A Geometry of Interaction Machine for Gödel’s System T

Godel’s System T is the simply typed lambda calculus extended with numbers and an iterator. The higher-order nature of the language gives it enormous expressive power—the language can represent all the primitive recursive functions and beyond, for instance Ackermann’s function. In this paper we use System T as a minimalistic functional language. We give an interpretation using a data-flow model that incorporates ideas from the geometry of interaction and game semantics. The contribution is a reversible model of higher-order computation which can also serve as a novel compilation technique.