Abstract
This paper establishes a strong completeness property of compositional program logics for pure and imperative higher-order functions introduced in [18, 16, 17, 19, 3]. This property, called descriptive completeness, says that for each program there is an assertion fully describing the program’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.
Work is partially supported by EPSRC GR/R03075/01, GR/T04236/01, GR/S55538/01, GR/T04724/01, GR/T03208/01 and IST-2005-015905 MOBIUS.
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Honda, K., Berger, M., Yoshida, N. (2006). Descriptive and Relative Completeness of Logics for Higher-Order Functions. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4052. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11787006_31
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