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34
A survey and classification of some program transformation approaches and techniques
 Program Specification and Tranformation
, 1987
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Hope: An Experimental Applicative Language
, 1980
"... An applicative language called HOPE is described and discussed. The underlying goal of the design and implementation effort was to produce a very simple programming language which encourages the construction of clear and manipulable programs. HOPE does not include an assignment statement; this is fe ..."
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Cited by 39 (3 self)
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An applicative language called HOPE is described and discussed. The underlying goal of the design and implementation effort was to produce a very simple programming language which encourages the construction of clear and manipulable programs. HOPE does not include an assignment statement; this is felt to be an important simplification. The user may freely define his own data types, without the need to devise a complicated encoding in terms of lowlevel types. The language is very strongly typed, and as implemented it incorporates a typechecker which handles polymorphic types and overloaded operators. Functions are defined by a set of recursion equations; the lefthand side of each equation includes a pattern used to determine which equation to use for a given argument. The availability of arbitrary higherorder types allows functions to be defined which 'package' recursion. Lazilyevaluated lists are provided, allowing the use of infinite lists which could be used to provide interactive input/output and concurrency.
Derivation of Data Intensive Algorithms by Formal Transformation: The SchorrWaite Graph Marking Algorithm
, 1996
"... In this paper we consider a particular class of algorithms which present certain difficulties to formal verification. These are algorithms which use a single data structure for two or more purposes, which combine program control information with other data structures or which are developed as a comb ..."
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Cited by 36 (25 self)
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In this paper we consider a particular class of algorithms which present certain difficulties to formal verification. These are algorithms which use a single data structure for two or more purposes, which combine program control information with other data structures or which are developed as a combination of a basic idea with an implementation technique. Our approach is based on applying proven semanticspreserving transformation rules in a wide spectrum language. Starting with a set theoretical specification of "reachability" we are able to derive iterative and recursive graph marking algorithms using the "pointer switching" idea of Schorr and Waite. There have been several proofs of correctness of the SchorrWaite algorithm, and a small number of transformational developments of the algorithm. The great advantage of our approach is that we can derive the algorithm from its specification using only generalpurpose transformational rules: without the need for complicated induction arg...
Modular Data Structure Verification
 EECS DEPARTMENT, MASSACHUSETTS INSTITUTE OF TECHNOLOGY
, 2007
"... This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java ..."
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Cited by 36 (21 self)
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This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java programs with dynamically allocated data structures. Developers write Jahob specifications in classical higherorder logic (HOL); Jahob reduces the verification problem to deciding the validity of HOL formulas. I present a new method for proving HOL formulas by combining automated reasoning techniques. My method consists of 1) splitting formulas into individual HOL conjuncts, 2) soundly approximating each HOL conjunct with a formula in a more tractable fragment and 3) proving the resulting approximation using a decision procedure or a theorem prover. I present three concrete logics; for each logic I show how to use it to approximate HOL formulas, and how to decide the validity of formulas in this logic. First, I present an approximation of HOL based on a translation to firstorder logic, which enables the use of existing resolutionbased theorem provers. Second, I present an approximation of HOL based on field constraint analysis, a new technique that enables
Deciding Boolean Algebra with Presburger Arithmetic
 J. of Automated Reasoning
"... Abstract. We describe an algorithm for deciding the firstorder 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 ..."
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Cited by 31 (26 self)
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Abstract. We describe an algorithm for deciding the firstorder 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
An Efficient Representation for Sparse Sets
 ACM LETTERS ON PROGRAMMING LANGUAGES AND SYSTEMS
, 1993
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Complete Functional Synthesis
"... Synthesis of program fragments from specifications can make programs easier to write and easier to reason about. To integrate synthesis into programming languages, synthesis algorithms should behave in a predictable way—they should succeed for a welldefined class of specifications. They should also ..."
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Cited by 30 (13 self)
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Synthesis of program fragments from specifications can make programs easier to write and easier to reason about. To integrate synthesis into programming languages, synthesis algorithms should behave in a predictable way—they should succeed for a welldefined class of specifications. They should also support unbounded data types such as numbers and data structures. We propose to generalize decision procedures into predictable and complete synthesis procedures. Such procedures are guaranteed to find code that satisfies the specification if such code exists. Moreover, we identify conditions under which synthesis will statically decide whether the solution is guaranteed to exist, and whether it is unique. We demonstrate our approach by starting from decision procedures for linear arithmetic and data structures and transforming them into synthesis procedures. We establish results on the size and the efficiency of the synthesized code. We show that such procedures are useful as a language extension with implicit value definitions, and we show how to extend a compiler to support such definitions. Our constructs provide the benefits of synthesis to programmers, without requiring them to learn new concepts or give up a deterministic execution model.
Realtime simulation of a set machine on a ram
 Computing and Information, volume II of ICCI 89
, 1989
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Mechanical Translation of Set Theoretic Problem Specifications Into Efficient RAM Code  A Case Study
 Proc. EUROCAL 85
, 1985
"... This paper illustrates a fully automatic topdown approach to program development in which formal problem specifications are mechanically translated into efficient RAM code. This code is guaranteed to be totally correct and an upper bound on its worst case asymptotic running time is automatically de ..."
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Cited by 26 (8 self)
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This paper illustrates a fully automatic topdown approach to program development in which formal problem specifications are mechanically translated into efficient RAM code. This code is guaranteed to be totally correct and an upper bound on its worst case asymptotic running time is automatically determined. The user is only required to supply the system with a formal problem specification, and is relieved of all responsibilities in the rest of the program development process. These results are obtained, in part, by greatly restricting the system to handle a class of determinate, set theoretic, tractable problems. The most essential transformational techniques that are used are fixed point iteration, finite differencing, and data structure selection. Rudimentary forms of these techniques have been implemented and used effectively in the RAPTS transformational programming system. This paper explains the conceptual underpinnings of our approach by considering the problem of attribute closure for relational databases and systematically deriving a program that implements a linear time solution. 1.
An algorithm for deciding BAPA: Boolean Algebra with Presburger Arithmetic
 In 20th International Conference on Automated Deduction, CADE20
, 2005
"... Abstract. We describe an algorithm for deciding the firstorder 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 a priory u ..."
Abstract

Cited by 26 (13 self)
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Abstract. We describe an algorithm for deciding the firstorder 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 a priory unbounded finite sets, and supports arbitrary quantification over sets and integers. Our 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, and have applications in constraint databases. We give a formal description of a decision procedure for BAPA, which implies the decidability of BAPA. We analyze our algorithm and obtain an elementary upper bound on the running time, thereby giving the first complexity bound for BAPA. 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. Our algorithm can also be used to yield an optimal decision procedure for BA through a reduction to PA with bounded quantifiers. 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 with the algorithm is promising. 1