Denotational Semantics Research Articles

Construction of Remote Sensing Indices Knowledge Graph (RSIKG) Based on Semantic Hierarchical Graph

Remote sensing indices are widely used in various fields of geoscience research. However, there are limits to how effectively the knowledge of indices can be managed or analyzed. One of the main problems is the lack of ontology models and research on indices, which makes it difficult to acquire and update knowledge in this area. Additionally, there is a lack of techniques to analyze the mathematical semantics of indices, making it difficult to directly manage and analyze their mathematical semantics. This study utilizes an ontology and mathematical semantics integration method to offer a novel knowledge graph for a remote sensing index knowledge graph (RSIKG) so as to address these issues. The proposed semantic hierarchical graph structure represents the indices of knowledge with an entity-relationship layer and a mathematical semantic layer. Specifically, ontologies in the entity-relationship layer are constructed to model concepts and relationships among indices. In the mathematical semantics layer, index formulas are represented using mathematical semantic graphs. A method for calculating similarity for index formulas is also proposed. The article describes the entire process of building RSIKG, including the extraction, storage, analysis, and inference of remote sensing index knowledge. Experiments provided in this article demonstrate the intuitive and practical nature of RSIKG for analyzing indices knowledge. Overall, the proposed methods can be useful for knowledge queries and the analysis of indices. And the present study lays the groundwork for future research on analysis techniques and knowledge processing related to remote sensing indices.

Formally verified animation for RoboChart using interaction trees

RoboChart is a core notation in the RoboStar framework. It is a timed and probabilistic domain-specific and state machine-based language for robotics. RoboChart supports shared variables and communication across entities in its component model. It has formal denotational semantics given in CSP. The semantic technique of Interaction Trees (ITrees) represents behaviours of reactive and concurrent programs interacting with their environments. Recent mechanisation of ITrees, ITree-based CSP semantics and a Z mathematical toolkit in Isabelle/HOL bring new applications of verification and animation for state-rich process languages, such as RoboChart. In this paper, we use ITrees to give RoboChart novel operational semantics, implement it in Isabelle, and use Isabelle's code generator to generate verified and executable animations. We illustrate our approach using an autonomous chemical detector and patrol robot models, exhibiting nondeterminism and using shared variables. With animation, we show two concrete scenarios for the chemical detector when the robot encounters different environmental inputs and three for the patrol robot when its calibrated position is in other corridor sections. We also verify that the animated scenarios are trace refinements of the CSP denotational semantics of the RoboChart models using FDR, a refinement model checker for CSP. This ensures that our approach to resolve nondeterminism using CSP operators with priority is sound and correct.

Focusing on Refinement Typing

We present a logically principled foundation for systematizing, in a way that works with any computational effect and evaluation order, SMT constraint generation seen in refinement type systems for functional programming languages. By carefully combining a focalized variant of call-by-push-value, bidirectional typing, and our novel technique of value-determined indexes, our system generates solvable SMT constraints without existential (unification) variables. We design a polarized subtyping relation allowing us to prove our logically focused typing algorithm is sound, complete, and decidable. We prove type soundness of our declarative system with respect to an elementary domain-theoretic denotational semantics. Type soundness implies, relatively simply, the total correctness and logical consistency of our system. The relative ease with which we obtain both algorithmic and semantic results ultimately stems from the proof-theoretic technique of focalization.

Explanatory Denotational Semantics for Complex Event Patterns

Recent years brought popularity and importance of complex event processing (CEP) and associated query languages. CEP systems can be hard to understand. It is often non-trivial to determine streams of events matched by a query, and sometimes we may not notice important edge cases. Hence, the desirability of formal semantics permitting reasoning about resulting complex events and checking if actual matchings agree with our intentions follows. In the article, we introduce a pattern language PatLang with some unique syntactic features related to variable binding. We provide two distinct denotational semantics for PatLang : Minimal semantics , sufficient to describe when patterns match, and tree semantics , which provides detailed information about subpatterns with which the matched events actually match, i.e., information about interpretation of matched events induced by the pattern matching. The tree semantics is unnecessary for verifying correctness of pattern matching execution. However, we show that neither minimal semantics, nor semantics from the prior work suffices to effectively locate errors in patterns with respect to their intended meaning, and that the additional information provided by the tree semantics is crucial for that purpose. We prove that tree semantics can be mapped to minimal semantics. Finally, we provide some practical evaluation.

