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Sun Jul 19 16:44:16 EDT 2015

Causal or not?

Let's take a more abstract view.

Signal processors are Arrows.  In fact they are the school book
example[1].

The "growing state" problem is because of the "view".  Some symmetry
is broken because of extra constraints introduced:

Signal processors are constrained to the causal kind: those that can
be represented by difference equations.  (s,i) -> (s,o)

This then breaks the Arrow abstraction.  How to create a morphism that
allows to reconstruct operations in the SSM domain from Arrow
operations in the specification domain?  I.e. the important question
is:

   Arrows are the right abstraction.
   How to "lift" those to "Implementation Arrows"?


What would an implementation arrow look like?  Essentially, this is a
version of the arrow laws that has an extra parameter that is somehow
constrained.

[1] https://www.haskell.org/arrows/




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