The Extended Theory of Trees and Algebraic (Co)datatypes

Fabian Zaiser
(University of Oxford)
C.-H. Luke Ong
(University of Oxford)

The first-order theory of finite and infinite trees has been studied since the eighties, especially by the logic programming community. Following Djelloul, Dao and Frühwirth, we consider an extension of this theory with an additional predicate for finiteness of trees, which is useful for expressing properties about (not just datatypes but also) codatatypes. Based on their work, we present a simplification procedure that determines whether any given (not necessarily closed) formula is satisfiable, returning a simplified formula which enables one to read off all possible models. Our extension makes the algorithm usable for algebraic (co)datatypes, which was impossible in their original work due to restrictive assumptions. We also provide a prototype implementation of our simplification procedure and evaluate it on instances from the SMT-LIB.

In Laurent Fribourg and Matthias Heizmann: Proceedings 8th International Workshop on Verification and Program Transformation and 7th Workshop on Horn Clauses for Verification and Synthesis (VPT/HCVS 2020), Dublin, Ireland, 25-26th April 2020, Electronic Proceedings in Theoretical Computer Science 320, pp. 167–196.
Published: 7th August 2020.

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