The form of BASIC I remember learning about 15 years ago was a very ugly language. There were no functions, so I would use gotos all over the place to roll my own. The code was a mess, and kludgy.
Even if a BASIC => Perl translator existed, or even if you could code one, you most likely would not want to translate your program. The 4000 lines of code would go from being maintainable in XBASIC to very cryptic perl and pretty hard to change without breaking anything.
I would recommend creating the program in Perl from scratch. Make use of an Object Oriented programming paradigm so your code is more efficient and maintainable, and write lots of test cases along the way to make sure everything does what it is supposed to.
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