Skip to main content

pattern matching - Bug in RepeatedNull?


RepeatedNull appears to be buggy (versions 8.0, and 9.0).


Define f as follows:


In[1]:= f@s:{h_@___...} := List @@@ s

f is intended to accept (possibly empty) List of non-atomic (possibly empty) expressions with the same head and change that head to List. It seems to work properly at first:



In[2]:= f@{g[x], g[y]}
Out[2]= {{x}, {y}}

(Calculates as intended.)


In[3]:= f@{g[x], h[y]}
Out[3]= f[{g[x], h[y]}]

(Pattern does not match.)


However, f behaves unexpectedly on an empty List:


In[4]:= f@{}

Out[4]= {1}

The pattern does match, as it should, but the appearance of 1 is a complete mystery. I expected f@{} to be List @@@ {}, which is {}. Tracing didn't tell me anything:


In[5]:= Trace[f@{}, TraceInternal -> True]
Out[5]= {f[{}], List@@{1}, {1}}

It's probably a bug. Defining f@{} as a special case seems to fix the problem. However, 1) it's not actually a special case, and 2) I'm not sure in the correctness of the definition since there may be something wrong with the pattern I picked.




  1. Was {h_@___...} the right choice of pattern for “(possibly empty) List of non-atomic (possibly empty) expressions with the same head”?





  2. Is there a plausible explanation where does 1 come from?




UPD:


To clear things up I'll elaborate on a test example by @m_goldberg (from the answer) and a note by @sebhofer (from a comment):


In[6]:= ReleaseHold[ClearAll /@ Hold[test1, test2]];
In[7]:= test1[patt1: {h_@___ ...}] := Row@{"With named head: ", patt1}
test2[patt2: {_@___ ...}] := Row@{"Without named head: ", patt2}


Results vary with use of named vs unnamed pattern. That's one aspect convincing me to calssify the issue as bug:


In[9]:= {test1@{}, test2@{}} // Column
Out[9]= "With named head:"
"Without named head:" {}

(Here and after, output formatting is adjusted manually.)


What also concerns me is that existing definitions don't get overwritten:


In[10]:= ClearAll@test
In[11]:= test[patt1 : {h_@___ ...}] := Row@{"With named head: ", patt1}

test[patt2 : {_@___ ...}] := Row@{"Without named head: ", patt2}
DownValues@test
Out[13]= {HoldPattern[test[patt2:{_[___]...}]] :> "Without named head:" patt2,
HoldPattern[test[patt1:{h_[___]...}]] :> "With named head:" patt1}
In[14]:= test@{}
Out[14]= "Without named head:" {}

DownValues is prepended with the subsequent ones:


In[15]:= test[patt1 : {h_@___ ...}] := Row@{"Newdef, with named head: ", patt1}
test[patt2 : {_@___ ...}] := Row@{"Newdef, without named head: ", patt2}

DownValues@test
Out[17]= {HoldPattern[test[patt2:{_[___]...}]] :> "Newdef, without named head:" patt2,
HoldPattern[test[patt1:{h_[___]...}]] :> "Newdef, with named head:" patt1,
HoldPattern[test[patt2:{_[___]...}]] :> "Without named head:" patt2,
HoldPattern[test[patt1:{h_[___]...}]] :> "With named head:" patt1}
In[18]:= test@{}
Out[18]= "Newdef, without named head:" {}

While output satisfactorily corresponds to new definition, this probably should not happen due to 1) unpredictability; 2) garbage accumulation.


(Additional examples of unstable pattern matching with RepeatedNull may be found in comments.)




Answer



Here is some evidence concerning what is going wrong.


ff[arg : {(h : _)@___ ...}] := Row @ {h, " : ", arg}

ff @ {u[x]}


u : {u[x]}

ff @ {{x}}



List : {{x}}

ff @ {{}}


List : {{}}

All the above show what one would expect, but



ff @ {}


{} : 

In this last case, I conclude that h has been matched with {} and arg has been matched with Sequence[]. I can not but think that this is a bug.


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...

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...