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Xah's Edu Corner: The Concepts and Confusions of Pre-fix, In-fix, Post-fix and Fully Functional NotationsThe Concepts and Confusions of Pre-fix, In-fix, Post-fix and Fully
Functional Notations Xah Lee, 2006-03-15 Let me summarize: The LISP notation, is a functional notation, and is not a so-called pre-fix notation or algebraic notation. Algebraic notations have the concept of operators, meaning, symbols placed around arguments. In algebraic in-fix notation, different symbols have different stickiness levels defined for them. e.g. “3+2*5>7” means “(3+(2*5))>7”. The stickiness of operator symbols are normally called “Operator Precedence”. It is done by giving a order specification for the symbols, or equivalently, give each symbol a integer index, so that for example if we have “a⊗b⊙c”, we can unambiguously understand itto mean one of “(a⊗b)⊙c” or “a⊗(b⊙c)”. In a algebraic post-fix notation known as Polish Notation, there needs not to have the concept of Operator Precedence. For example, the in-fix notation “(3+(2*5))>7” is written as “3 2 5 * + 7 >”, where the operation simply evaluates from left to right. Similarly, for a pre-fix notation syntax, the evaluation goes from right to left, as in “> 7+ * 5 2 3”. While functional notations, do not employ the concept of Operators, because there is no operators. Everything is a syntactically a “function”, written as f(a,b,c...). For example, the same expression above is written as “>( +(3, *(2,5)), 7)” or “greaterThan( plus(3, times(2,5)), 7)”. For lisps in particular, their fully functional notation is historically termed sexp (short for S-Expression, where S stands for Symbolic). It is sometimes known as Fully Parenthesized Notation. For example, in lisp it would be (f a b c ...). In the above example it is: “(> (+ 3 (* 2 5)) 7)”. The common concepts of “pre-fix, post-fix, in-fix” are notions in algebraic notations only. Because in Full Functional Notation, there is no concept of where one places the “operator” or function. There is always just a single position given with explicitly enclosed arguments. Another way to see that lisp notation are not “pre” anything, is by realizing that the “head” f in (f a b c) can be defined to be placed anywhere. e.g. (a b c f) or even (a f b c), and it's still not pre- or in- or post- anything. For example, in the language Mathematica, f(a b c) would be written as f[a,b,c] where the argument enclosure symbols is the square bracket instead of parenthesis, and argument separator is comma instead of space, and the function symbol (or head) is placed in outside and in front of the argument enclosure symbols. The reason for the misconception that lisp notations are “pre-fix” is because the head appears before the enclosed arguments. Such “pre-fix” has no signifance in Full Functional Notation systems and can only engender confusion in the Algebraic Pre-fix Notation systems where the term has significance. 2000-02-21 The common name for the lisp way is Fully Parenthesized Notation. This syntax is the most straightforward to represent a tree, but it's not the only choice. For example, one could have Fully Parenthesized Notation by simply moving the semantics of the first element to the last. You write (arg1 arg2 ... f) instead of the usual (f arg1 arg2). Like wise, you can essentially move f anywhere and still make sense. In Mathematica, they put the f in front of the paren, and use square brackets instead. e.g. f[a,b,c], Sin[3], Map[f,list] ... etc. The f in front of parent makes better conventional sense until f is itself a list which then we'll see things like f[a,b][c, g[3,h]] etc. It's worse when there are arbitrary nesting of heads. A pre-fix notation in Mathematica is represented as “f@arg”. Essentially, a pre-fix notation in this context limits it to uses for function that has only one argument. More example: “f@a@b@c” is equivalent to “f[a[b[c]]]” or in lispy “(f (a (b c)))”. A post-fix notation is similar. In Mathematica it is, e.g. “c//b//a//f”. For example “List[1,2,3]//Sin” is syntactically equivalent to “Sin[List[1,2,3]]” or “Sin@List[1,2,3]”. (and they are semantically equivalent to “Map[Sin, List[1,2,3]]”in Mathematica) For in-fix notation, the function symbol is placed between its arguments. In Mathematica, the generic form for in-fix notation is by sandwiching the tilde symbol around the function name. e.g. “Join[List[1,2],List[3,4]]” can be written as “List[1,2] ~Join~ List[3,4]”. In general, when we say C is a in-fix notation language, we don't mean it's strictly in-fix but the situation is one-size-fits-all for convenience. Things like “i++”, “++i”, “for(;;)”, 0x123, “sprint(...%s...,...)”, ... are syntax whimsies. (that is, a ad hoc syntax soup) In Mathematica for example, there is quite a lot syntax sugars beside the above mentioned systimatic constructs. For instance, Plus[a,b,c] can be written in the following ways: “(a+b)+c” or “a+b+c” or “(a+b)~Plus~c” The gist being that certain functions such as Plus is assigned a special symbol '+' with a particular syntax form to emulate the irregular and inefficient but nevertheless well-understood conventional notation. For another example: Times[a,b] can be also written as “a*b” or just “a b”. Mathematica also have C language's convention of “i++”, “++i”, “i+=1” for examples. As a side note, the Perl mongers are proud of their slogan of There Are More Than One Way To Do It in their gazillion ad hoc syntax sugars but unaware that in functional languages (such as Mathematica, Haskell, Lisp) that there are consistent and generalized constructs that can generate far far more syntax variations than the ad hoc prefixed Perl both in theory AND in practice. (in lisps, their power syntax variation comes in the guise of macros.) And, more importantly, Perlers clamor about Perl's “expressiveness” more or less on the useless syntax level but don't realize that semantic expression is what's really important. ---- This post is archived at: http://xahlee.org/UnixResource_dir/writ/notations.html Xah xah@xahlee.org ∑ http://xahlee.org/ |

