In this paper, the syntax and semantics for a fragment of English will be provided within the framework of Martin-L?f's Type Theory. The first to explore the potential benefits of this application was Aarne Ranta [7]. The motivation for the present work is to develop a more traditional approach (Montague-style semantics) to semantics based upon the constructive framework. The work is focused on the parsing problem, which consists of providing the interpretation of a given English sentence as an expression in the Type Theory. In this paper it is shown that the parsing and semantic interpretation of a sentence can be accomplished in a compositional fashion by defining semantic rules that work in a one-to-one correspondence with the syntactic ones.