We consider an extension of logic programs, called ω-programs, that can be used to define predicates over infinite lists. ω-programs allow us to specify properties of the infinite behavior of reactive systems and, in general, properties of infinite sequences of events. The semantics of ω-programs is an extension of the perfect model semantics. We present variants of the familiar unfold/fold rules which can be used for transforming ω-programs. We show that these new rules are correct, that is, their application preserves the perfect model semantics. Then we outline a general methodology based on program transformation for verifying properties of ω-programs. We demonstrate the power of our transformation-based verification methodology by proving some properties of Buechi automata and ω-regular languages.
Termination is an important and well-studied property for logic programs. However, almost all approaches for automated termination analysis focus on definite logic programs, whereas real-world Prolog programs typically use the cut operator. We introduce a novel pre-processing method which automatically transforms Prolog programs into logic programs without cuts, where termination of the cut-free program implies termination of the original program. Hence after this pre-processing, any technique for proving termination of definite logic programs can be applied. We implemented this pre-processing…
We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs allow one to describe classical data-structures (possibly with pointers) such as doubly-linked lists, circular lists etc. We show how the proposed logic can faithfully describe (i) termgraphs as well as (ii) the application of a termgraph rewrite rule (i.e. matching and replacement) and (iii) the computation of normal forms with respect to a given rewrite syste…
Program transformations are widely used in synthesis, optimization, and maintenance of software. Correctness of program transformations depends on preservation of some important properties of the input program. By regarding programs as Kripke structures, many interesting properties of programs can be expressed in temporal logics. In temporal logic, a formula is interpreted on a single program. However, to prove correctness of transformations, we encounter formulae which contain some subformulae interpreted on the input program and some on the transformed program. An example where such a situat…
In prior work, we showed that logic programming compilation can be given a proof-theoretic justification for generic abstract logic programming languages, and demonstrated this technique in the case of hereditary Harrop formulas and their linear variant. Compiled clauses were themselves logic formulas except for the presence of a second-order abstraction over the atomic goals matching their head. In this paper, we revisit our previous results into a more detailed and fully logical justification that does away with this spurious abstraction. We then refine the resulting technique to support wel…
We extend a technique called Compiling Control. The technique transforms coroutining logic programs into logic programs that, when executed under the standard left-to-right selection rule (and not using any delay features) have the same computational behavior as the coroutining program. In recent work, we revised Compiling Control and reformulated it as an instance of Abstract Conjunctive Partial Deduction. This work was mostly focused on the program analysis performed in Compiling Control. In the current paper, we focus on the synthesis of the transformed program. Instead of synthesizing a ne…
Fuzzy logic programming is a growing declarative paradigm aiming to integrate fuzzy logic into logic programming. One of the most difficult tasks when specifying a fuzzy logic program is determining the right weights for each rule, as well as the most appropriate fuzzy connectives and operators. In this paper, we introduce a symbolic extension of fuzzy logic programs in which some of these parameters can be left unknown, so that the user can easily see the impact of their possible values. Furthermore, given a number of test cases, the most appropriate values for these parameters can be automat…
Program correctness (in imperative and functional programming) splits in logic programming into correctness and completeness. Completeness means that a program produces all the answers required by its specification. Little work has been devoted to reasoning about completeness. This paper presents a few sufficient conditions for completeness of definite programs. We also study preserving completeness under some cases of pruning of SLD-trees (e.g. due to using the cut). We treat logic programming as a declarative paradigm, abstracting from any operational semantics as far as possible. We argue t…
Higher-order logic programming is an interesting extension of traditional logic programming that allows predicates to appear as arguments and variables to be used where predicates typically occur. Higher-order characteristics are indeed desirable but on the other hand they are also usually more expensive to support. In this paper we propose a program specialization technique based on partial evaluation that can be applied to a modest but useful class of higher-order logic programs and can transform them into first-order programs without introducing additional data structures. The resulting fir…
This paper presents an example of formal reasoning about the semantics of a Prolog program of practical importance (the SAT solver of Howe and King). The program is treated as a definite clause logic program with added control. The logic program is constructed by means of stepwise refinement, hand in hand with its correctness and completeness proofs. The proofs are declarative - they do not refer to any operational semantics. Each step of the logic program construction follows a systematic approach to constructing programs which are provably correct and complete. We also prove that correctness…
This volume constitutes the pre-proceedings of the 26th International Workshop on Functional and Logic Programming (WFLP 2018). It is formed of those papers selected by the program committee for presentation at the workshop. After discussion at the workshop, the program committee will select a number of papers to be invited for the second round of refereeing and selection for the formal proceedings.
