A method for computing the complete meaning of sentences with anaphoric reference is presented, that is, the method for implementing the substitution of an appropriate antecedent to accompany the anaphoric reference. Our method is similar to the one applied in general by Hans Kamp's Discourse Representation Theory (DRT). ‘DRT’ is an umbrella term for a collection of logical and computational linguistic methods developed for a dynamic interpretation of natural language, where each sentence is interpreted within a certain discourse, which is a sequence of sentences uttered by a group of speakers. Interpretation conditions are given via instructions for updating the discourse representation. Yet these methods are mostly based on first-order logics. Thus, only expressions denoting individuals (indefinite or definite noun phrases) can introduce so-called discourse referents, which are free variables that are updated when interpreting the discourse. Our background theory is Pavel Tichý's Transparent Intensional Logic with its procedural rather than set-theoretic model semantics. Since our semantics is procedural, hence hyperintensional and higher-order, not only individuals, but entities of any type, like properties of individuals, propositions and hyperpropositions, relations-in-intension, and even constructions (i.e., meanings of antecedent expressions), can be linked to anaphoric variables. Moreover, the thoroughgoing typing of the universe of TIL makes it possible to determine the respective type-theoretically appropriate antecedent, which is one of the novel contributions of this paper. The second novelty is the specification of the algorithm for dynamic discourse representation within TIL.