What is the meaning of language expressions and how to compute or calculate it? In this paper, we give an answer to this question by analysing the meanings of aspects and tenses in natural languages inside the formal model of an grammar of applicative, cognitive and enunciative operations (GRACE) (Desclés and Ro in Math Sci Hum 194:39–70, 2011), using the applicative formalism, functional types of categorial grammars and combinatory logic (CL) (Curry and Feys in Combinatory Logic. North-Holland Publishing, Amsterdam, 1958). In the enunciative theory (Benveniste in Problèmes de linguistique générale, 1, 2. Gallimard, Paris, 1974; Culioli in Formalisation et opérations de repérage, tome 2. Ophrys, Paris, 1999; Desclés in Une articulation entre syntaxe et sémantique cognitive: la grammaire applicative et cognitive, mémoires de la société de linguistique de Paris, nouvelle série, tome XX, l’architecture des théories, les modules et leurs interfaces. Peeters, Louvain, 2011) and following (Bally in Linguistique générale et linguistique française. Berne, Franke, 1965), an utterance can be decomposed into two components: a modus and a dictum (or a proposition). In GRACE, the modus is a complex operator applied to a proposition (a dictum) and is generated from more elementary operators of the categories of tense, aspect, and modality. The dictum is a proposition generated by a predicative relation. In this way, we can attribute a semantic meaning to different grammatical aspecto-temporal operators. The applicative expressions of CL can be easily translated into a functional programming language such as HASKELL or CAML (Ro in Les référentiels et opérateurs aspecto-temporels: définitions, formalisation logique et informatique. PhD thesis, Université de Paris-Sorbonne, Paris, 2012).