Friday, February 25, 2005

Delta Classes and my thoughts

Just read Avishek's post on delta classes. This got me thinking. Delta classes as defined by Avishek are basically Deltas in the classic sense of the work. They denote differences. So if we had such classes we might be able to get away with one start class and many delta classes being applied in various orders or number of times to generate all sorts of classes and code. We might even be able to get to the holy grail of mathematically proven code using lambda calculus.

Let us now assume for the sake of discussion that we have a framework which accepts and understands an initial class and many delta classes and a set of mathematically correct rules (ok...ok..there will many of them) to apply on these delta classes to acquire a set of useful classes and operations. Now whenever a transition is applied it can be proved that the transition is mathematically correct as the general set of rules to be applied are proven to be mathematically correct (including the order and number of times they are being applied). For this maybe one just needs to prove that all the rules are derivatives of alpha,beta or gamma reduction/deductions. This is non-trivial but not too though. If we keep out things like dynamic typing maybe we will get mathematically proven correct programs.

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