Programming by Refinement, as Exemplified by the SETL Representation Sublanguage

Dewar, Robert; Grand, Arthur; Liu, Ssu-Cheng; Schwartz, Jacob T.; Schonberg, Edmond

doi:10.1145/357062.357064

Cited by 89 publications

(41 citation statements)

References 4 publications

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“…The useful content in the data structure is stored in the data fields of the elements of nodes. The nodes set can be either explicitly manipulated through a library data type or built-in type [7], or it can be verified to correspond to a set of reachable objects using techniques such as [27]. The content of the list, stored in the content specification variable, is then an image of nodes under the function data.…”

Section: Motivating Examplesmentioning

confidence: 99%

Collections, Cardinalities, and Relations

Yessenov

Piskač

Kunčak

2010

Lecture Notes in Computer Science

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Section: Motivating Examplesmentioning

confidence: 99%

Collections, Cardinalities, and Relations

Yessenov

Piskač

Kunčak

2010

Lecture Notes in Computer Science

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“…The SETL representation sublanguage [8] maps abstract SETL set and map objects to implementations, although the details are quite different from our work. Unlike SETL, we handle relations of arbitrary arity, using functional dependencies to enforce complex sharing invariants.…”

Section: Synthesizing Data Representationsmentioning

confidence: 93%

An introduction to data representation synthesis

et al. 2012

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We consider the problem of specifying combinations of data structures with complex sharing in a manner that is both declarative and results in provably correct code. In our approach, abstract data types are specified using relational algebra and functional dependencies. We describe a language of decompositions that permits the user to specify different concrete representations for relations, and show that operations on concrete representations soundly implement their relational specification. We also describe an auto-tuner that automatically identifies the best decomposition for a particular workload. It is easy to incorporate data representations synthesized by our compiler into existing systems, leading to code that is simpler, correct by construction, and comparable in performance to the code it replaces.

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“…Such languages can either be directly executed (Dewar, 1979) or can arise as abstractions of programs in standard languages (Lam et al, 2005). The program in Figure 4 manipulates a global set of objects content and an integer field size.…”

Section: Verifying Data Structure Consistencymentioning

confidence: 99%

Deciding Boolean Algebra with Presburger Arithmetic

Kunčak¹,

Nguyen

Rinard

2006

J Autom Reasoning

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Abstract. We describe an algorithm for deciding the first-order multisorted theory BAPA, which combines 1) Boolean algebras of sets of uninterpreted elements (BA) and 2) Presburger arithmetic operations (PA). BAPA can express the relationship between integer variables and cardinalities of unbounded finite sets, and supports arbitrary quantification over sets and integers.Our original motivation for BAPA is deciding verification conditions that arise in the static analysis of data structure consistency properties. Data structures often use an integer variable to keep track of the number of elements they store; an invariant of such a data structure is that the value of the integer variable is equal to the number of elements stored in the data structure. When the data structure content is represented by a set, the resulting constraints can be captured in BAPA. BAPA formulas with quantifier alternations arise when verifying programs with annotations containing quantifiers, or when proving simulation relation conditions for refinement and equivalence of program fragments. Furthermore, BAPA constraints can be used for proving the termination of programs that manipulate data structures, as well as in constraint database query evaluation and loop invariant inference.We give a formal description of an algorithm for deciding BAPA. We analyze our algorithm and show that it has optimal alternating time complexity, and that the complexity of BAPA matches the complexity of PA. Because it works by a reduction to PA, our algorithm yields the decidability of a combination of sets of uninterpreted elements with any decidable extension of PA. When restricted to BA formulas, the algorithm can be used to decide BA in optimal alternating time. Furthermore, the algorithm can eliminate individual quantifiers from a formula with free variables and therefore perform projection onto a desirable set of variables.We have implemented our algorithm and used it to discharge verification conditions in the Jahob system for data structure consistency checking of Java programs; our experience suggest that a straightforward implementation of the algorithm is effective on non-trivial formulas as long as the number of set variables is small. We also report on a new algorithm for solving the quantifier-free fragment of BAPA.

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Programming by Refinement, as Exemplified by the SETL Representation Sublanguage

Cited by 89 publications

References 4 publications

Collections, Cardinalities, and Relations

Collections, Cardinalities, and Relations

An introduction to data representation synthesis

Deciding Boolean Algebra with Presburger Arithmetic

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