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Satisfiability of Constrained Horn Clauses on Algebraic Data Types: A Transformation-based Approach [article]

Emanuele De Angelis
<span title="2021-11-23">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We address the problem of checking the satisfiability of Constrained Horn Clauses (CHCs) defined on Algebraic Data Types (ADTs), such as lists and trees.  ...  We propose a new technique for transforming CHCs defined on ADTs into CHCs where the arguments of the predicates have only basic types, such as integers and booleans.  ...  Acknowledgements We warmly thank Francesco Calimeri, Simona Perri, and Ester Zumpano for inviting us to submit this improved, extended version of the paper we presented at the 35th Italian Conference on  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2111.11819v1">arXiv:2111.11819v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hoh3yc5udvaf3oiwjscc56rbhq">fatcat:hoh3yc5udvaf3oiwjscc56rbhq</a> </span>
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Removing Algebraic Data Types from Constrained Horn Clauses Using Difference Predicates [article]

Emanuele De Angelis
<span title="2020-04-16">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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.  ...  Introduction Constrained Horn Clauses (CHCs) constitute a fragment of the first order predicate calculus, where the Horn clause format is extended by allowing constraints on specific domains to occur in  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2004.07749v1">arXiv:2004.07749v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hrk6t3la3be67ftgcqi224dsu4">fatcat:hrk6t3la3be67ftgcqi224dsu4</a> </span>
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Removing Algebraic Data Types from Constrained Horn Clauses Using Difference Predicates [chapter]

Emanuele De Angelis, Fabio Fioravanti, Alberto Pettorossi, Maurizio Proietti
<span title="">2020</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
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.  ...  Introduction Constrained Horn Clauses (CHCs) constitute a fragment of the first order predicate calculus, where the Horn clause format is extended by allowing constraints on specific domains to occur in  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-030-51074-9_6">doi:10.1007/978-3-030-51074-9_6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q67crx2venc4hofmm64mr63lcm">fatcat:q67crx2venc4hofmm64mr63lcm</a> </span>
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Higher-Order Constrained Horn Clauses and Refinement Types [article]

Toby Cathcart Burn, C.-H. Luke Ong, Steven J. Ramsay
<span title="2017-08-01">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability  ...  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.  ...  Research was partially completed while the second and third authors were visiting the Institute for Mathematical Sciences, National University of Singapore in 2016.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1705.06216v2">arXiv:1705.06216v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qc4rib7saragnbcnzshaxt4hpu">fatcat:qc4rib7saragnbcnzshaxt4hpu</a> </span>
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Beyond the Elementary Representations of Program Invariants over Algebraic Data Types [article]

Yurii Kostyukov, Dmitry Mordvinov, Grigory Fedyukovich
<span title="2021-04-14">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Although such representations are expressive for some theories, they fail to express many interesting properties of algebraic data types (ADTs).  ...  We present an approach to automatically infer program invariants of ADT-manipulating programs by a reduction to a finite model finder.  ...  We say that a sentence (a formula) in an assertion language is satisfiable modulo theory of ADTs ⟨ 1 , 1 ⟩ , . . . , ⟨ , ⟩, iff ℋ |= . Constrained Horn Clauses.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2104.04463v2">arXiv:2104.04463v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nbk34cumzvg7xfemtfn4u6cole">fatcat:nbk34cumzvg7xfemtfn4u6cole</a> </span>
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Coinductive Soundness of Corecursive Type Class Resolution [article]

František Farka, Ekaterina Komendantskaya, Kevin Hammond
<span title="2016-12-08">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Horn clauses and first-order resolution are commonly used to implement type classes in Haskell.  ...  Several corecursive extensions to type class resolution have recently been proposed, with the goal of allowing (co)recursive dictionary construction where resolution does not termi- nate.  ...  Applications -a Software Engineering Approach" (ICT-644235), and by COST Action IC1202 (TACLe), supported by COST (European Cooperation in Science and Technology).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1608.05233v2">arXiv:1608.05233v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/w5h4djfwizgsroan7gbmac2rie">fatcat:w5h4djfwizgsroan7gbmac2rie</a> </span>
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Constrained types for object-oriented languages

Nathaniel Nystrom, Vijay Saraswat, Jens Palsberg, Christian Grothoff
<span title="2008-10-27">2008</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xu5bk2lj5rbdxlx6222nw7tsxi" style="color: black;">SIGPLAN notices</a> </i> &nbsp;
We present the design and implementation of constrained types, a natural, simple, clean, and expressive extension to object-oriented programming: A type C{c} names a class or interface C and a constraint  ...  c on the immutable state of C and in-scope final variables.  ...  This material is based upon work supported by the Defense Advanced Research Projects Agency under its Agreement No. HR0011-07-9-0002.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1449955.1449800">doi:10.1145/1449955.1449800</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/y5xzbjhqmfalzmkoufvbqwylqe">fatcat:y5xzbjhqmfalzmkoufvbqwylqe</a> </span>
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Constrained types for object-oriented languages

