On bounded functional interpretations

Abstract Bounded functional interpretations are variants of functional interpretations where bounds (rather than precise witnesses) are extracted from proofs. These have been particularly useful in computationally interpreting non-computational principles such as weak Konig’s lemma. This paper presents a family of bounded functional interpretations — in the form of a parametrized interpretation — of both intuitionistic logic and (a fragment of) intuitionistic linear logic. We show how three different instantiations of the parameters give rise to three recently developed bounded interpretations: the bounded functional interpretation, bounded modified realizability and confined modified realizability.