This volume constitutes the informal proceedings of the 32nd International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2022), held on 21-23rd September 2022 as a hybrid (blended) meeting, both in-person (at the Ivane Javakhishvili Tbilisi State University -TSU- in Tbilisi, Georgia) and virtual, and co-located with the 24th International Symposium on Principles and Practice of Declarative Programming (PPDP 2022) as part of the Computational Logic Autumn Summit 2022 (CLAS 2022).
Research on deductive verification of probabilistic programs has considered expectation-based logics, where pre- and post-conditions are real-valued functions on states, and assertion-based logics, where pre- and post-conditions are boolean predicates on state distributions. Both approaches have developed over nearly four decades, but they have different standings today. Expectation-based systems have managed to formalize many sophisticated case studies, while assertion-based systems today have more limited expressivity and have targeted simpler examples. We present Ellora, a sound and relativ…
We present a program logic for Pitts and Stark's ν-calculus, an extension of the call-by-value simply-typed λ-calculus with a mechanism for the generation of fresh names. Names can be compared for (in)-equality, producing programs with subtle observable properties. Hidden names produced by interactions between generation and abstraction are captured logically with a second-order quantifier over type contexts. We illustrate usage of the logic through reasoning about well-known difficult cases from the literature.
Algorithmic skeletons are used as building-blocks to ease the task of parallel programming by abstracting the details of parallel implementation from the developer. Most existing libraries provide implementations of skeletons that are defined over flat data types such as lists or arrays. However, skeleton-based parallel programming is still very challenging as it requires intricate analysis of the underlying algorithm and often uses inefficient intermediate data structures. Further, the algorithmic structure of a given program may not match those of list-based skeletons. In this paper, we pres…
Since the first conference held in Marseille in 1982, ICLP has been the premier international event for presenting research in logic programming. Contributions are sought in all areas of logic programming, including but not restricted to: Foundations: Semantics, Formalisms, Nonmonotonic reasoning, Knowledge representation. Languages: Concurrency, Objects, Coordination, Mobility, Higher Order, Types, Modes, Assertions, Modules, Meta-programming, Logic-based domain-specific languages, Programming Techniques. Declarative programming: Declarative program development, Analysis, Type and mode infere…
Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable functions into predicates in order to stay in the logic programming framework. Since amalgamated functional logic languages offer flexible as well as efficient evaluation strategies, we propose an opposite approach in this paper. By mapping logic programs into functional logic programs with a transformation based on inferring functional dependencies, we develop a f…
We survey the landscape of Hoare logics for quantum programs. We review three papers: "Reasoning about imperative quantum programs" by Chadha, Mateus and Sernadas; "A logic for formal verification of quantum programs" by Yoshihiko Kakutani; and "Floyd-hoare logic for quantum programs" by Mingsheng Ying. We compare the mathematical foundations of the logics, their underlying languages, and the expressivity of their assertions. We also use the languages to verify the Deutsch-Jozsa Algorithm, and discuss their relative usability in practice.
