Editing System F (section)

==The Girard-Reynolds Isomorphism==
In second-order [[intuitionistic logic]], the second-order polymorphic lambda calculus (F2) was discovered  by Girard (1972)  and independently by Reynolds (1974).<ref name=gr2 /> Girard proved the ''Representation Theorem'': that in second-order intuitionistic predicate logic (P2), functions from the natural numbers to the natural numbers that can be proved total, form a projection from P2 into F2.<ref name=gr2 /> Reynolds proved the ''Abstraction Theorem'': that every term in F2 satisfies a logical relation, which can be embedded into the logical relations P2.<ref name=gr2 /> Reynolds proved  that a Girard projection followed by a Reynolds embedding form the identity, i.e., the '''Girard-Reynolds Isomorphism'''.<ref name=gr2>[[Philip Wadler]] (2005) [http://homepages.inf.ed.ac.uk/wadler/papers/gr2/gr2.pdf  The Girard-Reynolds Isomorphism (second edition)] [[University of Edinburgh]], [http://wcms.inf.ed.ac.uk/lfcs/research/groups-and-projects/pl/programming-research-at-lfcs  Programming Languages and Foundations at Edinburgh]</ref>