<div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr">I was asking Bing Copilot questions to better understand the order of precedence in:<br><br><span style="color:rgb(0,0,0);font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">sequence :: Monad m => [m a] -> m [a]</span><br style="box-sizing:border-box;color:rgb(0,0,0);font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px"><span style="color:rgb(0,0,0);font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">sequence = foldr mcons (return [])</span><br style="box-sizing:border-box;color:rgb(0,0,0);font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px"><span style="color:rgb(0,0,0);font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">             where mcons p q = p >>= \x -> q >>= \y -> return (x:y) <br></span><br>I noticed that for evaluation (e.g. binding variables to real world data), the left most "->" seems to have it's lambda variables bound first but with regards parsing this left most "->" seems to be the least deeply nested which in a strick language would suggest a low order of precedence. In the summary part of bing's answer, bing actually said that "->" has the highest order of precedence but if you read the whole answer you see it is only for type construction where Bing specifically made claims of the order of precedence and in the other case (parsing & fixity), bing said that the fixity of "->" is not defined in the Haskell 98 report, and nuanced it by saying that the parsing rules depend on both fixity and associativity. <br><br>Here is my Question to bing:<br><br><span style="color:rgb(0,0,0);font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> Related to the above there seems to be ambiguity in the<br>> phrase “order of precedence here”. With regards to evaluation<br>> the order -- in the case of mcons (shown above) -- the “->” <br>> operator seems to get bound first, with real world data.<br>> This suggests a higher order of precedence for “->” than<br>> the other operators. However, with regards to parsing the<br>> operator “->” is associated with less deeply nested brackets,<br>> which in a strict language would suggest a lower order of<br>> precedence, or equivalently in Haskell lingual, a lower fixity.<br>> Fixity is defined in Talb 2 at but this table doesn’t give the<br>> fixity for “->”. </span><span class="gmail-link" style="box-sizing:border-box;color:rgb(41,80,111);font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px"><a href="http://www.haskell.org/onlinereport/decls.html#nested">www.haskell.org/onlinereport/decls.html#nested</a></span><br><font color="#1155cc"><u><a href="https://www.pearltrees.com/s243a/question-evaluation-questions/id76447605/item582390761">https://www.pearltrees.com/s243a/question-evaluation-questions/id76447605/item582390761</a> <br></u></font><br>and here is bing's answer:<br><p style="box-sizing:border-box"><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> You’ve raised an interesting point regarding the perceived</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> ambiguity in the phrase “order of precedence” when it</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> comes to the -> operator in Haskell. Let’s delve into this</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">>  topic and clarify the nuances.</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> </font><b style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(0,0,0);box-sizing:border-box">1. Operator Precedence and Associativity:<br>> * </b><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">In Haskell, operator precedence determines</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> the order in which operators are evaluated. It</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> ensures that expressions are parsed unambiguously.</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> * The associativity of an operator determines whether</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> it is evaluated from left to right (left-associative) or from</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> right to left (right-associative).</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> * The -> operator (function type constructor) has a</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> specific precedence and associativity.</font><br><span style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(0,0,0);box-sizing:border-box"><b>> 2. Function Type Constructor (->) Precedence:<br></b></span><b style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(0,0,0)">> * </b><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">The -> operator has the </font><b style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(0,0,0);box-sizing:border-box">highest precedence</b><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px"> among</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> all operators in Haskell.</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> It is used to specify a function’s type signature, such</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> as Int -> Int -> Float.</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> * Being right-associative, it means that function types</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> associate from right to left. For example,</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">>  Int -> Int -> Float is equivalent to Int -> (Int -> Float).</font><br><span style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(0,0,0);box-sizing:border-box">> </span><span style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(0,0,0);box-sizing:border-box"><b>3. Parsing and Fixity:<br></b></span><b style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(0,0,0)">> * </b><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">When parsing expressions, Haskell follows specific</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> rules for each operator, including the -> operator.</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> * The compiler determines how to group expressions based on the fixity (precedence and associativity) of operators.</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> * Fixity declarations allow you to control how</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> operators are parsed.</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> *Unfortunately, the Haskell 98 Report does not</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> explicitly list the fixity of the -> operator.