{- |

Copyright   :  (c) Henning Thielemann 2007
License     :  GPL

Maintainer  :  synthesizer@henning-thielemann.de
Stability   :  provisional
Portability :  requires multi-parameter type classes (OccasionallyScalar)

Light-weight sample parameter inference which will fit most needs.
We only do \"poor man's inference\", only for sample rates.
The sample rate will be provided in a Reader monad.
We almost do not need monad functionality
but only "Control.Applicative" functionality.

In contrast to the run-time inference approach,
we have the static guarantee that the sample rate is fixed
before passing a signal to the outside world.
module Synthesizer.Inference.Reader.Process (
      run, share,
      injectParam, extractParam, convertTimeParam,
      loop, pure,
      ($:), ($::), ($^), ($#),
      (.:), (.^),
      liftP, liftP2, liftP3, liftP4,
   ) where

import Control.Monad.Fix (MonadFix(mfix), )
import Synthesizer.ApplicativeUtility
import qualified Control.Applicative as App
import Control.Applicative (Applicative)

import NumericPrelude
import PreludeBase as P

{- |
This wraps a function which computes a sample rate dependent result.
Sample rate tells how many values per unit are stored
for representation of a signal.
newtype T t t' a = Cons {process :: t' -> a}

instance Functor (T t t') where
   fmap f x = Cons (f . process x)

instance Applicative (T t t') where
   pure  = pure
   (<*>) = apply

instance Monad (T t t') where
   return = pure
   (>>=)  = share

instance MonadFix (T t t') where
   mfix = loop . injectParam

run ::
   t' -> T t t' a -> (t', a)
run sr (Cons p) = (sr, p sr)

{- |
Re-use a result several times without recomputing.
With a simple @let@ you can re-use a result
but it must be recomputed due to the dependency on the sample rate.
share ::
      T t t' a        {-^ process that provides a result -}
   -> (a -> T t t' b) {-^ function that can re-use that result as much as it wants -}
   -> T t t' b
share p f = Cons $ \sr ->
   process (f (process p sr)) sr

{- |
This corresponds to 'Control.Applicative.pure'
pure :: a -> T t t' a
pure x = Cons $ const x

apply :: T t t' (a -> b) -> T t t' a -> T t t' b
apply f proc = Cons $ \sr ->
   process f sr (process proc sr)

extractParam :: T t t' (a -> b) -> (a -> T t t' b)
extractParam = ($#)

injectParam :: (a -> T t t' b) -> T t t' (a -> b)
injectParam f = Cons $ \sr x ->
   process (f x) sr

{- |
The first argument will be a function like 'InferenceReader.Signal.toTimeScalar'.
If you use this function instead of 'InferenceReader.Signal.toTimeScalar' directly,
the type @t@ can be automatically infered.
convertTimeParam :: (t' -> t' -> t) -> t' -> (t -> a) -> T t t' a
convertTimeParam convert t' f = Cons $ \sr ->
   f (convert sr t')