PPDP 2022 Accepted Papers with Abstracts

Abstract: Imperative and object-oriented programming languages are among the most common languages for general-purpose programming. These languages work well for handling many common tasks necessary for most applications. However, there are still many hard problems that remain difficult to implement directly in imperative languages. Declarative languages have worked well for solving many of these problems by providing a syntax that allows the user to focus on modeling the problem rather than on designing an algorithm. Logic programming languages, like Prolog, have seen success in constraint satisfaction problems, logical databases, and various NP-Hard problems. Unfortunately, these languages have not seen the same success in general-purpose programming, and most of the problems they solve do not exist in isolation. Furthermore, many imperative programmers are still unfamiliar with and unaware of logic programming.
In this work, we aim to integrate a logical predicate, borrowed from logic programming, into an imperative language to facilitate a model-based approach to programming. Rather than attempting to embed Prolog directly into the language, we provide a logic for reasoning over imperative expressions using the common Boolean operators familiar to imperative programmers. While logic programming relies on unification, our predicate relies on variable assignment which is standard in imperative languages. We have implemented the predicate into the syntax of the Python programming language along with a solver built into the runtime for solving queries on the predicate. We demonstrate the use of the construct through solving commonly-known problems, such as graph coloring and the N-Queens problem. To evaluate the viability of our predicate, we compare the performance results of our predicate against current implementations of Prolog. By bringing this predicate construct to imperative languages, it is our hope that we can help to bridge the gap between imperative and logic programming as well as provide an approach to logic programming that is more intuitive for imperative programmers.

Abstract: DLV2 is an AI reasoner for Knowledge Representation and Reasoning which supports Answer Set Programming (ASP) – a logic-based declarative formalism, successfully used in both academic and industrial applications. Given a logic program modelling a computational problem, an execution of DLV2 produces the so-called answer sets that correspond one-to-one to the solutions. The computational process relies on the typical Ground&Solve approach where the grounding step transforms the input program into a new, equivalent ground program, and the subsequent solving step applies propositional algorithms to search for the answer sets. Recently, emerging applications in contexts such as stream reasoning and event processing demand for multi-shot reasoning: here, the system is expected to be reactive while repeatedly executed over rapidly changing data. In this work, we present a new incremental reasoner obtained from the evolution of DLV2 towards multi-shot reasoning. Rather than restarting the computation from scratch, the system remains alive and incrementally handles the internal grounding process: in a completely transparent fashion for the user, at each shot, it reuses previous computations for building and maintaining a large, more general ground program, from which a smaller yet equivalent portion is determined and used for computing answer sets. We describe the system, its usage, its applicability and performance in some practically relevant domains.

Abstract: We present an ongoing formalization of algorithms of ECMAScript, the specification describing the semantics of JavaScript, in a tiny functional meta-language.
We show that this formalization is concise, readable, maintainable, and textually close to the specification.
We extract an OCaml interpreter from our description and run small JavaScript programs whose semantics is based on these algorithms.

Abstract: Intersection types have the power to type expressions which are all of many different types. Gradual types combine type checking at both compile-time and run-time. Here we combine these two approaches in a new typed calculus that harness both of their strengths. We incorporate these two contributions in a single typed calculus and define an operational semantics with type cast annotations. We also prove several crucial properties of the type system, namely that types are preserved during compilation and evaluation, and that the refined criteria for gradual typing holds.

Abstract: Functional logic languages are a high-level approach to programming by combining the most important declarative features. They abstract from small-step operational details so that programmers can concentrate on the logical aspects of an application. This is supported by appropriate evaluation strategies. Demand-driven evaluation from functional programming is amalgamated with non-determinism from logic programming so that solutions or values are computed whenever they exist. This frees the programmer from considering the influence of an operational strategy to the success of a computation but it is a challenge to the language implementer. A non-deterministic demand-driven strategy might duplicate unevaluated choices of an expression which could duplicate the computational efforts. In recent implementations, this problem has been tackled by adding a kind of memoization of non-deterministic choices to the expression under evaluation. Since this has been implemented in imperative target languages, it was unclear whether this could also be supported in a functional programming environment, like Haskell. This paper presents a solution to this challenge by transforming functional logic programs into a monadic representation. Although this transformation is not new, we present an implementation of the monadic interface which supports memoization in non-deterministic branches. We demonstrate that our approach yields a promising performance that outperforms current compilers for Curry.

