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Authored by: Anonymous on Monday, October 15 2012 @ 03:38 PM EDT |
>I contend that hardware executes instructions contained in software.
This is an inadequate understanding. In the "lambda calculus" there
are no instructions, and a better model becomes apparent. Hardware "applies
mathematical transformations on date as represented by symbols". There is
an enormous range of possible representations of a computation; "list of
instructions to be executed sequentially" is only one of them. The basic
mathematical models of computation have been mathematically proven to have
equivalent power (that is, any mathematical process you can describe with one
model, you can describe with any of them.)
The mathematician would say, "here is a mathematical algorithm. Now, one of
the ways we may represent it is by a series of instructions that can be executed
serially by such-and-such a machine."
But, regardless of whether you're looking at a typical Intel processor or
lambda-calculus pattern-matching hardware, it IS fair to say, "hardware is
simply applying logical transformations to the input."
Think of an "interpreter", where the "program" and the
"data" are both simply items in the same symbol-stream (bytestream, if
you like.) You can't logically distinguish between 'program' and 'data'. It's
all just data.
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