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The story you read about Feynman is this one: http://longnow.org/essays/richard-feynman-connection-machine...

I remember seeing a program that would output Haskell functions given just their type signatures. If you think of type signatures as invariants, this is exactly what drostie described. Alas my Google-fu was unable to find a reference to it.

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I know that one :D, here I can help: http://hackage.haskell.org/cgi-bin/hackage-scripts/package/d...

I have considered this road, see this LtU discussion to see why this approach though wonderful, is still too limited for general programming. http://lambda-the-ultimate.org/node/1178

Essentially, as is found in many automatic program derivation attempts, recursion explodes complexity.

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