We present a formal study of semantics for the relational programming language miniKanren. First, we formulate a denotational semantics which corresponds to the minimal Herbrand model for definite logic programs. Second, we present operational semantics which models interleaving, the distinctive feature of miniKanren implementation, and prove its soundness and completeness w.r.t. the denotational semantics. Our development is supported by a Coq specification, from which a reference interpreter can be extracted. We also derive from our main result a certified semantics (and a reference interpreter) for SLD resolution with cut and prove its soundness.
Expressive static typing disciplines are a powerful way to achieve high-quality software. However, the adoption cost of such techniques should not be under-estimated. Just like gradual typing allows for a smooth transition from dynamically-typed to statically-typed programs, it seems desirable to support a gradual path to certified programming. We explore gradual certified programming in Coq, providing the possibility to postpone the proofs of selected properties, and to check "at runtime" whether the properties actually hold. Casts can be integrated with the implicit coercion mechanism of Coq…
We present an experimental system strongly inspired by miniKanren, implemented on top of the tactics mechanism of the HOL~Light theorem prover. Our tool is at the same time a mechanism for enabling the logic programming style for reasoning and computing in a theorem prover, and a framework for writing logic programs that produce solutions endowed with a formal proof of correctness.
Programming communicating processes is challenging, because it requires writing separate programs that perform compatible send and receive actions at the right time during execution. Leaving this task to the programmer can easily lead to bugs. Choreographic programming addresses this challenge by equipping developers with high-level abstractions for codifying the desired communication structures from a global viewpoint. Given a choreography, implementations of the involved processes can be automatically generated by endpoint projection (EPP). While choreographic programming prevents manual mis…
Functional programming comes in two flavours: one where ``functions are first-class citizens'' (we call this applicative) and one which is based on equations (we call this declarative). In relational programming clauses play the role of equations. Hence Prolog is declarative. The purpose of this paper is to provide in relational programming a mathematical basis for the relational analog of applicative functional programming. We use the cylindric semantics of first-order logic due to Tarski and provide a new notation for the required cylinders that we call tables. We define the Table/Relation A…
We present an implementation of the relational programming language miniKanren as a set of combinators and syntax extensions for OCaml. The key feature of our approach is polymorphic unification, which can be used to unify data structures of arbitrary types. In addition we provide a useful generic programming pattern to systematically develop relational specifications in a typed manner, and address the problem of integration of relational subsystems into functional applications.
We present Leapfrog, a Coq-based framework for verifying equivalence of network protocol parsers. Our approach is based on an automata model of P4 parsers, and an algorithm for symbolically computing a compact representation of a bisimulation, using "leaps." Proofs are powered by a certified compilation chain from first-order entailments to low-level bitvector verification conditions, which are discharged using off-the-shelf SMT solvers. As a result, parser equivalence proofs in Leapfrog are fully automatic and push-button. We mechanically prove the core metatheory that underpins our approach,…
Relational lenses are a modern approach to the view update problem in relational databases. As introduced by Bohannon et al. (2006), relational lenses allow the definition of updatable views by the composition of lenses performing individual transformations. Horn et al. (2018) provided the first implementation of incremental relational lenses, which demonstrated that relational lenses can be implemented efficiently by propagating changes to the database rather than replacing the entire database state. However, neither approach proposes a concrete language design; consequently, it is unclear ho…
While many applications export data in hierarchical formats like XML and JSON, it is often necessary to convert such hierarchical documents to a relational representation. This paper presents a novel programming-by-example approach, and its implementation in a tool called Mitra, for automatically migrating tree-structured documents to relational tables. We have evaluated the proposed technique using two sets of experiments. In the first experiment, we used Mitra to automate 98 data transformation tasks collected from StackOverflow. Our method can generate the desired program for 94% of these b…
Quantum computing technology may soon deliver revolutionary improvements in algorithmic performance, but these are only useful if computed answers are correct. While hardware-level decoherence errors have garnered significant attention, a less recognized obstacle to correctness is that of human programming errors -- "bugs". Techniques familiar to most programmers from the classical domain for avoiding, discovering, and diagnosing bugs do not easily transfer, at scale, to the quantum domain because of its unique characteristics. To address this problem, we have been working to adapt formal meth…
RelationalAI（关系人工智能）；University of Edinburgh（爱丁堡大学）；Univ of Edinburgh（爱丁堡大学）；LIGM, Univ. Gustave Eiffel, CNRS（法国盖埃夫大学信息与数字科学实验室，法国国家科学研究中心）；University of Bayreuth（拜罗伊特大学）；University of Warsaw（华沙大学）；Hebrew University（耶路撒冷希伯来大学）；Université Paris Cité, CNRS, IRIF（巴黎西岱大学，法国国家科学研究中心，信息学与随机系统研究所）；PUC Chile（智利天主教Pontificia大学）
Choreographic programming is a paradigm where developers write the global specification (called choreography) of a communicating system, and then a correct-by-construction distributed implementation is compiled automatically. Unfortunately, it is possible to write choreographies that cannot be compiled, because of issues related to an agreement property known as knowledge of choice. This forces programmers to reason manually about implementation details that may be orthogonal to the protocol that they are writing. Amendment is an automatic procedure for repairing uncompilable choreographies. W…
We present a technique for deriving semantic program analyses from a natural semantics specification of the programming language. The technique is based on a particular kind of semantics called pretty-big-step semantics. We present a pretty-big-step semantics of a language with simple objects called O'While and specify a series of instrumentations of the semantics that explicitates the flows of values in a program. This leads to a semantics-based dependency analysis, at the core, e.g., of tainting analysis in software security. The formalization has been realized with the Coq proof assistant.
