool -> (a -> a) -> a -> a
    applyUnless Bool
    b a -> a
    f = if Bool
    b then a -> a
    forall a. a -> a
    id else a -> a
    f

    -- | Monadic version of @applyWhen@
    applyWhenM :: (Monad m) => m Bool -> (m a -> m a) -> m a -> m a
    applyWhenM :: forall (m :: * -> *) a.
    Monad m =>
    m Bool -> (m a -> m a) -> m a -> m a
    applyWhenM m Bool
    mb m a -> m a
    f m a
    x = m Bool
    mb m Bool -> (Bool -> m a) -> m a
    forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
    >>= \ Bool
    b -> Bool -> (m a -> m a) -> m a -> m a
    forall a. Bool -> (a -> a) -> a -> a
    applyWhen Bool
    b m a -> m a
    f m a
    x

    -- | Monadic version of @applyUnless@
    applyUnlessM :: (Monad m) => m Bool -> (m a -> m a) -> m a -> m a
    applyUnlessM :: forall (m :: * -> *) a.
    Monad m =>
    m Bool -> (m a -> m a) -> m a -> m a
    applyUnlessM m Bool
    mb m a -> m a
    f m a
    x = m Bool
    mb m Bool -> (Bool -> m a) -> m a
    forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
    >>= \ Bool
    b -> Bool -> (m a -> m a) -> m a -> m a
    forall a. Bool -> (a -> a) -> a -> a
    applyUnless Bool
    b m a -> m a
    f m a
    x