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Recursive algebraic data types (term algebras, ADTs) are one of the mostwell-studied theories in logic, and find application in contexts includingfunctional programming, modelling languages, proof assistants, andverification. At this point, several state-of-the-art theorem provers and SMTsolvers include tailor-made decision procedures for ADTs, and version 2.6 ofthe SMT-LIB standard includes support for ADTs. We study an extremely simpleapproach to decide satisfiability of ADT constraints, the reduction of ADTconstraints to equisatisfiable constraints over uninterpreted functions (EUF)and linear integer arithmetic (LIA). We show that the reduction approach givesrise to both decision and Craig interpolation procedures in (extensions of)ADTs.

Deciding and Interpolating Algebraic Data Types by Reduction (Technical Report)