Mechanization of the Ravenscar Profile in Coq

The Ravenscar profile has been added to the Ada language as part of the 2005 revision. It is a pragmatic definition of concurrency patterns for real-time systems for mono-core processor. In this paper, we report on an ongoing effort to mechanize a toy language derived from IMP that embeds the Ravenscar profile constructs as they are specified in the Ada Reference Manual. We define the denotational semantics of the language and derive two interpreters for the language.

Formalizing the Semantics of a Classical-Quantum Imperative Language in Coq

In order to verify the functional correctness of quantum circuits or algorithms, a prominent approach is to specify them as quantum programs and semi-automatically deduce them in a theorem prover. It is indispensable to first formalize the semantics of the basic quantum language. We formalize in Coq an imperative language which allows for classical and quantum information interactions. We define small-step operational semantics and state-based denotational semantics. Then we prove a consistency theorem between these two semantics. A distribution-based denotational semantics is also defined and related to the state-based one. Finally, we describe a few typical quantum algorithms and utilize the distribution-based denotational semantics to verify their correctness.

Seeing is believing

Abstract Verbs of perception are known for their prolific use in various non-literal functions that are usually argued to have developed from their denotational semantics (San Roque, Kendrick, Norcliffe & Majid 2018). In this study we document interactional practices involving the Estonian 2nd person verb form näed ’you see’ to demonstrate that its usage is anchored in face-to-face situations where the speaker guides a co-present other’s visual attention. Through multimodal analysis we show how näed is coordinated with the participants’ body orientations, gestures, and gazes to point to visually available proof for one’s current arguments, rendering it an evidential meaning even in its most “literal” uses of seeing, when a co-participant is invited to consider the visual evidence. We argue that the spatially anchored uses constitute a natural habitat of verbs of seeing, as visual perception is a mutually calibrated interactional accomplishment. Relevant syntactic constructions emerge in real time conversation where näed, calling for a visual orientation, is either preceded or followed by clausal specifications of what is to be seen, which makes it look like a particle. This challenges the argument that perception verbs start out as syntactic predicates in full clauses to then develop other uses.

A Domain-theoretic Approach to Statistical Programming Languages

We give a domain-theoretic semantics to a statistical programming language, using the plain old category of dcpos, in contrast to some more sophisticated recent proposals. Remarkably, our monad of minimal valuations is commutative, which allows for program transformations that permute the order of independent random draws, as one would expect. A similar property is not known for Jones and Plotkin’s monad of continuous valuations. Instead of working with true real numbers, we work with exact real arithmetic, providing a bridge towards possible implementations (implementations by themselves are not addressed here). Rather remarkably, we show that restricting ourselves to minimal valuations does not restrict us much: All measures on the real line can be modeled by minimal valuations on the domain I ℝ ⊥ of exact real arithmetic. We give three operational semantics for our language, and we show that they are all adequate with respect to the denotational semantics. We also explore quite a few examples to demonstrate that our semantics computes exactly as one would expect and to debunk the myth that a semantics based on continuous maps would not be expressive enough to encode measures with non-compact support using only measures with compact support, or to encode measures via non-continuous density functions, for instance. Our examples also include some useful, non-trivial cases of distributions on higher-order objects.

Formal Specification and Testing for Reinforcement Learning

The development process for reinforcement learning applications is still exploratory rather than systematic. This exploratory nature reduces reuse of specifications between applications and increases the chances of introducing programming errors. This paper takes a step towards systematizing the development of reinforcement learning applications. We introduce a formal specification of reinforcement learning problems and algorithms, with a particular focus on temporal difference methods and their definitions in backup diagrams. We further develop a test harness for a large class of reinforcement learning applications based on temporal difference learning, including SARSA and Q-learning. The entire development is rooted in functional programming methods; starting with pure specifications and denotational semantics, ending with property-based testing and using compositional interpreters for a domain-specific term language as a test oracle for concrete implementations. We demonstrate the usefulness of this testing method on a number of examples, and evaluate with mutation testing. We show that our test suite is effective in killing mutants (90% mutants killed for 75% of subject agents). More importantly, almost half of all mutants are killed by generic write-once-use-everywhere tests that apply to any reinforcement learning problem modeled using our library, without any additional effort from the programmer.

