Mizar System
The Mizar project has completely formalized and automatically checked a proof of Hilbert's basis theorem in the HILBASIS file.
Read more about this topic: Hilbert's Basis Theorem
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“Hence, a generative grammar must be a system of rules that can iterate to generate an indefinitely large number of structures. This system of rules can be analyzed into the three major components of a generative grammar: the syntactic, phonological, and semantic components.”
—Noam Chomsky (b. 1928)