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Proving Partial Correctness of Partial Functions ? Jurgen Giesl

Summary: Proving Partial Correctness of Partial Functions ?
J¨urgen Giesl
FB Informatik, TH Darmstadt, Alexanderstr. 10, 64283 Darmstadt, Germany,
E­mail: giesl@inferenzsysteme.informatik.th­darmstadt.de
Abstract. We present a method for automated induction proofs about
partial functions. This method cannot only be used to verify the partial
correctness of functional programs, but it also solves some other chal­
lenge problems where reasoning about partial functions is necessary. For
a further analysis of partial functions we also developed a method to
determine (non­trivial subsets of) their domains automatically.
1 Introduction
Induction is the essential proof method for the verification of functional pro­
grams. For that reason, several techniques 1 have been developed to perform
induction proofs automatically, cf. e.g. [BM79, Bu + 93, Wa94a]. However, most
of these techniques are only sound if all occurring functions are total.
In this paper we show that by slightly restricting the prerequisites of these
techniques it is nevertheless possible to use them for partial functions, too. In
particular, the successful proof technique of performing inductions w.r.t. algo­
rithms can also be applied for partial functions, i.e. (under certain conditions)
one may even perform inductions w.r.t. non­terminating algorithms.


Source: Ábrahám, Erika - Fachgruppe Informatik, Rheinisch Westfälische Technische Hochschule Aachen (RWTH)


Collections: Computer Technologies and Information Sciences