There is a great deal of mathematical theory concerning the syntax of languages. This theory is based on the work of Chomsky.
Formal syntax has proved to be better at describing artificial languages such as programming languages than at describing natural languages. Nevertheless, it is useful to understand this theory.
A recursive language is one that can be recognized by a program; that is, given a string, a program can tell within finite time whether the string is or is not in the language.
A recursively enumerable language is one for which all strings in the language can be enumerated by a program. All languages described by phrase structure grammars are R.E., but not all R.E. languages are recursive.
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