Algebraic syntax

Recursive categorical syntax is an algebraic theory of syntax developed by Michael Brame as an alternative to transformational-generative grammar. Brame formulated an algebra (technically a nonassociative groupoid with inverses) of lexical items (words and phrases), or lexes for short. A lex is a string representation of a word or phrase together with a string of directed types. A directed type is a symbol representing a syntactic type together with a direction (up, down, left, right) usually given by an arrow beside or above the symbol. In this article left and down arrows will be placed to the left and right and up arrows to the right of symbols.
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