Explicit Refinement Types

We present λ ert , a type theory supporting refinement types with <em>explicit proofs</em>. Instead of solving refinement constraints with an SMT solver like DML and Liquid Haskell, our system requires and permits programmers to embed proofs of properties within the program text, letting us support a rich logic of properties including quantifiers and induction. We show that the type system is sound by showing that every refined program erases to a simply-typed program, and by means of a denotational semantics, we show that every erased program has all of the properties demanded by its refined type. All of our proofs are formalised in Lean 4.

Generic Programming with Extensible Data Types: Or, Making Ad Hoc Extensible Data Types Less Ad Hoc

We present a novel approach to generic programming over extensible data types. Row types capture the structure of records and variants, and can be used to express record and variant subtyping, record extension, and modular composition of case branches. We extend row typing to capture generic programming over rows themselves, capturing patterns including lifting operations to records and variations from their component types, and the duality between cases blocks over variants and records of labeled functions, without placing specific requirements on the fields or constructors present in the records and variants. We formalize our approach in System R𝜔, an extension of F𝜔 with row types, and give a denotational semantics for (stratified) R𝜔 in Agda.

Specification and verification of concurrent systems by causality and realizability

A logical theory for interface specification and verification of distributed, concurrent, interactive, real-time systems is worked out based on a semantic foundation including operational and denotational semantics. It supports a calculus for the specification and verification of concurrent interactive systems by interface assertions. Systems are composed acting concurrently and interacting via streams exchanged over their channels forming feedback loops. A denotational semantics is defined handling feedback communication by recursion and fixpoints based on strong causality and realizability instead of monotonicity. The resulting verification calculus for the specification logic is proved to be sound and relatively complete with respect to an operational semantics in terms of generalized Moore machines. Actually, two models of concurrent systems are defined, a more abstract one with communication and interaction modeled by untimed streams and a more concrete one working with timed streams. The untimed model is an abstraction of the timed model. The timed model allows expressing the laws of causality and realizability. Moreover, the timed model can be used to specify real-time properties.

From semantics to types: The case of the imperative λ-calculus

We study the logical semantics of an untyped λ-calculus equipped with operators representing read and write operations from and to a global store. Such a logic consists of an intersection type assignment system, which we derive from the denotational semantics of the calculus, based on the monadic approach to model computational λ-calculi.The system is obtained by constructing a filter model in the category of ω-algebraic lattices, such that the typing rules can be recovered out of the term interpretation. By construction, the so-obtained type system satisfies the “type-semantics” property and completeness.

METHODS OF STUDYING THE SEMANTICS OF PROGRAMMING LANGUAGES BY THE STUDENTS OF PROFESSIONAL EDUCATION INSTITUTIONS

The article shows that in institutions of professional (vocational and technical) education, the inclusion of a block of questions devoted to the semiotics of programming languages into the content of learning languages and programming methods will contribute to the successful implementation of the system of their fundamental training in the subject field «Information Technologies». The methodological system of education, built within the framework of the methodologicalical theory, helps students acquire knowledge and skills in the semiotics of programming languages. The main theoretical and methodological provisions are outlined, on the basis of which a methodical system of teaching the semiotics of programming languages ​​and a metamodel of the teaching method itself in the form of a methodical theory have been built. On the basis of the classification of models of syntax and semantics of programming languages, carried out to build a conceptual basis for the methodological theory of teaching semiotics of programming languages, there have been selected the following sections for teaching semiotics of programming languages: formal syntax of programming languages; meaningful operational semantics of programming languages; formal operational semantics of programming languages; formal deductive semantics of programming languages; denotational semantics of programming languages. At the stage of selecting the content of the elements of the model of the methodical system for teaching the semiotics of programming languages, the central place is occupied by the problem of setting learning goals, since the selection of the content of other elements is aimed at achieving the set goals. Semiotic educational models include a system of tasks, in which the subject area of activity is developed within the framework of specific teaching methods, which involve textual statements of educational problems or tasks. The goals and content of learning the semiotics of programming languages, largely influencing each other, determine the choice of teaching methods for the section in question. For example, when considering the last block of learning content, there has been chosen a simulation or social learning model, which provides for the student’s assimilation of new information, as well as attempts to get involved in the situation of solving professional tasks based on it.