Nathaniel Nystrom, Vijay Saraswat, Jens Palsberg, Christian Grothoff
<span title="">2008</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6y3m32grtnfktkp2oo6oqjbvta" style="color: black;">Proceedings of the 23rd ACM SIGPLAN conference on Object oriented programming systems languages and applications - OOPSLA &#39;08</a> </i> &nbsp;
We present the design and implementation of constrained types, a natural, simple, clean, and expressive extension to object-oriented programming: A type C{c} names a class or interface C and a constraint  ...  c on the immutable state of C and in-scope final variables.  ...  This material is based upon work supported by the Defense Advanced Research Projects Agency under its Agreement No. HR0011-07-9-0002.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1449764.1449800">doi:10.1145/1449764.1449800</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/oopsla/NystromSPG08.html">dblp:conf/oopsla/NystromSPG08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k2mlt72pgvdpnajxrqqkemsv6u">fatcat:k2mlt72pgvdpnajxrqqkemsv6u</a> </span>
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A Typed Hybrid Description Logic Programming Language with Polymorphic Order-Sorted DL-Typed Unification for Semantic Web Type Systems

Adrian Paschke
<span title="2007-04-03">2007</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
term typing of LP rules based on a polymorphic, order-sorted, hybrid DL-typed unification as procedural semantics of hybrid DLPs.  ...  In this paper we elaborate on a specific application in the context of hybrid description logic programs (hybrid DLPs), namely description logic Semantic Web type systems (DL-types) which are used for  ...  Based on this definition of a combined signature I now describe the concrete syntax of typed ContractLog.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/cs/0610006v2">arXiv:cs/0610006v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/szfxxjpbvzej5jq6mjgbrgnmka">fatcat:szfxxjpbvzej5jq6mjgbrgnmka</a> </span>
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Data Flow Refinement Type Inference [article]

Zvonimir Pavlinovic, Yusen Su, Thomas Wies
<span title="2020-11-10">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Algorithms for statically inferring refinement types typically work by reduction to solving systems of constrained Horn clauses extracted from typing derivations.  ...  We then derive an accompanying parametric inference algorithm as an abstract interpretation of a novel data flow semantics of functional programs.  ...  All existing refinement type inference tools that follow this approach of generating a context-insensitive Horn clause abstraction of the program therefore fail to verify Program 1.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2011.04876v1">arXiv:2011.04876v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3gn6kn2cgfeobnjfxwraf56qte">fatcat:3gn6kn2cgfeobnjfxwraf56qte</a> </span>
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SolType: Refinement Types for Solidity [article]

Bryan Tan, Benjamin Mariano, Shuvendu Lahiri, Isil Dillig, Yu Feng
<span title="2021-10-01">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
SolType incorporates a rich vocabulary of refinement terms that allow expressing relationships between integer values and aggregate properties of complex data structures.  ...  To evaluate the usefulness of our type system, we use Solid to prove arithmetic safety of a total of 120 smart contracts.  ...  incorporates a type inference procedure based on Constrained Horn Clause solvers. • We evaluate Solid on 120 real-world smart contracts and show that it is useful for eliminating many run-time checks  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2110.00677v1">arXiv:2110.00677v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zxdefj4dyrcxfpzbgpcdy4a7iu">fatcat:zxdefj4dyrcxfpzbgpcdy4a7iu</a> </span>
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Refinement Type Directed Search for Meta-Interpretive-Learning of Higher-Order Logic Programs [article]

Rolf Morel
<span title="2021-02-18">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Additionally we are able to infer polymorphic types of synthesized clauses and of entire programs. The other advancement is in developing an approach to leveraging refinement types in ILP.  ...  The introduction of polymorphic type checking to the MIL approach to logic program synthesis is validated by strong theoretical and experimental results, showing a cubic reduction in the size of the search  ...  Based on the theory one would expect a polynomials of degree 9 to best explain the experimental data.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2102.12553v1">arXiv:2102.12553v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2kzu7fb7efg4no4cqyngzmpvvq">fatcat:2kzu7fb7efg4no4cqyngzmpvvq</a> </span>
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Horn Clause Solvers for Program Verification [chapter]

Nikolaj Bjørner, Arie Gurfinkel, Ken McMillan, Andrey Rybalchenko
<span title="">2015</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
This paper complements these strides as we summarize main useful properties of Horn clauses, illustrate encodings of procedural program verification into Horn clauses and then highlight a number of useful  ...  A theme pursued in the past years by the authors of this paper has been to encode symbolic model problems directly as Horn clauses and develop dedicated solvers for Horn clauses.  ...  Note that upper bounds constraints on cardinalities preserve least fixed-points: If there is a solution not exceeding a bound, then any conjunction of solutions also will not exceed a bound.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-23534-9_2">doi:10.1007/978-3-319-23534-9_2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hsmmbrr35nfsveszovx67isifq">fatcat:hsmmbrr35nfsveszovx67isifq</a> </span>
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The ELDARICA Horn Solver

Hossein Hojjat, Philipp Rummer
<span title="">2018</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/m7zbvrubpncrdirtdbkz3zch4m" style="color: black;">2018 Formal Methods in Computer Aided Design (FMCAD)</a> </i> &nbsp;
Over the last years we have been developing and maintaining ELDARICA as a state-of-the-art solver for Horn clauses over integer arithmetic.  ...  In the version 2, we have extended the solver to support also algebraic data types and bit-vectors, theories that are commonly applied in verification, but currently unsupported by most Horn solvers.  ...  with algebraic data types, and (iv) optimisation.  ... 
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Page 4535 of Mathematical Reviews Vol. , Issue 93h [page]

<span title="">1993</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
out in a similar way as in the case of first-order Horn clauses Software 93h:68022 (goals and definite sentences, Herbrand base and universe, unifi- cation, proofs).  ...  The kinds of substitutions for predicate variables necessary in the context of these extended Horn clauses—while quite complex in general—are tightly constrained, so that the computations can be carried  ... 
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