This paper is a review of the formal definitions of a description language of functional models of Constraint-Based Lexicalized Grammar (CBLG), with a notion of well-formedness, models of linguistic objects, and the corresponding denotation function. The language uses feature-value descriptions. A formalization of CBLG is presented via definitions of several classes of objects by this formal language using mutual recursion. The core engine of the CBLG formal grammar is a hierarchical type system associated with constraints for representation of linguistic information. The constraints are classified as linguistic principles, grammar rules, lexical entries, lexical rules, and semantic representations. The formal system of CBLG targets a computational approach to human language grammar.