</font><br><span style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(0,0,0);box-sizing:border-box">> </span><span style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(0,0,0);box-sizing:border-box"><b>4. Custom Operators and Readability:<br></b></span><b style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(0,0,0)">> * </b><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">Custom operators (including symbolic ones)</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> can indeed decrease readability and maintainability.</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> * When encountering unfamiliar operators, it’s</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> challenging to deduce their meaning solely from</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> their names.</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> * The arbitrary-looking names lack hints for understanding</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> their purpose, especially for newcomers.</font><br><span style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(0,0,0);box-sizing:border-box">> 5. </span><span style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(0,0,0);box-sizing:border-box"><b>Using $ to Clarify Expressions:<br></b></span><b style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(0,0,0)">> * </b><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">The $ operator is defined with very low precedence.</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> * Writing f $ x is equivalent to f x, but it helps avoid</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> parentheses.</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> * By using $, you can explicitly indicate the evaluation</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> order without relying on operator precedence.</font><br><span style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(0,0,0);box-sizing:border-box">> </span><span style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(0,0,0);box-sizing:border-box"><b>6. Conclusion:<br></b></span><b style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(0,0,0)">> * </b><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">While the -> operator has the highest precedence,</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> its behavior is influenced by associativity and context.</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> * Fixity declarations (such as infixr 0 ->) can help</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> control how operators are parsed.</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> * Understanding operator behavior and using $ judiciously </font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> can lead to more idiomatic and maintainable code.</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">></font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> In summary, the -> operator’s precedence is indeed high,</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> but its behavior is nuanced due to associativity and</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> parsing rules. Fixity declarations and careful usage of</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> operators contribute to code clarity.</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">></font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> For more details, refer to the </font><span class="gmail-link" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(41,80,111);box-sizing:border-box">Haskell 98 Report</span><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">.</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">></font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> Feel free to ask if you have further questions or need additional clarification! 😊</font><br><font color="#000000" style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">>Learn more<br>> </font><span style="font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px;color:rgb(41,80,111)">1 </span><font color="#29506f" face="OpenSansRegular, Helvetica, sans-serif"><span style="font-size:17px"><a href="https://stackoverflow.com/questions/23553139/operator-and-function-precedence-in-haskell">https://stackoverflow.com/questions/23553139/operator-and-function-precedence-in-haskell</a><br></span></font><span style="color:rgb(41,80,111);font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> 2 </span><font color="#29506f" face="OpenSansRegular, Helvetica, sans-serif"><span style="font-size:17px"><a href="https://www.haskellsos.com/basics/what-order-would-haskell-evaluate-2-operands-of-the-same-precedence/">https://www.haskellsos.com/basics/what-order-would-haskell-evaluate-2-operands-of-the-same-precedence/</a><br></span></font><span style="color:rgb(41,80,111);font-family:OpenSansRegular,Helvetica,sans-serif;font-size:17px">> 3 </span><font color="#29506f" face="OpenSansRegular, Helvetica, sans-serif"><span style="font-size:17px"><a href="https://devhubby.com/thread/what-is-the-precedence-of-and-in-haskell">https://devhubby.com/thread/what-is-the-precedence-of-and-in-haskell</a><br>> 4 <a href="https://studentprojectcode.com/blog/how-to-change-precedence-of-constructor-in-haskell">https://studentprojectcode.com/blog/how-to-change-precedence-of-constructor-in-haskell</a><br>> 5 <a href="https://stackoverflow.com/questions/3125395/haskell-operator-vs-function-precedence">https://stackoverflow.com/questions/3125395/haskell-operator-vs-function-precedence</a><br>> 6 <a href="https://stackoverflow.com/questions/56202894/what-is-the-precedence-of-and-in-haskell">https://stackoverflow.com/questions/56202894/what-is-the-precedence-of-and-in-haskell</a><br>> 7 <a href="https://codereview.stackexchange.com/questions/120900/expression-parser-in-haskell-using-operator-precedence-table">https://codereview.stackexchange.com/questions/120900/expression-parser-in-haskell-using-operator-precedence-table</a><br>> 8 <a href="https://kowainik.github.io/posts/fixity">https://kowainik.github.io/posts/fixity</a><br>> 9 <a href="https://devtut.github.io/haskell/infix-operators.html">https://devtut.github.io/haskell/infix-operators.html</a><br>> 10 <a href="https://www.haskell.org/onlinereport/decls.html">https://www.haskell.org/onlinereport/decls.html</a></span></font></p><a href="https://sl.bing.net/gHzlncNjtLw">https://sl.bing.net/gHzlncNjtLw</a><br><a href="https://www.pearltrees.com/s243a/question-evaluation-questions/id76447605/item582390849">https://www.pearltrees.com/s243a/question-evaluation-questions/id76447605/item582390849</a><br><br>I wonder how people would rate Bing's answer. </div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div></div>