Template-Coq is a plugin for Coq, originally implemented by Malecha, which provides a reifier for Coq terms and global declarations , as represented in the Coq kernel, as well as a denotation command. Initially, it was developed for the purpose of writing functions on Coq's AST in Gallina. Recently, its use was extended for the needs of the CertiCoq certified compiler project, which uses it as its front-end language and to derive parametricity properties, and the work of Forster on extracting Coq terms to a CBV λ-calculus. However, the syntax currently lacks semantics, be it typing semantics or operational semantics, which should reflect, as formal specifications in Coq, the semantics of Coq itself. This is an issue for CertiCoq where both a non-deterministic small step semantics and a deterministic call-by-value big step semantics had to be defined and preserved, without an " official " reference specification to refer to. Our hope with this work is to remedy this situation and provide a formal semantics of Coq's implemented type theory, that can independently be refined and studied. By implementing a (partial) independent checker in Coq, we can also help formalize certified translations from Coq to Coq.