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by aninhumer
3636 days ago
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Some things just make more sense with infix or postfix notation. Not least of which being mathematical expressions. I think Haskell handles it really well, where everything is just function application, but identifiers made of symbols apply infix (and there's syntax to switch between them). It's just enough syntax that you can usually structure things how you want, but the rules are still simple enough that it's easy see the tree structure. Sometimes people go a bit crazy with adding their own operators, but for the most part I think the community is getting over that. |
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There are pretty much only four binary operators in modern mathematical notation that make sense infix (addition, subtraction, multiplication, and variable assignment) and only in very short, unambiguous expressions. Pretty much everything else is either prefix (function application, derivatives, summation, etc) or uses special layout formatting rules (division, exponentiation) or both (matrix multiplication).
Even with all of this modern mathematical notation is full of ambiguities. A great short discussion about this is in the preface to Sussman and Wisdom's _Structure and Interpretation of Classical Mechanics_: https://mitpress.mit.edu/sites/default/files/titles/content/... which despite being all about "mathematical expressions" somehow manages to have all of its code in Lisp...
I also recommend reading Munroe's _The Language of Mathematics_ for a better understanding of modern mathematical notation and its weaknesses.
Note also that this is only modern mathematical notation. There is nothing "natural" about infix operators and for most of mathematical history they did not exist (see for example Bashmakova and Smirnova's _The Beginnings and Evolution of Algebra_ or any other book on the history of algebraic notation).