Abstract
We prove two theorems about the completeness of Hoare's logic for the partial correctness of while-programs over an axiomatic specification. The first result is a completion theorem: any specification (Σ,E) can be refined to a specification (Σ 0, E 0), conservative over (Σ, E), whose Hoare's logic is complete. The second result is a normal form theorem: any complete specification (Σ, E) possessing some complete logic for partial correctness can be refined to an effective specification (Σ 0, E 0) conservative over (Σ, E), which generates all true partial correctness formulae with Hoare's standard rules.
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