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I'm studying a code with the following function declaration :

FindChain[ x:__ ,y_?FindChainQ,z:__] := { {x},y,{z} }

What is the meaning of the colon ":" after the arguments x and z ?

What would be the diference(s) with this declaration (without the colons) :

FindChain[ x__,y_?FindChainQ,z__] := { {x},y,{z} }

Thank you,

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    $\begingroup$ Check the documentation of SetDelayed. $\endgroup$
    – bbgodfrey
    Jul 27 at 17:37
  • $\begingroup$ Check the documentation for Pattern too. It says: The form s_ is equivalent to s:_ Similarly ... s__ to s:__. You can see this by doing FullForm[s__] and FullForm[s : __] . The purpose of it is a shorthand so you don't need to write the full Pattern and for when you have one symbol but a complex pattern object on the rhs. $\endgroup$
    – flinty
    Jul 28 at 12:38
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It is useful when your pattern does not start with _. Suppose your pattern is a list of integers,

total[list : {__Integer}] := Total[list]
total[___] := $Failed

Or a variable that can be true or false:

func[arg:(True | False)] := If[arg, foo, bar]
func[___] := $Failed
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  • $\begingroup$ I m sorry but i don t understand your first explanation. Can you develop a bit more ? $\endgroup$
    – Bendesarts
    Jul 28 at 10:58
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A colon is useful to name a filter with the following syntax: name:filter. For example, polarPlot[r_, domain:{t_, tmin_, tmax_}]:=ParametricPlot[{r Cost[t], r Sin[t]}, domain] domain specifies a list of 3 éléments.

It can be useful also to factor a filter as r_Integer|r_Rational in r:(_Integer,_Rational)

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