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symbols - Why did Mathematica choose brackets for function arguments over parentheses?



This is a non-technical question. I'm just curious why Mathematica breaks the convention that parentheses are widely used for function arguments. What's the advantage of f[x] over f(x)?


Again, for the derivative of a function, f'(x) and f''(x) are more familiar than f'[x] and f''[x]. I think these conventions in math textbooks have already existed for hundreds of years.


If function arguments are denoted as f(x), then array[i] could be used as array index. (c.f. Mathematica uses array[[i]] here.)


To quote from the official documentation:



The Four Kinds of Bracketing in the Wolfram Language


(term) parentheses for grouping


f[x] square brackets for functions


{a, b, c} curly braces for lists


v[[i]] double brackets for indexing (Part[v, i])




Are there any historical or antithetical reasons for choosing these notations?



Answer



The answer is quite simple. Most people want to multiply numbers without having to use the * symbol, e.g. 3x vs 3*x.


So given that this exists in Mathematica, using () for function arguments would introduce ambiguity.


Is f(x + y) meant to be f[x + y] or f*(x + y)?


This is actually a problem Wolfram|Alpha can face since we try to allow for all forms of inputs.


Other languages like C chose the other route, which means you must use * to indicate multiplication (something that annoys me). Given that Mathematica's original purpose was for mathematics, I think the right choice was made.


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