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Solving Horn Clauses on Inductive Data Types Without Induction
2018
Theory and Practice of Logic Programming
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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]
2017
Lecture Notes in Computer Science
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, 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]
2016
arXiv
pre-print
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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]
2020
Lecture Notes in Computer Science
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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]
2020
arXiv
pre-print
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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]
2021
arXiv
pre-print
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2021 pre-print arXiv:2108.00225v1 fatcat:ma4uepmhanfsfl4gshqo4gzhci
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
2020
Proceedings of the 9th ACM SIGPLAN International Workshop on Numerical and Symbolic Abstract Domains
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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]
2015
Lecture Notes in Computer Science
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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]
2017
arXiv
pre-print
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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]
2005
Lecture Notes in Computer Science
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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
1992
Machine Learning
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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
1999
The Journal of Logic Programming
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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]
1994
Lecture Notes in Computer Science
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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)
2016
Dagstuhl Reports
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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
1991
Theoretical Computer Science
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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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