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Predicate abstraction in a program logic calculus

Benjamin Weiß
2011 Science of Computer Programming  
Predicate abstraction is a form of abstract interpretation where the abstract domain is constructed from a finite set of predicates over the variables of the program.  ...  This paper explores a way to integrate predicate abstraction into a calculus for deductive program verification based on symbolic execution, where it allows us to infer loop invariants automatically that  ...  This paper presents an approach for integrating predicate abstraction into a deductive program verification calculus.  ... 
doi:10.1016/j.scico.2010.06.008 fatcat:qo4ujsuutncyvn76rbjsv5wr7a

Predicate Abstraction in a Program Logic Calculus [chapter]

Benjamin Weiß
2009 Lecture Notes in Computer Science  
Predicate abstraction is a form of abstract interpretation where the abstract domain is constructed from a finite set of predicates over the variables of the program.  ...  This paper explores a way to integrate predicate abstraction into a calculus for deductive program verification based on symbolic execution, where it allows us to infer loop invariants automatically that  ...  This paper presents an approach for integrating predicate abstraction into a deductive program verification calculus.  ... 
doi:10.1007/978-3-642-00255-7_10 fatcat:lpc5nexhgnfwdc2znxztym6rve

Dijkstra-Scholten predicate calculus: concepts and misconceptions

Lex Bijlsma, Rob Nederpelt
1998 Acta Informatica  
In doing so, we give DS predicate calculus and its abstract variants a firm basis, on a par with the foundations of the well-known first order logic.  ...  For proving the correctness of a program (i.e. the fact that the program satisfies its specifications), one often uses a special form of predicate calculus in this style of programming.  ...  Extended DS predicate calculus In [DS90] , the language of DS calculus is extended: each universal closure of a predicate over all occurring programming variables becomes a new logical formula.  ... 
doi:10.1007/s002360050150 fatcat:cxykslusmnabrfel5eyrj6ouxi

S-Program Calculus [article]

Aleksandar Kupusinac, Dusan Malbaski
2010 arXiv   pre-print
This paper presents a special subset of the first-order predicate logic named S-program calculus (briefly S-calculus).  ...  The S-calculus is a powerful mechanism for proving program correctness as well as for building additional proving tools using theorems of the predicate logic.  ...  Our idea is to develop a program calculus that associates Hoare logic with first-order predicate logic and clearly separates the interpretation domain from the abstract state domain (similarly to [27]  ... 
arXiv:1003.0773v1 fatcat:buwlq3pjwjclpisiozgatorwnq

Chapter 1

2001 Electronical Notes in Theoretical Computer Science  
In contrast, a programming language can bethought of as a syntactic formalism which provides a m e a n s for the communication of computations among people and (abstract) machines.  ...  Examples of programming languages are conventional languages like P ascal 196] or C++ 187], and also the more theoretical languages such as the -calculus 52,26] or CCS 144].  ...  In the rst part we consider predicates as subsets of an abstract set of states. In the second part we re ne the notion of predicates by considering a rmative predicates.  ... 
doi:10.1016/s1571-0661(05)80508-0 fatcat:lxwvz32qbrgmlkzxzxtv5rq4lu

Abstract

2001 Electronical Notes in Theoretical Computer Science  
In this monograph we study the relationship between two different approaches to define the semantics of a program, namely the denotational and the axiomatic one.  ...  The formal semantics of a programming language consists of assigning to every program of the language an element of a mathematical structure.  ...  The axiomatic semantics characterizes programs in a logical framework intended for reasoning about programs properties: computations are expressed by relating programs to assertions about their behaviour  ... 
doi:10.1016/s1571-0661(05)80520-1 fatcat:pg7zgvuszva7tflwckkvtu2vgq

Page 4801 of Mathematical Reviews Vol. , Issue 83m [page]

1983 Mathematical Reviews  
in predicate calculus.  ...  The author criticizes usual explications of Quine’s paradox and he claims that the paradox results from a logical mistake consisting in a misuse of abstract notions and in a false absolutization of modalities  ... 

Page 445 of Thought Vol. 61, Issue 243 [page]

1986 Thought  
It meant a computer in a single program could prove any theorem in mathematics, amenable to the axiomatic method as represented by the predicate calculus.  ...  Alan Robinson in 1965 proposed Binary Resolution (Machine Oriented Logic 23) as an inference principle based on Symbolic Logic which led to an algorithm (a computer program) capable of proving in a finite  ... 

