Skip to main content

programming - Why does Mathematica choose the second function definition?


While working on a solution to this question I've come across a case where I simply don't understand Mathematica's behaviour.


I've got the following definitions:


PatternImplies[(x:(Verbatim[Blank]

|Verbatim[BlankSequence]
|Verbatim[BlankNullSequence]))[h_],x[]]:=True

(*CatchAll rule*)
PatternImplies[_,_]:=Maybe;

Now I try this:


PatternImplies[_Integer,_]
(*
==> Maybe

*)

I would have expected True. My first thought was that I probably got the pattern wrong, so I tested:


MatchQ[PatternImplies[_Integer,_],
PatternImplies[(x:(Verbatim[Blank]
|Verbatim[BlankSequence]
|Verbatim[BlankNullSequence]))[h_],x[]]]
(*
==> True
*)


In other words, the pattern matches. Moreover, looking at Downvalues I see that the special rule is indeed stored before the catch-all rule.


So why does Mathematica chose the second definition (and more importantly, what can I do about it?)



Answer



As far as I can tell, it should match the catch all rule. That's because _ isn't of the form x[]


Now, when you test the MatchQ expression, both arguments are first evaluated. So, you're actually doing MatchQ[maybe, maybe] which of course returns True.


You can do the checking as you intended to by first holding the arguments


MatchQ[Hold@PatternImplies[_Integer, _], 
Hold@PatternImplies[(x : (Verbatim[Blank] | Verbatim[BlankSequence] |
Verbatim[BlankNullSequence]))[h_], x[]]]


False

EDIT:


I now see what you intended with x[]. You could do x_[] instead. That would mean "any no-argument expression whose head coincides with the previous pattern labelled x. If you write x[] it matches literally


Comments

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...