Self-reference puzzle

I was browsing the internet for self-referential sentences when I came across this puzzle:

Fill in the blanks in the following sentence with the correct numbers: In this sentence, the number of occurrences of 0 is _, 1 is _, 2 is _, 3 is _, 4 is _, 5 is _, 6 is _, 7 is _, 8 is _, 9 is _.

If it has a solution, find it; if not, prove it.

I wrote a Haskell program to help me.

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