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Predicate abstraction in a program logic calculus

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*. ...

##
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Predicate Abstraction in a Program Logic Calculus
[chapter]

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*. ...

##
###
Dijkstra-Scholten predicate calculus: concepts and misconceptions

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. ...

##
###
S-Program Calculus
[article]

2010
*
arXiv
*
pre-print

This paper presents

arXiv:1003.0773v1
fatcat:buwlq3pjwjclpisiozgatorwnq
*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] ...##
###
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*. ...

##
###
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 ...

##
###
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

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 ...

##
###
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]

2004
*
arXiv
*
pre-print

We construct role

arXiv:cs/0408018v1
fatcat:rs3rosm6k5frzbu7q43j5fb2wy
*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 ...##
###
A Specialization Calculus for Pruning Disjunctive Predicates to Support Verification
[chapter]

2011
*
Lecture Notes in Computer Science
*

While specialization is

doi:10.1007/978-3-642-22110-1_23
fatcat:nqhhvz2ctbeslb2z7t44e5tba4
*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. ...##
###
Reasoning about Computations Using Two-Levels of Logic
[chapter]

2010
*
Lecture Notes in Computer Science
*

We describe an approach to using one

doi:10.1007/978-3-642-17164-2_4
fatcat:rimxhzafvbhe3lfqqhq55kawlq
*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 ...##
###
The lambda mechanism in lambda calculus and in other calculi
[article]

2015
*
arXiv
*
pre-print

We call this the "lambda mechanism" and show how it can be used

arXiv:1503.00375v4
fatcat:57uj6jchbbbblhwubhu257n3ru
*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*. ...##
###
Logic and computer science

1992
*
Discrete Applied Mathematics
*

Providing scopes to function and

doi:10.1016/0166-218x(92)90241-2
fatcat:ytik62gsxvddpcvsqoxm3jfiri
*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. ...
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