Functional interpretations are powerful tools in mathematical logic with many applications, among them witnessing existential statements. The first class of functional interpretations provided precise witnesses for existential statements. A second class of functional interpretations provided bounds for existential statements by changing the target from precise witnesses to bounds in a last step. A third class of functional interpretations, called bounded functional interpretations, provided also bounds but targeting bounds from the first step.
Paulo Oliva, joined by Gilda Ferreira, has pursued a unification program: to show that different functional interpretations are instances of a parametrized functional interpretation. The first class of unifications took place in the context of the usual intuitionistic logic. A second class of unifications changed the context to classical linear logic. Then a third class of unifications changed the context to intuitionistic linear logic.
This being said, now we can easily describe the article in question: It presents a unification in the context of intuitionistic linear logic of bounded functional interpretations. More extensively, the article:

(1)

presents parametrized functional interpretations of the usual intuitionistic logic and of intuitionistic linear logic;

(2)

shows that the two parametrized functional interpretations are the same modulo embedding one logic in the other;

(3)

proves the soundness theorem / adequacy lemma for the parametrized functional interpretations;

(4)

shows that the parametrized functional interpretations instantiate into three bounded functional interpretations, namely the (simply called) bounded functional interpretation, the bounded modified realizability and the confined modified realizability;

(5)

sheds light on the comparison of the bounded functional interpretations by making clear in the parametrized functional interpretations what they have in common and in what they differ.