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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.


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