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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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