Maybe you want to use a proper templating system to replace variable names?

If you need to do this yourself, follow these steps:

1. Read the variable values
2. Read the statement
3. Replace the variable values in the statement
4. Execute the statement

For step three, I suggest the following data structure:

my %variables= (
    schema => 'myschema',
    name => 'my_name',
);

my $statement= 'select * from $schema.app_table where col1 = $name';

$statement =~ s/\$(\w+)/$variables{ $1 } || '$'.$1/ge;
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Note that you will either need to add proper quotes around $name in the SQL statement or add additional logic to recognize when a variable is used as a column value and then transform the logic to use SQL placeholders.