Deductive Semantics Research Articles

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.

ON FORMAL AND COGNITIVE SEMANTICS FOR SEMANTIC COMPUTING

Semantics is the meaning of symbols, notations, concepts, functions, and behaviors, as well as their relations that can be deduced onto a set of predefined entities and/or known concepts. Semantic computing is an emerging computational methodology that models and implements computational structures and behaviors at semantic or knowledge level beyond that of symbolic data. In semantic computing, formal semantics can be classified into the categories of to be, to have, and to do semantics. This paper presents a comprehensive survey of formal and cognitive semantics for semantic computing in the fields of computational linguistics, software science, computational intelligence, cognitive computing, and denotational mathematics. A set of novel formal semantics, such as deductive semantics, concept-algebra-based semantics, and visual semantics, is introduced that forms a theoretical and cognitive foundation for semantic computing. Applications of formal semantics in semantic computing are presented in case studies on semantic cognition of natural languages, semantic analyses of computing behaviors, behavioral semantics of human cognitive processes, and visual semantic algebra for image and visual object manipulations.

On the Cognitive Complexity of Software and its Quantification and Formal Measurement

The quantification and measurement of functional complexity of software are a persistent problem in software engineering. Measurement models of software complexities have been studied in two facets in computing and software engineering, where the former is machine-oriented in the small; while the latter is humanoriented in the large. The cognitive complexity of software presented in this paper is a new measurement for cross-platform analysis of complexities, functional sizes, and cognition efforts of software code and specifications in the phases of design, implementation, and maintenance in software engineering. This paper reveals that the cognitive complexity of software is a product of its architectural and operational complexities on the basis of deductive semantics. A set of ten Basic Control Structures (BCS’s) are elicited from software architectural and behavioral modeling and specifications. The cognitive weights of the BCS’s are derived and calibrated via a series of psychological experiments. Based on this work, the cognitive complexity of software systems can be rigorously and accurately measured and analyzed. Comparative case studies demonstrate that the cognitive complexity is highly distinguishable for software functional complexity and size measurement in software engineering.

Deductive Semantics of RTPA

Deductive semantics is a novel software semantic theory that deduces the semantics of a program in a given programming language from a unique abstract semantic function to the concrete semantics embodied by the changes of status of a finite set of variables constituting the semantic environment of the program. There is a lack of a generic semantic function and its unified mathematical model in conventional semantics, which may be used to explain a comprehensive set of programming statements and computing behaviors. This article presents a complete paradigm of formal semantics that explains how deductive semantics is applied to specify the semantics of real-time process algebra (RTPA) and how RTPA challenges conventional formal semantic theories. Deductive semantics can be applied to define abstract and concrete semantics of programming languages, formal notation systems, and large-scale software systems, to facilitate software comprehension and recognition, to support tool development, to enable semantics-based software testing and verification, and to explore the semantic complexity of software systems. Deductive semantics may greatly simplify the description and analysis of the semantics of complicated software systems specified in formal notations and implemented in programming languages.

On the informatics laws and deductive semantics of software

A fundamental finding in computer science is that software, an artifact of human creativity, is not constrained by the laws and properties known in the physical world. Thus, a natural question we have to ask is what are the constraints that software obeys? This paper attempts to demonstrate that software obeys the laws of informatics and mathematics. This paper explores a comprehensive set of informatics and semantic properties and laws of software as well as their mathematical models. In order to provide a rigorous mathematical treatment of both the abstract and concrete semantics of software, a new type of formal semantics known as the deductive semantics is developed. The deductive models of semantics, semantic function, and semantic environment at various composing levels of programs are formally described. The findings of this paper can be applied to perceive the basic characteristics of software and the development of fundamental theories that deal with the informatics and semantic properties of software.

Automatic synthesis of optimal invariant assertions

The problem of discovering invariant assertions of programs is explored in light of the fixpoint approach in the static analysis of programs, Cousot [1977a], Cousot[1977b]. In section 2 we establish the lattice theoric foundations upon which the synthesis of invariant assertions is based. We study the resolution of a fixpoint system of equations by Jacobi's successive approximations method. Under continuity hypothesis we show that any chaotic iterative method converges to the optimal solution. In section 3 we study the deductive semantics of programs. We show that a system of logical forward equations can be associated with a program using the predicate transformer rules which define the semantics of elementary instructions. The resolution of this system of semantic equations by chaotic iterations leads to the optimal invariants which exactly define the semantics of this program. Therefore these optimal invariants can be used for total correctness proofs (section 4). Next we show that usually a system of inequations is used as a substitute for the system of equations. Hence the solutions to this system of inequations are approximate invariants which can only be used for proofs of partial correctness (section 5). In section 6 we show that symbolic execution of programs consists in fact in solving the semantic equations associated with this program. The construction of the symbolic execution tree corresponds to the chaotic successive approximations method. Therefore symbolic execution permits optimal invariant assertions to be discovered provided that one can pass to the limit, that is consider infinite paths in the symbolic execution tree. Induction nrinciDles can be used for that purpose. In section 7 we show how difference equations can be utilized to discover the general term of the sequence of successive approximations so that optimal invariants are obtained by a mere passage to the limit. In section 8 we show that an approximation of the optimal solution to a fixpoint system of equations can be obtained by strengthening the term of a chaotic iteration sequence. This formalizes the synthesis of approximate invariants by heuristic methods. Various examples provide a helpful intuitive support to the technical sections.

Automatic synthesis of optimal invariant assertions

The problem of discovering invariant assertions of programs is explored in light of the fixpoint approach in the static analysis of programs, Cousot [1977a], Cousot[1977b]. In section 2 we establish the lattice theoric foundations upon which the synthesis of invariant assertions is based. We study the resolution of a fixpoint system of equations by Jacobi's successive approximations method. Under continuity hypothesis we show that any chaotic iterative method converges to the optimal solution. In section 3 we study the deductive semantics of programs. We show that a system of logical forward equations can be associated with a program using the predicate transformer rules which define the semantics of elementary instructions. The resolution of this system of semantic equations by chaotic iterations leads to the optimal invariants which exactly define the semantics of this program. Therefore these optimal invariants can be used for total correctness proofs (section 4). Next we show that usually a system of inequations is used as a substitute for the system of equations. Hence the solutions to this system of inequations are approximate invariants which can only be used for proofs of partial correctness (section 5). In section 6 we show that symbolic execution of programs consists in fact in solving the semantic equations associated with this program. The construction of the symbolic execution tree corresponds to the chaotic successive approximations method. Therefore symbolic execution permits optimal invariant assertions to be discovered provided that one can pass to the limit, that is consider infinite paths in the symbolic execution tree. Induction nrinciDles can be used for that purpose. In section 7 we show how difference equations can be utilized to discover the general term of the sequence of successive approximations so that optimal invariants are obtained by a mere passage to the limit. In section 8 we show that an approximation of the optimal solution to a fixpoint system of equations can be obtained by strengthening the term of a chaotic iteration sequence. This formalizes the synthesis of approximate invariants by heuristic methods. Various examples provide a helpful intuitive support to the technical sections.