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Constructing a function with Flat and OneIdentity attribute with the property that otimes[a]:>a


I want to have a function (called otimes) with the following two properties:



  1. it has the attribute OneIdentity and Flat

  2. if evaluated with a single argument it returns that argument


The built-in function Times has these properties; e.g., evaluating Times[a] yields a.



I am struggling with implementing my own function having the same behavior. What I tried is the obvious implementation


SetAttributes[otimes,{OneIdentity,Flat}]
otimes[a_]:=a

However this does not work and leads to an infinite recursion when I evaluate otimes[a,b]. I do not know how to implement the desired behavior consistently. Maybe somebody can help?



Answer



I see now. The problem arises with Flat then. Just set the attributes after setting the definitions. Or at least the Flat attribute


ClearAll[otimes];
SetAttributes[otimes, OneIdentity]
otimes[a_] := a

SetAttributes[otimes, Flat]

Check out this answer for more details on why this works.


Basically, MMA remembers if the symbol was Flat or not at the time each DownValue is defined. The infinite recursion is more related to this:


SetAttributes[f, Flat];
Replace[Hold@f[2], Hold@f[i_] :> Hold[i]]

So, when you did otimes[2] and it checked the otimes[a_]:=a downvalue, it matched a with otimes[2], so you got your infinite recursion


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