Abstract: Neural networks are increasingly relied upon as components of complex safety-critical systems such as autonomous vehicles. There is high demand for tools and methods that embed neural network verification in a larger verification cycle. However, neural network verification is difficult due to a wide range of verification properties of interest, each typically only amenable to verification in specialised solvers.
In this paper, we show how Imandra, a functional programming language and a theorem prover originally designed for verification, validation and simulation of financial infrastructure can offer a holistic infrastructure for neural network verification.
We develop a novel library, CheckINN, that formalises neural networks in Imandra, and covers different important facets of neural network verification.

Abstract: To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the calculus is a call-by-need strategy that performs lazy evaluation and implements sharing by recursive let-expressions.Expected convergence of expressions is the limit of the sum of all successful reduction outputs weighted by their probability.
We use contextual equivalence as program semantics: two expressions are contextually equivalent if and only if the expected convergence of the expressions plugged into any program context is always the same. We develop and illustrate techniques to prove equivalences including a context lemma, two derived criteria to show equivalences and a syntactic diagram-based method. This finally enables us to show correctness of a large set of program transformations with respect to the contextual equivalence.

Abstract: We present a method for generating possible proofs of a query with respect to a given Answer Set Programming (ASP) rule set using an abductive process where the space of abducibles is automatically constructed just from the input rules alone. Given a (possibly empty) set of user provided facts, our method infers any additional facts that may be needed for the entailment of a query and then outputs these extra facts, without the user needing to explicitly specify the space of all abducibles. We also present a method to generate a set of directed edges corresponding to the the justification graph for the query. Furthermore, through different forms of implicit term substitution, our method can take user provided facts into account and suitably modify the abductive solutions. Past work on abduction has been primarily based on goal directed methods. However these methods can result in solvers that are not truly declarative. Much less work has been done on realising abduction in a bottom up solver like the Clingo ASP solver. We describe novel ASP programs which can be run directly in Clingo to yield the abductive solutions and directed edge sets without needing to modify the underlying solving engine.

Abstract: A logic is presented for formalizing properties of specifications in the Edinburgh Logical Framework or LF. In this logic, typing judgments in LF serve as atomic formulas and quantification is permitted over LF terms and LF contexts. Quantifiers of the first variety are qualified by simple types that describe the functional structure associated with the variables they bind. Quantifiers over contexts are typed by context schemas that constrain their instantiations to adhere to a regular structure. The semantics of the logic is based ultimately on an understanding of derivability in LF. As such, valid formulas in the logic represent meta-theoretic properties of object systems that are encoded via LF signatures. The logic is complemented by a proof system that is briefly discussed. There are two categories to the rules in this proof system. One collection of rules captures the meanings of logical connectives and quantifiers. Another collection provides a means for analyzing atomic formulas based on an understanding of derivability in LF; these rules build in the capability for a case-analysis style reasoning about LF judgements and for induction over the heights of LF derivations.

Abstract: We introduce Nominal Matching Logic (NML) as an extension of Matching Logic with names and binding following the Gabbay-Pitts nominal approach. Matching logic is the foundation of the K framework, used to specify programming languages and automatically derive associated tools (compilers, debuggers, model checkers, program verifiers). Matching logic does not include a primitive notion of name binding, though binding operators can be represented via an encoding that internalises the graph of a function from bound names to expressions containing bound names. This approach is sufficient to represent computations involving binding operators, but has not been reconciled with support for inductive reasoning over syntax with binding (e.g., reasoning over $\lambda$-terms). Nominal logic is a formal system for reasoning about names and binding, which provides well-behaved and powerful principles for inductive reasoning over syntax with binding, and NML inherits these principles. We discuss design alternatives for the syntax and the semantics of NML, prove meta-theoretical properties and give examples to illustrate its expressive power. In particular, we show how induction principles for lambda-terms (alpha-structural induction) can be defined and used to prove standard properties of the lambda-calculus.

Abstract: We present an automatic translation of a skeletal semantics written in big-step style into an equivalent structural operational semantics. This translation is implemented on top of the Necro tool, which lets us automatically generate an OCaml interpreter for the small step semantics and a Coq mechanization of both semantics. We prove the framework correct in two ways: we provide a paper proof of the core of the transformation, and we generate Coq certification scripts alongside the transformation. We illustrate the approach using a simple imperative language and show how it scales to larger languages.