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Wed Feb 10 10:33:20 CET 2010

Normal forms

Using normal forms is useful for reducing nested expressions.

Let's try commutativity:


  (1 + 1)       -> 2                  [e1]
  (1 + (1 + a)) -> (2 + a)            [e2]
  (a + 1)       -> (1 + a)            [c]
  ((x + y) + z) -> (x + (y + z))      [a]


It's probably simplest to represent the sum/product of a value with a
fully reduced term as an intermediate object.

What I'm thinking now is that it might be better to abstract Ring /
Field first, such that abstract evaluation doesn't need any string
comparisons[1].  

[1] http://okmij.org/ftp/Computation/Generative.html#GE-generation



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