Descriptive and Relative Completeness of Logics for Higher-Order Functions (with Nobuko Yoshida and Kohei Honda)

This paper establishes a strong completeness property of compositional program logics for pure and imperative higher-order functions introduced by the authors. This property, called descriptive completeness, says that for each program there is an assertion fully describing the former's behaviour up to the standard observational semantics. This formula is inductively calculable from the program text alone. As a consequence we obtain the first relative completeness result for compositional logics of pure and imperative call-by-value higher-order functions in the full type hierarchy.

The implementation of a CAP generator referred to in the text can be found here.

extended abstract: coming soon!
long version: ps.gz, pdf. Status: draft.

More information about this line of work can be found here.

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