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Sun Aug 14 16:25:07 CEST 2011

Applicative Transformers

Some observations to make precise:

  * A DSP language (of combinators) would benefit from connections
    that happen behind the scenes.  Examples are state relations over
    time.

  * A recurrence relation / difference equation is essentially a state
    monad.

  * A Monad is also Applicative

  * Audio DSP is essentially a mix of State and List monads.

  * Monad transformers are a bit of a kludge.  There is not a lot
    known about the algebra of monad transformers.

  * Applicative Transformers do not exist because applicatives are
    "naturally composable". [1] -> Section 4.

  * Is it true that the direction that is inherent in the State monad
    -- the function s -> (s,t) -- is what causes State to be specific
    enough to be a Monad?  Is causality the essential element?

  * If a state space model can be run in reverse, would it stop being
    Monad?  This reminds me of Steele's parallel language..

[1] http://www.haskell.org/haskellwiki/Applicative_functor



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