On ‘Logical Relations’ in Program Semantics

Abstract

The simplest way to think about logical relations and invariance is to start with permutations on a ‘ground’ set D; a permutation m₁ is obviously lifted to a permutation m₂ on functionals F from D into D by

$${m_2}F = {m_1} \cdot F \cdot {\left( {{m_1}} \right)^{ - 1}}$$

and this process can be performed for all higher types as well. Then a functional G (of some type) is invariant with respect to a class M of permutations iff mG = G for all m in M.

This work was supported in part by NSF Grant No. A511190-DCR and by ONR Grant No. N00014-83-K-0125.