quantitative grammar

Grammar rules can be strings and functions, which take input strings and make output strings {quantitative grammar}. Strings can have unique integers, using Gödel numbering. String sets {enumerable set} can have unique integers. Quantitative grammars involve enumerable sets of input sentences, output sentences, and grammar rules. Recursive functions, algorithms, Turing machines, and Post axiomatic systems are mathematically equivalent ways to model quantitative grammars.

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