TU Dortmund University（多特蒙德工业大学）；University of Bonn（波恩大学）
We propose relational linear programming, a simple framework for combing linear programs (LPs) and logic programs. A relational linear program (RLP) is a declarative LP template defining the objective and the constraints through the logical concepts of objects, relations, and quantified variables. This allows one to express the LP objective and constraints relationally for a varying number of individuals and relations among them without enumerating them. Together with a logical knowledge base, effectively a logical program consisting of logical facts and rules, it induces a ground LP. This gro…
Android embodies security mechanisms at both OS and application level. In this platform application security is built primarily upon a system of permissions which specify restrictions on the operations a particular process can perform. The critical role of these security mechanisms makes them a prime target for (formal) verification. We present an idealized model of a reference monitor of the novel mechanisms of Android 6 (and further), where it is possible to grant permissions at run time. Using the programming language of the proof-assistant Coq we have developed a functional implementation …
We extend the λ-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify λ-expressions and still obtain a confluent theory, we depart from related approaches, such as λProlog, in that we do not attempt to solve higher-order unification. Instead, abstractions are decorated with a location, which intuitively may be understood as its memory address, and we impose a simple coherence invariant: abstractions in the same location must be equal. This allows us t…
Logic programming is sometimes described as relational programming: a paradigm in which the programmer specifies and composes n-ary relations using systems of constraints. An advanced logic programming environment will provide tools that abstract these relations to transform, optimise, or even verify the correctness of a logic program. This talk will show that these concepts, namely relations, constraints and abstractions, turn out to also be important in the reverse engineer process that underpins the discovery of bugs within the security industry.
University of Edinburgh（爱丁堡大学）；University of Oxford（牛津大学）；University of Zurich（苏黎世大学）
This paper introduces semi-ring dictionaries, a powerful class of compositional and purely functional collections that subsume other collection types such as sets, multisets, arrays, vectors, and matrices. We developed SDQL, a statically typed language that can express relational algebra with aggregations, linear algebra, and functional collections over data such as relations and matrices using semi-ring dictionaries. Furthermore, thanks to the algebraic structure behind these dictionaries, SDQL unifies a wide range of optimizations commonly used in databases (DB) and linear algebra (LA). As a…
Probabilistic logic programming is a major part of statistical relational artificial intelligence, where approaches from logic and probability are brought together to reason about and learn from relational domains in a setting of uncertainty. However, the behaviour of statistical relational representations across variable domain sizes is complex, and scaling inference and learning to large domains remains a significant challenge. In recent years, connections have emerged between domain size dependence, lifted inference and learning from sampled subpopulations. The asymptotic behaviour of stati…
We study conjunctive partial deduction, an advanced specialization technique aimed at improving the performance of logic programs, in the context of relational programming language miniKanren. We identify a number of issues, caused by miniKanren peculiarities, and describe a novel approach to specialization based on partial deduction and supercompilation. The results of the evaluation demonstrate successful specialization of relational interpreters. Although the project is at an early stage, we consider it as the first step towards an efficient optimization framework for miniKanren.
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we obtain compact and computationally efficient data structures for data collections corresponding to union and deletion, repeated union, Cartesian product and key-indexed data. Free modules naturally give rise to polysets, which generalise multisets and facilitate expressing database queries as multilinear maps with asymptotically efficient evaluation on polyset…
Program synthesis approaches struggle to learn programs with numerical values. An especially difficult problem is learning continuous values over multiple examples, such as intervals. To overcome this limitation, we introduce an inductive logic programming approach which combines relational learning with numerical reasoning. Our approach, which we call NUMSYNTH, uses satisfiability modulo theories solvers to efficiently learn programs with numerical values. Our approach can identify numerical values in linear arithmetic fragments, such as real difference logic, and from infinite domains, such …
Formal semantics provides rigorous, mathematically precise definitions of programming languages, with which we can argue about program behaviour and program equivalence by formal means; in particular, we can describe and verify our arguments with a proof assistant. There are various approaches to giving formal semantics to programming languages, at different abstraction levels and applying different mathematical machinery: the reason for using the semantics determines which approach to choose. In this paper we investigate some of the approaches that share their roots with traditional relationa…
This paper presents a generic web-based database interface implemented in Prolog. We discuss the advantages of the implementation platform and demonstrate the system's applicability in providing access to integrated biochemical data. Our system exploits two libraries of SWI-Prolog to create a schema-transparent interface within a relational setting. As is expected in declarative programming, the interface was written with minimal programming effort due to the high level of the language and its suitability to the task. We highlight two of Prolog's features that are well suited to the task at ha…
In this article, we give a brief overview of the current state and future potential of symbolic computation within the Python statistical modeling and machine learning community. We detail the use of miniKanren as an underlying framework for term rewriting and symbolic mathematics, as well as its ability to orchestrate the use of existing Python libraries. We also discuss the relevance and potential of relational programming for implementing more robust, portable, domain-specific "math-level" optimizations--with a slight focus on Bayesian modeling. Finally, we describe the work going forward a…
