The recent emergence of linguistic formalisms exclusively based on the simply-typed λ-calculus to represent both syntax and semantics led to the presentation of innovative techniques which apply to both the problems of parsing and generating natural languages. A common feature of these techniques consists in using strong relations between typing properties and syntactic structures of families of simply-typed λ-terms. Among significant results, an efficient algorithm based on Datalog programming is presented in [Kan07] for context-free grammar of almost linear λ-terms, which are linear λ-terms augmented with a restricted form of copy. We present an extension of this method to terms for which deletion is allowed.