As a mathematician, what programming language should you use when you need to do anything algorithmic? For some specific domains there are languages tailored for the task, for example Macaulay2 is great for some types of algebra. For general problems many turn to Mathematica or Maple. But although they are universal (in the sense of Turing) they're not great platforms for general purpose algorithm
In my last post I showed how to incrementally match long strings against regular expressions. I now want to apply similar methods to matching languages that can't be described by regular expressions. (Note that 'language' is just jargon for a set of strings that meet some criterion.) In particular, regular expressions can't be used to test a string for balanced parentheses. This is because we need
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