Almost every ProgrammingLanguage supporting InfixNotation for expressions has extensive operator precedence levels. This is required to disambiguate expressions:  does ''a + b * c'' mean ''(a + b) * c'' or ''a + (b * c)''?  And does it mean the same thing as ''c * b + a''?

Here are the precedence tables of some well-known languages:

CeeLanguage (from highest to lowest):

* () [] . ->
* ++ -- + - ! ~ (cast) * & sizeof
* * / %
* + -
* << >>
* < <= > >=
* == !=
* &
* ^
* |
* &&
* ||
* ?:
* = += -= *= /= %= &= ^= |= <<= >>=
* ,

PascalLanguage (from highest to lowest):

* ()
* @ not
* * / div mod and shl shr
* + - or xor
* = <> < > <= >= in

SmalltalkLanguage (highest to lowest):

* unary
* binary
* keyword
* assignment

All other ambiguity can is resolved by using left-to-right associativity. Thus, "1+1*2" would be parsed as "(1+1)*2", and "1<<2+3" as "(1<<2)+3".

LispLanguage gets along just fine without OperatorPrecedence. Well, OK, I suppose you could consider some macro characters to be unary operators with high precedence. :)  -- DanMuller 

ForthLanguage also does without precedence. Expressions strictly using PrefixNotation or PostfixNotation don't need it. (This is not strictly true... some words are IMMEDIATE and either parse the word(s) ahead of them or do some control flow magic at compile time.) -- IanOsgood

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PerlSix is going to be even more of a precedence hell; see http://www.ozonehouse.com/mark/blog/code/PeriodicTable.html.

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See IssuesForLanguageDesigners

CategoryMath