Journal of Logical and Algebraic Methods in Programming最新文献

We propose a dynamic logic ${\mathrm{DL}}_b$ called “dynamic logic with branching modalities”, which extends the temporal dynamic logic DLT with a “branching modality” for specifying safety properties of regular programs with tests (simply “regular programs”). Compared to the trace modality of DLT for while programs that do not abort, branching modality of ${\mathrm{DL}}_b$ does not exclude aborting traces introduced by regular programs, thus is able to capture a type of safety properties which are important for systems with failure behaviors. Moreover, it is congruent to the compositionality of regular programs so that the proof system naturally extended from that of DLT is proved to be complete for ${\mathrm{DL}}_b$. In this paper, we build the theory of ${\mathrm{DL}}_b$ on both propositional and first-ordered levels, defining two logics: propositional ${\mathrm{DL}}_b$ (${\mathrm{PDL}}_b$) and first-ordered ${\mathrm{DL}}_b$ (${\mathrm{FODL}}_b$). ${\mathrm{PDL}}_b$ forms the theoretical basis of ${\mathrm{DL}}_b$ while ${\mathrm{FODL}}_b$ is useful for practical verification. We propose the proof systems for ${\mathrm{PDL}}_b$ and ${\mathrm{FODL}}_b$, and analyze their decidability, soundness and (relative) completeness in a formal way, through comparing their expressiveness and deduction capabilities with propositional dynamic logic (PDL) and first-order dynamic logic (FODL) respectively. We show that ${\mathrm{FODL}}_b$ is actually an extension of DLT, and illustrate the motivations of using the branching modality through an example.

Narrowing and unification are very useful tools for symbolic analysis of rewrite theories, and thus for any model that can be specified in that way. A very clear example of their application is the field of formal cryptographic protocol analysis, which is why narrowing and unification are used in tools such as Maude-NPA, Tamarin and Akiss. In this work we present the implementation of a canonical narrowing algorithm, which improves the standard narrowing algorithm, extended to be able to process rewrite theories with conditional rules. The conditions of the rules will contain SMT constraints, which will be carried throughout the execution of the algorithm to determine if the solutions have associated satisfiable or unsatisfiable constraints, and in the latter case, discard them.

This paper investigates the adaptation of session types to provide behavioural information about Elixir modules. We devise a type system, called ElixirST, which statically determines whether functions in an Elixir module observe their endpoint specifications, expressed as session types; a corresponding tool automating this typechecking has also been constructed. In this paper we also formally validate this type system. An LTS-based operational semantics for the language fragment supported by the type system is developed, modelling its runtime behaviour when interacting with the module client. This operational semantics is then used to prove a form of session fidelity and progress for ElixirST.

A foundational theory of compositional categorical rewriting theory is presented, based on a collection of fibration-like properties that collectively induce and intrinsically structure the large collection of lemmata used in the proofs of theorems such as concurrency and associativity. The resulting highly generic proofs of these theorems are given. It is noteworthy that the proof of the concurrency theorem takes only a few lines and, while that of associativity remains somewhat longer, it would be unreadably long if written directly in terms of the basic lemmata. In essence, our framework improves the readability and ease of comprehension of these proofs by exposing latent modularity. A curated list of known instances of our framework is used to conclude the paper with a detailed discussion of the conditions under which the Double Pushout and Sesqui-Pushout semantics of graph transformation are compositional.

Liquidity is a liveness property of programs managing resources that pinpoints those programs not freezing any resource forever. We consider a simple stateful language whose resources are assets (digital currencies, non fungible tokens, etc.). Then we define a type system that tracks in a symbolic way the input-output behavior of functions with respect to assets. These types and their composition, which define types of computations, allow us to design two algorithms for liquidity that have different precisions and costs. We also demonstrate the correctness of the algorithms.

Communication is an essential element of modern software, yet programming and analysing communicating systems are difficult tasks.

A reason for this difficulty is the lack of compositional mechanisms that preserve relevant communication properties. This problem has been recently addressed for the well-known model of communicating systems, that is sets of components consisting of finite-state machines capable of exchanging messages. Two communicating systems can be composed by selecting one component per system, and transforming both of them into coupled gateways connecting the two systems. More precisely, a gateway forwards a message received from within its system to the other gateway, which then delivers the message to the other system. Suitable compatibility conditions between gateways have been proved sufficient for this composition mechanism to preserve properties such as deadlock freedom for asynchronous as well as symmetric synchronous communications (where sender and receiver play the same part in determining which message to exchange).

The present paper gives a comprehensive treatment of the case of synchronous communications. We consider both symmetric synchronous communications and asymmetric synchronous communications (where senders decide independently which message should be exchanged). The composition mechanism preserves different properties under different conditions depending on the considered type of synchronous communication. We show here that preservation of lock freedom requires an additional condition on gateways for asymmetric communication. Such condition is also needed for preservation of deadlock freedom, lock freedom or strong lock freedom for symmetric communications. This is not needed, instead, for preservation of either deadlock freedom or strong lock freedom with asymmetric interactions.

We extend a call-by-need variant of PCF with a binary probabilistic fair choice operator, which makes a lazy and typed variant of probabilistic functional programming. We define a contextual equivalence that respects the expected convergence of expressions and prove a corresponding context lemma. This enables us to show correctness of several program transformations with respect to contextual equivalence. Distribution-equivalence of expressions of numeric type is introduced. While the notion of contextual equivalence stems from program semantics, the notion of distribution equivalence is a direct description of the stochastic model. Our main result is that both notions are compatible: We show that for closed expressions of numeric type contextual equivalence and distribution-equivalence coincide. This provides a strong and often operationally feasible criterion for contextual equivalence of expressions and programs.

This special issue collects extended versions of selected papers presented at the 14th International Conference on Graph Transformation (ICGT 2021), held on June 24 and 25, 2021, as a virtual event due to ongoing COVID-19 countermeasures and travel restrictions.

Reverse derivative categories (RDCs) have recently been shown to be a suitable semantic framework for studying machine learning algorithms. Whereas emphasis has been put on training methodologies, less attention has been devoted to particular model classes: the concrete categories whose morphisms represent machine learning models. In this paper we study presentations by generators and equations of classes of RDCs. In particular, we propose polynomial circuits as a suitable machine learning model class. We give an axiomatisation for these circuits and prove a functional completeness result. Finally, we discuss the use of polynomial circuits over specific semirings to perform machine learning with discrete values.