Re: Xah's Edu Corner: The Concepts and Confusions of Pre-fix, In-fix, Post-fix and Fully Functional NotationsOn 15 Mar 2006 22:20:52 -0800, "Xah Lee" <xah@xahlee.org> wrote,
quoted or indirectly quoted someone who said : >e. For example, the in-fix >notation =E2=80=9C(3+(2*5))>7=E2=80=9D is written as =E2=80=9C3 2 5 * + 7 >= >=E2=80=9D, where the Not that Mr. Lee has ever shown much interest in feedback, but you pretty well have stick to vanilla ASCII to get your notation through unmangled on newsgroups. -- Canadian Mind Products, Roedy Green. http://mindprod.com Java custom programming, consulting and coaching. |

Re: Xah's Edu Corner: The Concepts and Confusions of Pre-fix, In-fix, Post-fix and Fully Functional Notations"""Not that Mr. Lee has ever shown much interest in feedback, but you
pretty well have stick to vanilla ASCII to get your notation through unmangled on newsgroups.""" It is the 21st century, so having to do that oughta inspire some sort of well earned anti Unix rant... :) |

Re: Xah's Edu Corner: The Concepts and Confusions of Pre-fix, In-fix, Post-fix and Fully Functional NotationsXah Lee wrote:
« The Concepts and Confusions of Pre-fix, In-fix, Post-fix and Fully Functional Notations http://xahlee.org/UnixResource_dir/writ/notations.html » A side note: the terminology “Algebraic” Notation is a misnomer. It seems to imply that such notations have something to do with the branch of math called algebra while other notation systems do not. The reason the name Algebraic Notation is used because when the science of algebra was young, around 1700s mathematicians are dealing with equations using symbols like “+ × =” written out similar to the way we use them today. This is before the activities of systimatic investigation into notation systems as necessitated in the studies of logic in 1800s or computer languages in 1900s. So, when notation systems are actually invented, the conventional way of infixing “+ × =” became known as algebraic because that's what people think of when seeing them. Xah xah@xahlee.org ∑ http://xahlee.org/ |

Roedy Green wrote: > On 15 Mar 2006 22:20:52 -0800, "Xah Lee" <xah@xahlee.org> wrote, > quoted or indirectly quoted someone who said : > > >e. For example, the in-fix > >notation =E2=80=9C(3+(2*5))>7=E2=80=9D is written as =E2=80=9C3 2 5 * + 7 >= > >=E2=80=9D, where the > > Not that Mr. Lee has ever shown much interest in feedback, but you > pretty well have stick to vanilla ASCII to get your notation through > unmangled on newsgroups. Hmmm... it displays fine via google groups. Maybe it's the reader which is 'non-compliant' ? Fuzzyman http://www.voidspace.org.uk/python/index.shtml > -- > Canadian Mind Products, Roedy Green. > http://mindprod.com Java custom programming, consulting and coaching. |

