UpValues, TagSet and UpSet, what's the difference, when should you use them?

Some of the big mysteries of ~~Universe~~ Mathematica for me is the application of UpValues. I know about this question and know the very poor Mathematica documentation on that. I'm very curious to know if someone that not @Leonid uses this too.

Just to get some clue on how it works, I would like to know what's the difference between TagSet and UpSet. Can I say that UpSet is subset of TagSet?

For instance, I can say these examples are equivalent.

name[alien]^= "Alf"    
alien /: name[alien] = "Alf"

In what situations should I apply each case?

Answer

UpSet and UpSetDelayed make multiple assignments:

UpSet associates an assignment with all the distinct symbols that occur either directly as arguments of lhs, or as the heads of arguments of lhs.

f[a[__], b[__], c[__]] ^:= "UpValue"

UpValues[a]
UpValues[b]
UpValues[c]

{HoldPattern[f[a[__], b[__], c[__]]] :> "UpValue"}

{HoldPattern[f[a[__], b[__], c[__]]] :> "UpValue"}

{HoldPattern[f[a[__], b[__], c[__]]] :> "UpValue"}

TagSet and TagSetDelayed make specific assignments:

k /: g[i[__], j[__], k[__]] := "UpValue"


UpValues[i]
UpValues[j]
UpValues[k]

{}

{}

{HoldPattern[g[i[__], j[__], k[__]]] :> "UpValue"}

Comments

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