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A categorical interpretation of assertion(axiomatic) semantics of programming languages is proposed. All of the preconditions, postconditions and programs are interpreted as (binary) relations in topo...ses by making use of relational calculus, and several fundamental properties of Dijkstra's weakest preconditions are proved. Assertions in the semantics depend on the intuitionistic logic, so this is an extension of the assertion semantics due to E.G. Manes and M.A. Arbib.show more
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