Roedy Green wrote:
> On 15 Mar 2006 22:20:52 -0800, "Xah Lee" <xah@xahlee.org> wrote, > quoted or indirectly quoted someone who said : > > >e. For example, the in-fix > >notation =E2=80=9C(3+(2*5))>7=E2=80=9D is written as =E2=80=9C3 2 5 * + 7 >= > >=E2=80=9D, where the > > Not that Mr. Lee has ever shown much interest in feedback, but you > pretty well have stick to vanilla ASCII to get your notation through > unmangled on newsgroups. That would be one of my last concerns with Mr. Lee's postings. If only someone could persuade this guy to stay away from CS... |

Re: Xah's Edu Corner: The Concepts and Confusions of Pre-fix, In-fix,Post-fix and Fully Functional NotationsFuzzyman schrieb:
> Roedy Green wrote: >> On 15 Mar 2006 22:20:52 -0800, "Xah Lee" <xah@xahlee.org> wrote, >> quoted or indirectly quoted someone who said : >> >>> e. For example, the in-fix >>> notation =E2=80=9C(3+(2*5))>7=E2=80=9D is written as =E2=80=9C3 2 5 * + 7 >= >>> =E2=80=9D, where the >> Not that Mr. Lee has ever shown much interest in feedback, but you >> pretty well have stick to vanilla ASCII to get your notation through >> unmangled on newsgroups. > > Hmmm... it displays fine via google groups. Maybe it's the reader which > is 'non-compliant' ? Other charsets than US-ASCII are widely accepted in non-english newsgroups as long as the charset is properly declared. Xah's posting was properly encoded and will display fine in every decent newsreader. Timo |

In comp.lang.perl.misc Timo Stamm <timo.stamm@arcor.de> wrote:
> Fuzzyman schrieb: >> Roedy Green wrote: >>> On 15 Mar 2006 22:20:52 -0800, "Xah Lee" <xah@xahlee.org> wrote, >>> quoted or indirectly quoted someone who said : >>> >>>> e. For example, the in-fix >>>> notation =E2=80=9C(3+(2*5))>7=E2=80=9D is written as =E2=80=9C3 2 5 * + 7 >= >>>> =E2=80=9D, where the >>> Not that Mr. Lee has ever shown much interest in feedback, but you >>> pretty well have stick to vanilla ASCII to get your notation through >>> unmangled on newsgroups. >> Hmmm... it displays fine via google groups. Maybe it's the reader which >> is 'non-compliant' ? > Other charsets than US-ASCII are widely accepted in non-english > newsgroups as long as the charset is properly declared. > Xah's posting was properly encoded and will display fine in every decent > newsreader. It is not just the question of the newsreader, it is also a question of whether the character set/font being used is capable of displaying the characters concerned. Axel |

Re: Xah's Edu Corner: The Concepts and Confusions of Pre-fix, In-fix,Post-fix and Fully Functional Notationsaxel@white-eagle.invalid.uk schrieb:
> In comp.lang.perl.misc Timo Stamm <timo.stamm@arcor.de> wrote: >> Other charsets than US-ASCII are widely accepted in non-english >> newsgroups as long as the charset is properly declared. > >> Xah's posting was properly encoded and will display fine in every decent >> newsreader. > > It is not just the question of the newsreader, it is also a question of whether > the character set/font being used is capable of displaying the characters > concerned. A character set doesn't display characters, it specifies the coupling of a character (grapheme) and its representation in a data format (number). Because the specification of internet text messages only allows 7 bit ASCII, Multipurpose Internet Mail Extensions have been introduced. They define, for example, the quoted-printable transfer encoding. Xah's posting properly declared a quoted-printable transfer encoding and the UTF-8 charset. There were no unspecified characters in the message, it was absolutely adhering to the recognized standards. If this message doesn't display properly on your system - because your newsreader doesn't know how to decode quoted printable or because your operating system lacks a font to display the characters, this may be a problem. But it's your newsreader or your OS that is broken or not up to date. BTW, the newsreader you are using should handle the posting fine. Timo |

On 17 Mar 2006 00:58:55 -0800, "Fuzzyman" <fuzzyman@gmail.com> wrote,
quoted or indirectly quoted someone who said : >Hmmm... it displays fine via google groups. Maybe it's the reader which >is 'non-compliant' ? I am using Agent. You configure your database with an encoding, which is by default the platform encoding, not UTF-8. I have just flipped it over to UTF-8. We'll see if that makes Xah's future UTF-8 messages more readable. -- Canadian Mind Products, Roedy Green. http://mindprod.com Java custom programming, consulting and coaching. |

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