Algol-like Language

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 rst signiicant 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 diiers from the one in 13] in that we now use a larger set of relations. In a certain sense it is thèlargest possible' set of relations, an idea which we have successfully used in 32] to obtain a fully abstract model for the second order subset of 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 speciic to the imperative (Algol-like) setting.