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# Difference between f1[a_, b_] := a[b]^2 and f2[a_][b_] := a[b]^2 etc.

Posted 10 years ago
 Colleagues, please - it is a difference betwen theese defintifions? It seems to me, that tey are equivalent -- it is true? In[1]:= f1[a_, b_] := a[b]*a[2 b] In[2]:= f2[a_][b_] := a[b]*a[2 b] In[3]:= f3[a_[b_]] := a[b]*a[2 b] In[4]:= {f1[Func, x], f2[Func][x], f3[Func[x]]} Out[4]= {Func[x] Func[2 x], Func[x] Func[2 x], Func[x] Func[2 x]}  Can you give me a link for study this theme? Thanks!
 The first two accomplish the very same thing, for as long as you keep them in this form.The third one won't always behave the same way though. Consider fun[x_] := x^2 f3[a_[b_]] := a[b]*a[2 b] Then f3[fun[z]] will evaluate to f3[z^2] because fun[z] evaluates first. However, if you set SetAttributes[f3, HoldAll], then it will behave more similarly to f1 and f2:f3[fun[z]] will now first evaluate to fun[z]*fun[2 z], then to 4 z^4.This is not the complete story, but giving full details is not always educational. So instead I'll leave you with this reference, which (I think) discusses all the relevant issues: In particular, look at the section on Nonstandard Evaluation and the Hold... attributes.