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@jemoka / Jemoka Knowledge Base / raw/concept/kbhcategorical_grammar.md
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--- title: "categorical grammar" source: https://www.jemoka.com/posts/kbhcategorical_grammar/ --- categorical grammar is a grammar in the language of categories. constituents \(A\), a set of “expressions” \(C\), a set of categories of “syntax” \(\varphi: A \to Pow( C)\), assigning each \(a \in A\) to a set of categories \(c \subset C\) \(G\): a family of sets of n-place operations where \(n=1, 2, \ldots\) (what does a “3-place” op mean? idk) \(R\): a set of rules encoded as tuples: \((f; \{c_1, \dots c_{k}\}; c_{k+1})\), where \(f\) is a \(k\) place operation, and \(c_{j} \in C\) requirements The operations of this grammar behaves like so: given a rule \(r \in R\), it tells you that given WLOG an expression in \(c_{1}, c_2, \ldots c_{k} \in C\) (i.e. they were mapped to that set \(\varphi\)), \(f\) will map that set of expressions into the same new category \(c_{k+1}\). additional information a basic categorical grammar one implementation of a basic categorical grammar is as follows: