On Sun, Jul 21, 2013 at 2:43 PM, Gath-Gealaich <[email protected]>wrote:
> On Sat, 20 Jul 2013 14:28:59 +0200 > Pavel Bažant <[email protected]> wrote: > > > On the other hand, imagine math notated the same way > > programming languages are. That would be awful! IMHO, it is awful for > > PL, too, but everyone got used to it. > > Actually, that would be anything but awful - it would be positively > splendid! Mathematical notation is fuzzy and ambiguous in places, a > luxury it can afford because it's ultimately processed by the human > brains of mathematicians - beings that, despite specializing in a field > renowned for exactitude in reasoning and results, are ultimately still > only human beings. Computers can't afford ambiguous notation, which is > why Sussman in his book on computational approach to classical > mechanics (Structure and Interpretation of Classical Mechanics) threw > mathematical notation out of the window and went with a functional, > machine-readable one. > > Mathematical notation is intended to be compact and easily readable by humans. It serves this purpose well. Some computer algebra systems use it, so it definitely can be made non-ambiguous. If manipulating richly notated expressions is perfectly possible in computer algebra systems, what's wrong with having a rich syntax for say Standard ML and manipulating it the same way? Even the good old DOS version of Derive edited formulas at the structure level! Like 20 years ago. The point is, everyone else already treats structured data as structured data, only the software development community treats structured data as the corresponding unstructured stream of bytes which happens to represent the data on the disk. It's almost like editing SVG files in a text editor instead of using a drawing software. It's almost as if the programmers subconsciously wanted source code to be really a "code" in the sense of something secret, incomprehensible.
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