Many-Sorted Equivalence of Shiny and Strongly Polite Theories

Casal, Filipe; Rasga, João

doi:10.1007/s10817-017-9411-y

Cited by 11 publications

(32 citation statements)

References 15 publications

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“…Later, a flaw in the original definition of politeness was found [14], and a corrected definition (here called strong politeness) was introduced. Strongly polite theories were further studied in [8], where the authors proved their equivalence with shiny theories.…”

Section: Related Workmentioning

confidence: 99%

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Politeness for the Theory of Algebraic Datatypes

Sheng¹,

Zohar²,

Ringeissen³

et al. 2020

Automated Reasoning

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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.

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Section: Related Workmentioning

confidence: 99%

“…In the following we decompose the politeness definition from [14,21] in order to distinguish between politeness and strong politeness (in terms of [8]) in various levels of the definition. In what follows, Σ is an arbitrary (many-sorted) signature, S ⊆ S Σ , and T is a Σ-theory.…”

Section: Polite Theoriesmentioning

confidence: 99%

Politeness for the Theory of Algebraic Datatypes

Sheng¹,

Zohar²,

Ringeissen³

et al. 2020

Automated Reasoning

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show abstract

“…Let Σ 2 be a signature with two sorts σ 1 and σ 2 and no function or predicate symbols (except =). Let T 2,3 be the Σ 2 -theory from [8], consisting of all Σ 2structures A such that either…”

Section: A Polite Theory That Is Not Strongly Politementioning

confidence: 99%

“…First, we give an affirmative answer to the question of whether politeness and strong politeness are different notions, by giving an example of a theory that is polite but not strongly polite. The given theory is over an empty signature and has two sorts, and was originally studied in [8] in the context of shiny theories. Here we state and prove the separation of politeness and strong politeness, without using shiny theories.…”

Section: Introductionmentioning

confidence: 99%

“…For the mono-sorted case, a sufficient condition for the equivalence of shiny theories and strongly polite theories was given by Casal and Rasga [7]. In later work [8], the same authors proposed a generalization of shiny theories to many-sorted signatures different from the one in [17], and proved that it is equivalent to strongly polite theories with a decidable quantifier-free fragment. The strong politeness of the theory of algebraic datatypes [4] was proven in [18].…”

Section: Introductionmentioning

confidence: 99%

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Politeness and Stable Infiniteness: Stronger Together

Sheng

Zohar

Ringeissen

et al. 2021

Automated Deduction – CADE 28

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We make two contributions to the study of polite combination in satisfiability modulo theories. The first is a separation between politeness and strong politeness, by presenting a polite theory that is not strongly polite. This result shows that proving strong politeness (which is often harder than proving politeness) is sometimes needed in order to use polite combination. The second contribution is an optimization to the polite combination method, obtained by borrowing from the Nelson-Oppen method. The Nelson-Oppen method is based on guessing arrangements over shared variables. In contrast, polite combination requires an arrangement over all variables of the shared sorts. We show that when using polite combination, if the other theory is stably infinite with respect to a shared sort, only the shared variables of that sort need be considered in arrangements, as in the Nelson-Oppen method. The time required to reason about arrangements is exponential in the worst case, so reducing the number of variables considered has the potential to improve performance significantly. We show preliminary evidence for this by demonstrating a speed-up on a smart contract verification benchmark.

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Combination of Theories

Rasga

Sernadas

2020

Studies in Universal Logic

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Many-Sorted Equivalence of Shiny and Strongly Polite Theories

Cited by 11 publications

References 15 publications

Politeness for the Theory of Algebraic Datatypes

Politeness for the Theory of Algebraic Datatypes

Politeness and Stable Infiniteness: Stronger Together

Combination of Theories

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