The paper presents NLC, a new formalism for modeling natural language (NL) compositionality. NLC is a functional type system (i.e. one based on mathematical functions and their types). Its main features include a close correspondence with NL and an integrated modeling of morphological, syntactic and semantic compositionality. The integration is effected with a subclass of compound types (types which are syntactic compounds of multiple types or their terms), while the correspondence is sought with function types and polymorphism. The paper also presents an implementation of NLC in Coq. The implementation formalizes a diverse fragment of NL, with NLC expressions type checking and failing to type check in exactly the same ways that NL expressions pass and fail their acceptability tests. Among other things, this demonstrates the possibility of reducing morphological, syntactic and semantic compositionality to a single level of description. The level is tentatively identified with semantic compositionality — an interpretation which, besides being supported by results from language processing, has interesting implications on NL structure and modeling.