Behavioural equivalence and indistinguishability in higher-order typed languages

We extend the study of the relationship between behavioural equivalence and the indistinguishability relation[4, 7] to the simply typed lambda calculus, where higher-order types are available. The relationship between these two notions is established in terms of factorisability[4]. The main technical tool of this study is pre-logical relations[8], which give a precise characterisation of behavioural equivalence. We then consider a higher-order logic to reason about models of the simply typed lambda calculus, and relate the resulting standard satisfaction relation to behavioural satisfaction