"Do What I Mean" - a suggestion for improving Mathematica experience

*To*: mathgroup at smc.vnet.net*Subject*: [mg96961] "Do What I Mean" - a suggestion for improving Mathematica experience*From*: David Bakin <davidbak at gmail.com>*Date*: Sat, 28 Feb 2009 06:42:20 -0500 (EST)

A few days ago I posted that Mathematica should have a "DWIM" feature - "Do What I Mean". In InterLisp, in the 80's, the DWIM facility was hooked into error messages, and when invoked on a user error would poke around on the stack and in the environment using some rules to describe common error situations and it would uncover user errors and offer to correct them. Many of the errors were simple spelling errors and it would correct a misspelled variable name if it found an unbound variable but a similarly spelled variable was bound in the environment. Mathematica could benefit from this, and in fact, we at mathgroup could supply the rules (and framework) as a useful group project. If some guru would write the framework - trapping error messages somehow, perhaps when they were written to the $Messages channel (by replacing the default $Messages channel with something that would hook into the DWIM function), or perhaps with some other hook like redefining Message[] - then the rest of us could supply rules for the common errors. Especially the common errors we see puzzling Mathematica newbies on this list. I would suggest that the rules provide messages, hopefully with hyperlinks to the documentation. A true DWIM might also offer to rewrite the current expression and try it again, but I don't know if that can be done given the hooks into Mathematica that are currently available. Some situations that could be addressed are: 1. User writes "xy" instead of "x y". Rule could inspect the expression under evaluation and find (unevaluated) symbols like "xy" of the form "<prefix><suffix>" where both "<prefix>" and "<suffix>" were either symbols used in the expression or symbols bound in the environment. Rule would explain the problem and offer to rewrite expression and try again. 2. Some expression using a user-defined function causes an error when evaluating, or doesn't evaluate. Looking at the function, a rule finds function calls where the function arguments' patterns include "_Integer" or similar but the arguments given to it are not integers. Rule points to documentation describing argument types required by the called function. 3. Similar to 2 above, but it finds function calls that do numeric evaluation only or are optimized for numeric evaluation but the arguments given to it are symbolic. 4. Result returned is machine precision very close to zero (that is, with large negative exponent), but an error message complained of singularity, or other ill-conditioning. Rule points to documentation explaining about machine precision, and/or singularity, and offers to retry the expression with more digits of precision, rewriting the expression to achieve this. Actually, now that I think of it, the DWIM facility needs also to be invoked by the user because some of these situations don't cause error messages, but only cause (wholly or partially) unevaluated expressions. So maybe the user could be trained to type a word, like "Explain[]" after he didn't get the result he wanted and the DWIM facility would look at the In[] and Out[] arrays to find out what he's been doing recently. I would be glad to contribute rules to the framework ... but I'm not yet up to writing the framework. Hopefully one of the gurus here will find this interesting (and possible) and provide a framework. Then the rest of us could contribute rules that would improve the Mathematica experience for all newcomers. (AES, I'm looking at you! :-) ) -- David