Since the first conference held in Marseille in 1982, ICLP has been the premier international event for presenting research in logic programming. Contributions are solicited in all areas of logic programming and related areas, including but not restricted to: - Foundations: Semantics, Formalisms, Answer-Set Programming, Non-monotonic Reasoning, Knowledge Representation. - Declarative Programming: Inference engines, Analysis, Type and mode inference, Partial evaluation, Abstract interpretation, Transformation, Validation, Verification, Debugging, Profiling, Testing, Logic-based domain-specific …
University of Athens（雅典大学）；University of Szeged（塞格德大学）
Extensional higher-order logic programming has been introduced as a generalization of classical logic programming. An important characteristic of this paradigm is that it preserves all the well-known properties of traditional logic programming. In this paper we consider the semantics of negation in the context of the new paradigm. Using some recent results from non-monotonic fixed-point theory, we demonstrate that every higher-order logic program with negation has a unique minimum infinite-valued model. In this way we obtain the first purely model-theoretic semantics for negation in extensiona…
We present a parallel implementation of Coalgebraic Logic Programming (CoALP) in the programming language Go. CoALP was initially introduced to reflect coalgebraic semantics of logic programming, with coalgebraic derivation algorithm featuring both corecursion and parallelism. Here, we discuss how the coalgebraic semantics influenced our parallel implementation of logic programming.
Logic program transformation by the unfold/fold method ad- vocates the writing of correct logic programs via the application of some rules to a naive program. This work focuses on how to overcome subgoal- introduction difficulties in synthesizing efficient sorting algorithms from an naive sorting algorithm, through logic program transformation and abductive reasoning.
University of Athens（雅典大学）；University of Victoria（维多利亚大学）
We propose a purely extensional semantics for higher-order logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique minimum Herbrand model which is the greatest lower bound of all Herbrand models of the program and the least fixed-point of an immediate consequence operator. We also propose an SLD-resolution proof procedure which is proven sound and complete with respect to the minimum model semantics. In other words, we provide a purely extensional theoretical framework f…
A first-order logic with quantum variables is needed as an assertion language for specifying and reasoning about various properties (e.g. correctness) of quantum programs. Surprisingly, such a logic is missing in the literature, and the existing first-order Birkhoff-von Neumann quantum logic deals with only classical variables and quantifications over them. In this paper, we fill in this gap by introducing a first-order extension of Birkhoff-von Neumann quantum logic with universal and existential quantifiers over quantum variables. Examples are presented to show our logic is particularly suit…
A Proof Theoretic Approach to Failure in Functional Logic Programming
如何从程序中提取负信息是逻辑程序设计中的一个重要问题。在这里，我们解决问题的功能逻辑程序，从证明理论的角度来看。我们工作的出发点是CRWL（Constructor based ReWriting Logic），它是一个成熟的函数逻辑编程理论框架，其基本概念是非严格非确定函数。我们提出了一个证明演算，CRWLF，这是能够推导出否定信息的CRWL程序。特别是，CRWLF能够证明CRWL内的复位有限失败。
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…
The semantic foundations for logic programming are usually separated into two different approaches. The operational semantics, which uses SLD-resolution, the proof method that computes answers in logic programming, and the declarative semantics, which sees logic programs as formulas and its semantics as models. Here, we define a new operational semantics called TSLD-resolution, which stands for Typed SLD-resolution, where we include a value "wrong", that corresponds to the detection of a type error at run-time. For this we define a new typed unification algorithm. Finally we prove the correctn…
Formal verification provides strong guarantees of correctness of software, which are especially important in safety or security critical systems. Hoare logic is a widely used formalism for rigorous verification of software against specifications in the form of pre-condition/post-condition assertions. The advancement of semantic parsing techniques and higher computational capabilities enable us to extract semantic content from natural language text as formal logical forms, with increasing accuracy and coverage. This paper proposes a formal framework for Hoare logic-based formal verification of …
Weighted logic programming, a generalization of bottom-up logic programming, is a well-suited framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm's output space, such as a path through a graph or a grammatical derivation, and are given a real-valued score (often interpreted as a probability) that depends on the real weights of the base axioms used in the proof. The desired output is a function over all possible proofs, such as a sum of scores or an optimal score. We describe the PRODUCT transformation, which can merge two weighted logic …
