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Solving Horn Clauses on Inductive Data Types Without Induction

EMANUELE DE ANGELIS, FABIO FIORAVANTI, ALBERTO PETTOROSSI, MAURIZIO PROIETTI
2018 Theory and Practice of Logic Programming  
AbstractWe address the problem of verifying the satisfiability of Constrained Horn Clauses (CHCs) based on theories of inductively defined data structures, such as lists and trees.  ...  We also show that our verification technique based on CHC transformation followed by CHC solving, is competitive with respect to CHC solvers extended with induction.  ...  In this paper we propose an alternative method to solve CHCs on inductively defined data structures.  ... 
doi:10.1017/s1471068418000157 fatcat:ovs527z7qjd45odoz2psaybax4

Automating Induction for Solving Horn Clauses [chapter]

Hiroshi Unno, Sho Torii, Hiroki Sakamoto
2017 Lecture Notes in Computer Science  
, higher-order, exception-raising, and over non-inductively defined data types.  ...  , and over non-inductively defined data types (recall that H mult axiomatizes the  ...  These automated provers are mostly based on logics of pure total functions over inductive data types.  ... 
doi:10.1007/978-3-319-63390-9_30 fatcat:pgt2xnaoevcn7otiddwkcsiwnm

Automating Induction for Solving Horn Clauses [article]

Hiroshi Unno, Sho Torii
2016 arXiv   pre-print
non-deterministic, higher-order, exception-raising, and over non-inductively defined data types.  ...  This paper presents a novel Horn constraint solving method based on inductive theorem proving: the method reduces Horn constraint solving to validity checking of first-order formulas with inductively defined  ...  reduced to problems of solving Horn clause constraints on predicate variables that represent unknown inductive invariants.  ... 
arXiv:1610.06768v1 fatcat:2rlylehenzdyjk5wjul36h4l3y

Removing Algebraic Data Types from Constrained Horn Clauses Using Difference Predicates [chapter]

Emanuele De Angelis, Fabio Fioravanti, Alberto Pettorossi, Maurizio Proietti
2020 Lecture Notes in Computer Science  
We address the problem of proving the satisfiability of Constrained Horn Clauses (CHCs) with Algebraic Data Types (ADTs), such as lists and trees.  ...  We prove that if the set of the transformed clauses is satisfiable, then so is the set of the original clauses.  ...  We assume that all non-basic types are specified by suitable data-type declarations (such as the declare-datatypes declarations adopted by SMT solvers), and are collectively called algebraic data types  ... 
doi:10.1007/978-3-030-51074-9_6 fatcat:q67crx2venc4hofmm64mr63lcm

Removing Algebraic Data Types from Constrained Horn Clauses Using Difference Predicates [article]

Emanuele De Angelis
2020 arXiv   pre-print
We address the problem of proving the satisfiability of Constrained Horn Clauses (CHCs) with Algebraic Data Types (ADTs), such as lists and trees.  ...  We prove that if the set of the transformed clauses is satisfiable, then so is the set of the original clauses.  ...  We assume that all non-basic types are specified by suitable data-type declarations (such as the declare-datatypes declarations adopted by SMT solvers), and are collectively called algebraic data types  ... 
arXiv:2004.07749v1 fatcat:hrk6t3la3be67ftgcqi224dsu4

Solving Constrained Horn Clauses over ADTs by Finite Model Finding [article]

Yurii Kostyukov, Dmitry Mordvinov, Grigory Fedyukovich
2021 arXiv   pre-print
Although the first-order representations are very expressive for some theories, they fail to express many interesting properties of algebraic data types (ADTs).  ...  Our evaluation shows that automata-based representation of invariants is more practical than the one based on first-order logic since invariants are capable of expressing more complex properties of the  ...  It is widely used in various techniques for verification, from Floyd-Hoare logic [20, 24] to constrained Horn clauses (CHC) [6] and refinement types [50] .  ... 
arXiv:2108.00225v2 fatcat:skd33ohnwfhkjdrfqt2f3wyczi

Proving array properties using data abstraction

Julien Braine, Laure Gonnord
2020 Proceedings of the 9th ACM SIGPLAN International Workshop on Numerical and Symbolic Abstract Domains  
This paper presents a framework to abstract data structures within Horn clauses that allows abstractions to be easily expressed, compared, composed and implemented.  ...  We study the case of arrays and our experimental evaluation show promising results on classical array programs.  ...  on arrays to solving integer Horn clauses.  ... 
doi:10.1145/3427762.3430179 fatcat:mewggb25jrazjakf5vupdei6oq

Horn Clause Solvers for Program Verification [chapter]

