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Sun Aug 14 15:53:24 CEST 2011

## State machines and applicative.

Again, what's an applicative Functor?
A Functor is something that has
fmap :: Functor f => (x -> y) -> f x -> f y
An Applicative functor is something that has <*> (map-apply?)
(<*>) :: Applicative a => a (x -> y) -> a x -> a y
So a functor is an abstraction that supports a lift from a function to
a function over abstractions. An applicative functor is something
that has a lift from an abstraction of a function to a function over
abstractions.
A state machine can be represented by an applicative functor. The
state threads behind the scenes, but the observable i/o behaviour is
what we can expose.
Smach s t = Smach s -> (s, t)
A state machine is a function that produces a value of type t (which
can be a function) and a next state s.
The iteration of this is also Applicative.
( construct! )
Why is this trivial? Because it is also a Monad (the state monad),
which is more specific than Applicative.
Is it really that simple? Pd is a state monad.
Is there a useful modification that can be made to the state monad
that will no longer make it monadic? Maybe causality?

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