scholarly journals Verification of Imperative Programs through Transformation of Constraint Logic Programs

10.29007/163x ◽  
2018 ◽  
Author(s):  
Emanuele De Angelis ◽  
Fabio Fioravanti ◽  
Alberto Pettorossi ◽  
Maurizio Proietti
Keyword(s):  
Program Transformation ◽  
Program Verification ◽  
Order Logic ◽  
Initial Configuration ◽  
First Order Logic ◽  
Logic Programs ◽  
Partial Correctness ◽  
First Order ◽  
Transformation Rules ◽  
Constraint Logic Programs

We present a method for verifying partial correctness properties of imperative programs by using techniques based on the transformation of constraint logic programs (CLP). We consider: (i) imperative programs that manipulate integers and arrays, and (ii) first order logic properties that define <i>configurations</i> of program executions. We use CLP as a metalanguage for representing imperative programs, their executions, and their properties. First, we encode the correctness of an imperative program, say Prog, as the negation of a predicate 'incorrect' defined by a CLP program T. By construction, 'incorrect' holds in the least model of T if and only if the execution of Prog from an initial configuration eventually halts in an error configuration. Then, we apply to program T a sequence of transformations that preserve its least model semantics. These transformations are based on well-known transformation rules, such as unfolding and folding, guided by suitable transformation strategies, such as specialization and generalization. The objective of the transformations is to derive a new CLP program TransfT where the predicate 'incorrect' is defined either by (i) the fact `incorrect.' (and in this case Prog is incorrect), or by (ii) the empty set of clauses (and in this case Prog is correct). In the case where we derive a CLP program such that neither (i) nor (ii) holds, we iterate the transformation. Since the problem is undecidable, this process may not terminate. We show through examples that our method can be applied in a rather systematic way, and is amenable to automation by transferring to the field of program verification many techniques developed in the field of program transformation.

scholarly journals Program Verification using Constraint Handling Rules and Array Constraint Generalizations

10.29007/dkxs ◽  
2018 ◽  
Author(s):  
Emanuele De Angelis ◽  
Fabio Fioravanti ◽  
Alberto Pettorossi ◽  
Maurizio Proietti
Keyword(s):  
Data Structures ◽  
Program Verification ◽  
Linear Constraints ◽  
Constraint Handling ◽  
Logic Programs ◽  
Replacement Strategy ◽  
Partial Correctness ◽  
Transformation Rules ◽  
Constraint Logic Programs ◽  
Additional Constraints

The transformation of constraint logic programs (CLP programs)has been shown to be an effective methodologyfor verifying properties of imperative programs.By following this methodology, we encode the negationof a partial correctness property of an imperativeprogram prog as a predicate incorrect defined by a CLP program P, and we show thatprog is correct by transforming P intothe empty program through the applicationof semantics preserving transformation rules.Some of these rules perform replacements of constraintsthat encode properties of the data structures manipulatedby the program prog.In this paper we show that Constraint Handling Rules (CHR)are a suitable formalism for representing and applyingconstraint replacements during the transformation of CLP programs.In particular, we consider programs that manipulate integerarrays and we present a CHR encoding of a constraint replacementstrategy based on the theory of arrays.We also propose a novel generalization strategy forconstraints on integer arrays that combinesthe CHR constraint replacement strategywith various generalization operator for linear constraints,such as widening and convex hull.Generalization is controlled by additional constraintsthat relate the variable identifiers in the imperativeprogram and the CLP representation of their values.The method presented in this paper has been implemented andwe have demonstrated itseffectiveness on a set ofbenchmark programs taken from the literature.

scholarly journals Learning Relational Representations with Auto-encoding Logic Programs

2019 ◽  
Author(s):  
Sebastijan Dumancic ◽  
Tias Guns ◽  
Wannes Meert ◽  
Hendrik Blockeel
Keyword(s):  
Deep Learning ◽  
Relational Learning ◽  
Order Logic ◽  
First Order Logic ◽  
Relational Data ◽  
Logic Programs ◽  
Learning Methods ◽  
First Order ◽  
Relational Structures ◽  
Representation Language

Deep learning methods capable of handling relational data have proliferated over the past years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these methods aim at re-representing symbolic relational data in Euclidean space. They offer better scalability, but can only approximate rich relational structures and are less flexible in terms of reasoning. This paper introduces a novel framework for relational representation learning that combines the best of both worlds. This framework, inspired by the auto-encoding principle, uses first-order logic as a data representation language, and the mapping between the the original and latent representation is done by means of logic programs instead of neural networks. We show how learning can be cast as a constraint optimisation problem for which existing solvers can be used. The use of logic as a representation language makes the proposed framework more accurate (as the representation is exact, rather than approximate), more flexible, and more interpretable than deep learning methods. We experimentally show that these latent representations are indeed beneficial in relational learning tasks.

scholarly journals Ordered completion for first-order logic programs on finite structures

2012 ◽  
Vol 177-179 ◽  
pp. 1-24 ◽  
Author(s):  
Vernon Asuncion ◽  
Fangzhen Lin ◽  
Yan Zhang ◽  
Yi Zhou
Keyword(s):  
Order Logic ◽  
First Order Logic ◽  
Logic Programs ◽  
First Order ◽  
Finite Structures

First-Order Logic Reasoning Support for the Semantic Web

2009 ◽  
Vol 19 (12) ◽  
pp. 3091-3099 ◽  
Author(s):  
Gui-Hong XU ◽  
Jian ZHANG
Keyword(s):  
Semantic Web ◽  
Order Logic ◽  
First Order Logic ◽  
First Order ◽  
Logic Reasoning

Boolean-valued structures

2018 ◽  
Author(s):  
Tim Button ◽  
Sean Walsh
Keyword(s):  
Model Theory ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Rules ◽  
Mathematical Concepts ◽  
Semantic Framework ◽  
First Order ◽  
Standard Models ◽  
Boolean Valued Model ◽  
Semantic Values

Chapters 6-12 are driven by questions about the ability to pin down mathematical entities and to articulate mathematical concepts. This chapter is driven by similar questions about the ability to pin down the semantic frameworks of language. It transpires that there are not just non-standard models, but non-standard ways of doing model theory itself. In more detail: whilst we normally outline a two-valued semantics which makes sentences True or False in a model, the inference rules for first-order logic are compatible with a four-valued semantics; or a semantics with countably many values; or what-have-you. The appropriate level of generality here is that of a Boolean-valued model, which we introduce. And the plurality of possible semantic values gives rise to perhaps the ‘deepest’ level of indeterminacy questions: How can humans pin down the semantic framework for their languages? We consider three different ways for inferentialists to respond to this question.

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