Making a list of patterns of arbitrary length

I would like to create a list of arbitrary length:

x1_, x2_, ...


Where each of the elements of the list has the full form:

Pattern[xi, Blank]


This answer shows how to create a list of symbols:

x1, x2, ...


but I don't know how to adapt that to obtain the above.

I intend to use this list in the definition of a function as in here.

4 Answers
4

Array[ToExpression["x" <> ToString @ # <> "_"] &, 5]


x1_, x2_, x3_, x4_, x5_

FullForm @ %


List[Pattern[x1,Blank], Pattern[x2, Blank], Pattern[x3, Blank], Pattern[x4, Blank], Pattern[x5, Blank]]

Also

Thread[Pattern[Evaluate@Array[Symbol["x" <> ToString@#] &, 5], Blank]]


x1_, x2_, x3_, x4_, x5_

and

ToExpression[Table["x" <> i <> "_", i, ToString /@ Range[5]]]


x1_, x2_, x3_, x4_, x5_

x1=1

If you construct a list of strings instead, you can take advantage of the fact that ToExpression is listable, and supports a 3rd argument that post-processes the output. For example:

ToExpression

ToExpression[
"x1", "x2", "x3",
StandardForm,
Pattern[#,Blank]&
]


x1_, x2_, x3_

Or, creating the list and converting:

ToExpression[
Table["x" <> ToString@i, i, 5],
StandardForm,
Pattern[#, Blank]&
]


x1_, x2_, x3_, x4_, x5_

x1 = 1

Function[sym,Pattern[sym,Blank],HoldFirst]

Pattern[#,Blank]&

x1 = 1

xi

Pattern[1, Blank]

Nothing new but shorter:

StringTemplate["x``_"] /@ Range[10] // ToExpression


x1_, x2_, x3_, x4_, x5_, x6_, x7_, x8_, x9_, x10_


Here is an example of how to make the solution in the link work for this case:

patt = Table[
With[
s = Symbol["x" <> ToString[i]],
Pattern[s, Blank]
], i, 10];

Range[10] /. patt :> x5, x8


5, 8

5, 8

Using With here is a trick to insert the symbol into Pattern. Since Pattern has the attribute HoldFirst, it would not work to write e.g.

With

Pattern

Pattern

HoldFirst

Pattern[Symbol["x" <> ToString[i]], Blank]


because Symbol["x" <> ToString[i]] would not be evaluated before it was passed to Pattern, i.e. Pattern would not receive a string as is required.

Symbol["x" <> ToString[i]]

Pattern

Pattern

x1 = 1

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