Datatypes with Shared Selectors

Politeness for the Theory of Algebraic Datatypes

“…There are several directions for further research that we plan to explore. First, we plan to continue to prove that more important theories are strongly polite, with an eye to recent extensions of the datatypes theory, namely datatypes with shared selectors [23] and co-datatypes [22]. Second, we envision to further investigate the possibility to prove politeness using superposition-based satisfiability procedures.…”

“…Detailed information on this theory, including a decision procedure and related work, can be found in [4]. Later work extends this procedure to handle shared selectors [23] and co-datatypes [22]. More recent approaches for solving formulas about datatypes use, e.g., theorem provers [15], variant satisfiability [12,19], and reduction-based decision procedures [1,6,13].…”

Syntax-Guided Quantifier Instantiation

“…in the original theory where s is a term of sort Int. In more detail, for a datatype term d, we write is C (d) to denote the discriminator predicate, which is satisfied exactly when d is interpreted as a datatype value whose top constructor is C. We write sel σ,n (d) to denote a shared selector [28] applied to d, interpreted as the n th child of d with sort σ if one exists, and as an arbitrary element of σ otherwise. These symbols are used for constructing blocking constraints.…”

cvc4sy: Smart and Fast Term Enumeration for Syntax-Guided Synthesis

“…We will use these datatypes as a running example. For a datatype term t, we write is C (t) to denote the discriminator predicate that is satisfied exactly when t is interpreted as a datatype whose top constructor is C. We write sel τ n (t) to denote a shared selector [15] applied to t, interpreted as the n th child of t with type τ if one exists, and interpreted as an arbitrary element of τ otherwise. A term consisting of zero or more consecutive nested applications of shared selectors applied to a term t is a shared selector chain (for t).…”