Mechanised Operational Reasoning for C11 Programs with Relaxed Dependencies

Verification techniques for C11 programs have advanced significantly in recent years with the development of operational semantics and associated logics for increasingly large fragments of C11. However, these semantics and logics have been developed in a restricted setting to avoid the thin-air-read problem. In this article, we propose an operational semantics that leverages an intra-thread partial order (called semantic dependencies ) induced by a recently developed denotational event-structure-based semantics. We prove that our operational semantics is sound and complete with respect to the denotational semantics. We present an associated logic that generalises a recent Owicki–Gries framework for RC11 RAR (repaired C11) with relaxed and release-acquire accesses. We describe the mechanisation of the logic in the Isabelle/HOL theorem prover, which we use to prove correctness of a number of examples.

Morlille kan ikke flyve

This paper deals with natural language (NL) semantics an the computer. It presents two major theoretical vicwpoints in linguistic semantics: representational and denotational. In linguistic theory, these two issues are mostly understood as mutually exclusive, as can be seen from Chomskyan and Montague Grammar. The paper discusses representational semantics in connection with the autonomous syntax approach of mainstream transformational grammar, denotational semantics in connection with the model-theoretic approach of Montague grammar. In the next step, I consider the implementation of model-theoretic NL comprehension systems on the computer. In the present context, they are viewed principally as a means to make experimental studies in the formalizations of NL. It is shown that the correct handling of referential NL terms in such systems can be achicved only if these systems combine methods and techniques from both types of semantics. Finally, the cognitive meaning of the concept of computer understanding is touched upon.

On Giving Meanings to Programs

In a short section on the semantics of programs within his discussion of program correctness, Primiero seems to endorse the received view on the Scott-Strachey approach to denotational semantics as directly related to correctness. While this is true to some extent, I argue that the mathematical entities associated with programs play a lesser role in reasoning on program correctness, while the mathematical foundations of denotational semantics, namely the theory of domains, have contributed significantly to the conceptual understanding of programming and of computation in general

Testing using CSP Models: Time, Inputs, and Outputs

The existing testing theories for CSP cater for verification of interaction patterns (traces) and deadlocks, but not time. We address here refinement and testing based on a dialect of CSP, called tock -CSP, which can capture discrete time properties. This version of CSP has been of widespread interest for decades; recently, it has been given a denotational semantics, and model checking has become possible using a well established tool. Here, we first equip tock -CSP with a novel semantics for testing, which distinguishes input and output events: the standard models of ( tock -)CSP do not differentiate them, but for testing this is essential. We then present a new testing theory for timewise refinement, based on novel definitions of test and test execution. Finally, we reconcile refinement and testing by relating timed ioco testing and refinement in tock -CSP with inputs and outputs. With these results, this paper provides, for the first time, a systematic theory that allows both timed testing and timed refinement to be expressed. An important practical consequence is that this ensures that the notion of correctness used by developers guarantees that tests pass when applied to a correct system and, in addition, faults identified during testing correspond to development mistakes.

Qunity: A Unified Language for Quantum and Classical Computing

We introduce Qunity, a new quantum programming language designed to treat quantum computing as a natural generalization of classical computing. Qunity presents a unified syntax where familiar programming constructs can have both quantum and classical effects. For example, one can use sum types to implement the direct sum of linear operators, exception-handling syntax to implement projective measurements, and aliasing to induce entanglement. Further, Qunity takes advantage of the overlooked BQP subroutine theorem, allowing one to construct reversible subroutines from irreversible quantum algorithms through the uncomputation of "garbage" outputs. Unlike existing languages that enable quantum aspects with separate add-ons (like a classical language with quantum gates bolted on), Qunity provides a unified syntax and a novel denotational semantics that guarantees that programs are quantum mechanically valid. We present Qunity's syntax, type system, and denotational semantics, showing how it can cleanly express several quantum algorithms. We also detail how Qunity can be compiled into a low-level qubit circuit language like OpenQASM, proving the realizability of our design.

CoqQ: Foundational Verification of Quantum Programs

CoqQ is a framework for reasoning about quantum programs in the Coq proof assistant. Its main components are: a deeply embedded quantum programming language, in which classic quantum algorithms are easily expressed, and an expressive program logic for proving properties of programs. CoqQ is foundational: the program logic is formally proved sound with respect to a denotational semantics based on state-of-art mathematical libraries (MathComp and MathComp Analysis). CoqQ is also practical: assertions can use Dirac expressions, which eases concise specifications, and proofs can exploit local and parallel reasoning, which minimizes verification effort. We illustrate the applicability of CoqQ with many examples from the literature.