TACAS 2003 Special Issue—Preface

Hubert Garavel, John Hatcliff
2006 Theoretical Computer Science  
In their paper "Counter-Example Guided Predicate Abstraction of Hybrid Systems", Alur, Dang, and Ivančić show how to adapt well-known concepts used in predicate abstraction for discrete systems to hybrid  ...  In their paper "On the Universal and Existential Fragments of the -Calculus", Henzinger, Kupferman, and Majumdar study classic decision problems for the -calculus in universal fragment of the logic (in  ...  At this point, we hope that these brief accounts have convinced you to plunge into this special issue of TCS and we wish you a fruitful reading. Hubert Garavel  ... 
doi:10.1016/j.tcs.2005.11.014 fatcat:wayjlqolubgvpkwhidau222pha

Page 6408 of Mathematical Reviews Vol. , Issue 92k [page]

1992 Mathematical Reviews  
techniques of developing a sequent calculus and a natural deduction system for a three-valued logic.  ...  We also discuss the extension of this logic by a nonmonotone-predicate ‘is true’.”  ... 

On Role Logic [article]

Viktor Kuncak, Martin Rinard
2004 arXiv   pre-print
We construct role logic using the ideas of de Bruijn's notation for lambda calculus, an encoding of first-order logic in lambda calculus, and a simple rule for implicit arguments of unary and binary predicates  ...  We present role logic, a notation for describing properties of relational structures in shape analysis, databases, and knowledge bases.  ...  Acknowledgements We thank Patrick Lam for useful discussions, comments on the paper, and an implementation of an early version of role logic normalization algorithm in Fall 2001, we thank Andreas Podelski  ... 
arXiv:cs/0408018v1 fatcat:rs3rosm6k5frzbu7q43j5fb2wy

A Specialization Calculus for Pruning Disjunctive Predicates to Support Verification [chapter]

Wei-Ngan Chin, Cristian Gherghina, Răzvan Voicu, Quang Loc Le, Florin Craciun, Shengchao Qin
2011 Lecture Notes in Computer Science  
While specialization is a familiar technique for code optimization, its use in program verification is new.  ...  Separation logic-based abstraction mechanisms, enhanced with userdefined inductive predicates, represent a powerful, expressive means of specifying heap-based data structures with strong invariant properties  ...  We have proposed in this paper a specialization calculus for disjunctive predicates in a separation logic-based abstract domain. Our specialization calculus is proven sound and is terminating.  ... 
doi:10.1007/978-3-642-22110-1_23 fatcat:nqhhvz2ctbeslb2z7t44e5tba4

Reasoning about Computations Using Two-Levels of Logic [chapter]

Dale Miller
2010 Lecture Notes in Computer Science  
We describe an approach to using one logic to reason about specifications written in a second logic.  ...  While computation can be specified using a number of formal techniques-e.g., Petri nets, process calculus, and state machines-we shall illustrate the merits and challenges of using logic programming-like  ...  The key development was the shift from viewing a logic program as a theory that provided some of the meaning of undefined predicates to viewing logic programs as recursive definitions that completely describe  ... 
doi:10.1007/978-3-642-17164-2_4 fatcat:rimxhzafvbhe3lfqqhq55kawlq

The lambda mechanism in lambda calculus and in other calculi [article]

M. H. van Emden
2015 arXiv   pre-print
We call this the "lambda mechanism" and show how it can be used in other calculi. In first-order predicate logic it can be used to define new functions and new predicates in terms of existing ones.  ...  In a purely imperative programming language it can be used to provide an Algol-like procedure facility.  ...  Predicate logic as programming language A functional programming language is one that is based on the lambda calculus or on combinatory logic.  ... 
arXiv:1503.00375v4 fatcat:57uj6jchbbbblhwubhu257n3ru

Logic and computer science

1992 Discrete Applied Mathematics  
Providing scopes to function and predicate symbols. A higher-order logic. Two higher-order logic programming languages. gigher-order programming. Conclusions.  ...  Nuprl as a General Logic (R.L. Constabie and D.J. Howe). Introduction (Overview of the syntactic method. Implementations. Faithfulness). The classical predicate calculus in Nuprl (Background.  ... 
doi:10.1016/0166-218x(92)90241-2 fatcat:ytik62gsxvddpcvsqoxm3jfiri
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