Abstract

We define an axiomatic semantics for a common kernel of existing data-parallel languages. We introduce an assertional language which enables us to define a weakest liberal precondition calculus which has the Definability Property, and a proof system ({\it a la\/} Hoare) which has the Completeness Property. Moreover, our axiomatic semantics integrates two previous works in the definition of proof systems for data-parallel programs. This work sheds a new light on the logical complexity of proving data-parallel programs.

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