Full abstraction for the second order subset of an ALGOL-like language

Abstract

We present a denotational semantics for an ALGOL-like language ALG, which is fully abstract for the second order subset of ALG. This constitutes the first significant full abstraction result for a block structured language with local variables. As all the published "test equivalences" [13, 8, 23 for Algol-like languages are contained in the second order subset, they can all be validated (easily) in our denotational model. The general technique for our model construction -- namely "relationally structured locally complete partial orders" with "relation preserving locally continuous functions" -- has already been developed in [13], but our particular model differs from the one in [13] in that we now use a larger set of relations. In a certain sense it is the "largest possible" set of relations, an idea which we have successfully used in [32] to obtain a fully abstract model for the second order subset ot the functional language PCF [26]. The overall structure of our full abstraction proof is also taken from [32], but for the single parts of the proof we had to solve considerable new problems which are specific to the imperative (Algol- like) setting.