Politeness for the Theory of Algebraic Datatypes

by   Ying Sheng, et al.

Algebraic datatypes, and among them lists and trees, have attracted a lot of interest in automated reasoning and Satisfiability Modulo Theories (SMT). Since its latest stable version, the SMT-LIB standard defines a theory of algebraic datatypes, which is currently supported by several mainstream SMT solvers. In this paper, we study this particular theory of datatypes and prove that it is strongly polite, showing also how it can be combined with other arbitrary disjoint theories using polite combination. Our results cover both inductive and finite datatypes, as well as their union. The combination method uses a new, simple, and natural notion of additivity, that enables deducing strong politeness from (weak) politeness.



page 1

page 2

page 3

page 4


On the Convexity of a Fragment of Pure Set Theory with Applications within a Nelson-Oppen Framework

The Satisfiability Modulo Theories (SMT) issue concerns the satisfiabili...

The Extended Theory of Trees and Algebraic (Co)datatypes

The first-order theory of finite and infinite trees has been studied sin...

Politeness and Stable Infiniteness: Stronger Together

We make two contributions to the study of polite combination in satisfia...

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

Recursive algebraic data types (term algebras, ADTs) are one of the most...

Smtlink 2.0

Smtlink is an extension of ACL2 with Satisfiability Modulo Theories (SMT...

Isotropy and Combination Problems

In a previous paper, the author and his collaborators studied the phenom...

Computing Tropical Prevarieties with Satisfiability Modulo Theory (SMT) Solvers

I am presenting a novel way to use SMT (Satisfiability Modulo Theory) to...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.