Reasoning About Set Comprehensions
نویسندگان
چکیده
Set comprehension is a mathematical notation for defining sets on the basis of a property of their members. Although set comprehension is widely used in mathematics and some programming languages, direct support for reasoning about it is still not readily available in state-of-the-art SMT solvers. This paper presents a technique for translating formulas which express constraints involving set comprehensions into first-order formulas that can be verified by off-the-shelf SMT solvers. More specifically, we have developed a lightweight Python library that extends the popular Z3 SMT solver with the ability to reason about the satisfiability of set comprehension patterns. This technique is general and can be deployed in a broad range of SMT solvers.
منابع مشابه
Constructing Tournament Representations: An Exercise in Pointwise Relational Programming
List or set comprehensions are a wonderful means to define nondeterministic or relational programs. Despite their beauty, comprehensions are somewhat underused in program calculation. The purpose of this paper is to remind the program-calculation community that comprehensions provide a convenient language for specifying and deriving nondeterministic programs in a pointwise manner. We illustrate...
متن کاملAn old new notation for elementary probability theory
The Eindhoven approach to quantifier notation is 40 years old. We extend it by adding “distribution comprehensions” systematically to its repertiore; we believe the resulting notation for elementary probability theory is new. After a step-by-step explanation of the proposed notational innovations, with small examples, we give as our exemplary case study the probabilistic reasoning associated wi...
متن کاملOn Bounded Reachability of Programs with Set Comprehensions
We analyze the bounded reachability problem of programs that use abstract data types and set comprehensions. Such programs are common as high-level executable specifications of complex protocols. We prove decidability and undecidability results of restricted cases of the problem and extend the Satisfiability Modulo Theories approach to support analysis of set comprehensions over tuples and bag ...
متن کاملTranslating OQL into Monoid Comprehensions — Stuck with Nested Loops?
This work tries to employ the monoid comprehension calculus — which has proven to be an adequate framework to capture the semantics of modern object query languages featuring a family of collection types like sets, bags, and lists — in a twofold manner: First, serving as a target language for the translation of ODMG OQL queries. We review work done in this field and also give comprehension calc...
متن کامل