Nikolaj Bjørner, Arie Gurfinkel, Ken McMillan, Andrey Rybalchenko
2015 Lecture Notes in Computer Science  
Our solvers are called Duality, HSF, SeaHorn, and µZ and we have devoted considerable attention in recent papers to algorithms for solving Horn clauses.  ...  Solving Horn clauses amounts to establishing Existential positive Fixed-point Logic formulas, a perspective that was promoted by Blass and Gurevich.  ...  Lower-bound constraints, on the other hand, are more subtle to capture. Rybalchenko et al. use a symbolic version of Barvinok's algorithm [7] to solve cardinality constraints.  ... 
doi:10.1007/978-3-319-23534-9_2 fatcat:hsmmbrr35nfsveszovx67isifq

Higher-Order Constrained Horn Clauses and Refinement Types [article]

Toby Cathcart Burn, C.-H. Luke Ong, Steven J. Ramsay
2017 arXiv   pre-print
This result can be used to show that properties of higher-order functions that are definable using refinement types are also expressible using higher-order constrained Horn clauses.  ...  Finally, we show that an extension of the decision problem in which refinement types are used directly as guards on existential quantifiers can be reduced to the original problem.  ...  data at certain program points, which can often be expressed as first-order constrained Horn clause solving.  ... 
arXiv:1705.06216v2 fatcat:qc4rib7saragnbcnzshaxt4hpu

CLASSIC'CL: An Integrated ILP System [chapter]

Christian Stolle, Andreas Karwath, Luc De Raedt
2005 Lecture Notes in Computer Science  
We report on the implementation, the integration issues as well as on some experiments that compare Classic'cl with its predecessors. 1. query is true if and only if the head of the clause is empty, i.e  ...  A novel inductive logic programming system, called Classic'cl is presented.  ...  with one variable and without constants may be used.  ... 
doi:10.1007/11563983_31 fatcat:sjn6p7gsarehxay2r5gym6cjvu

The utility of knowledge in inductive learning

Michael Pazzani, Dennis Kibler
1992 Machine Learning  
In this paper, we demonstrate how different forms of background knowledge can be integrated with an inductive method for generating function-free Horn clause rules.  ...  Furthermore, we evaluate, both theoretically and empirically, the effect that these forms of knowledge have on the cost and accuracy of learning.  ...  We would like to thank Ross Quinlan for his advice on FOIL, Dan Hirschberg for deriving the new recurrence, William Cohen for discussions on types of imperfect domain theories, and Cliff Brunk, Tim Cain  ... 
doi:10.1007/bf00993254 fatcat:wn7a5uqkfrcathjn4hbmjlrwye

A pragmatic reconstruction of λProlog

Catherine Belleannée, Pascal Brisset, Olivier Ridoux
1999 The Journal of Logic Programming  
kProlog is a logic programming language in which hereditary Harrop formulas generalize Horn formulas, and simply typed k-terms generalize Prolog terms.  ...  The starting point of the network is the demand for programming by structural induction on k-terms, and the necessity links give a rationale for such a programming style. Ó  ...  If a data-structure type is inductive then it is easy to deduce an induction scheme on its constructors [4, 55] .  ... 
doi:10.1016/s0743-1066(98)10038-9 fatcat:fzvsrr3zzfcrzesim7r32s56xu

On the utility of predicate invention in inductive logic programming [chapter]

Irene Stahl
1994 Lecture Notes in Computer Science  
However, whether predicate invention really helps to make learning succeed in the extended language depends on the bias that is currently employed.  ...  Acknowledgements This work has been supported by the European Community ESPRIT BRA 6020 ILP (Inductive Logic Programming).  ...  It is employed in the context of inductive data engineering [Fla93] .  ... 
doi:10.1007/3-540-57868-4_64 fatcat:4eocmnkog5e7damzqeb3kcmv5a

Language Based Verification Tools for Functional Programs (Dagstuhl Seminar 16131)

Marco Gaboardi, Suresh Jagannathan, Ranjit Jhala, Stephanie Weirich, Marc Herbstritt
2016 Dagstuhl Reports  
crucial correctness properties, and the dramatic increase in adoption of higher-order functional languages due to the web, multicore and "big data" revolutions.  ...  These techniques include advanced type systems, contract systems, model checking and program analyses specially tailored to exploit the structure of functional languages.  ...  without requiring the user to provide full inductive invariants.  ... 
doi:10.4230/dagrep.6.3.59 dblp:journals/dagstuhl-reports/GaboardiJJW16 fatcat:zeqdceqvzrgplfdpsbt6deoi2i

An efficient strategy for non-Horn deductive databases

Robert Demolombe
1991 Theoretical Computer Science  
In this paper we present an efficient strategy to deal with non-Horn clauses in pure logic, i.e. without any kind of assumption.  ...  Most of them deal with definite Horn clauses.  ...  The proofs here are only more complex due to non-Horn clauses. The proof is by induction on j in the computation of T~ ..  ... 
doi:10.1016/0304-3975(51)90010-2 fatcat:ads47vptqva7hdv4fjw3f36h5i
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