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Topic: Notations for functional application
Replies: 1   Last Post: Jan 11, 2013 7:42 AM

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Stefan Ram

Posts: 49
Registered: 9/14/05
Notations for functional application
Posted: Jan 11, 2013 3:15 AM
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Newsgroups: comp.lang.lisp,sci.math

IIRC recently, I read in the german Wikipedia that the LISP
style functional application notation, such as - for example:

( sin 0 )

was »polish notation«. I deem polish notation to be

sin 0

, while

( sin 0 )

to me is Cambridge notation, of course, we also have UPN:

0 sin

and infix

0 + 0

. Why do I write this post? I am asking a question I already
had asked before, but never got an answer:

How is the notation called that is used in most programming
languages, i.e.,

sin( 0 )

? It does not seem to have a name! One might be inclined to
call it »prefix« notation, but this can be confused with PN:

sin 0

without obligatory parentheses.

Desperately, I even tried to find a name myself, searching
for the person who first used this notation in history. But
I was even unable to find this person. It seems that Euler
did use that notation, but not necessarily with obligatory
parentheses and not necessarily as the first one.

Also it should be a name, not a long description as »prefix
notation with obligatory parentheses around the argument
list and commas used to separate multiple arguments«.

What about calling

sin( 0 )

»standard notation«? Other suggestions?

What about »FORTRAN-Notation«? Could it be that FORTRAN
was the first entity in history where the parentheses
around the argument where obligatory, while in mathematics
they were always optional?

sin 0 prefix notation, polish notation
0 sin postfix notation, reverse polish notation
0 + 0 infix notation
( sin 0 ) Cambridge notation
( 0 sin ) reverse Cambridge notation
sin( 0 ) ???

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