  We present three different functional interpretations of intuitionistic
linear logic ILL and show how these correspond to well-known functional
interpretations of intuitionistic logic IL via embeddings of IL into ILL. The
main difference from previous work of the second author is that in
intuitionistic linear logic (as opposed to classical linear logic) the
interpretations of !A are simpler and simultaneous quantifiers are no longer
needed for the characterisation of the interpretations. We then compare our
approach in developing these three proof interpretations with the one of de
Paiva around the Dialectica category model of linear logic.
