General Structural Operational Semantics Through Categorical Logic

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Sep 5, 2018. Logical Methods in Computer Science. Vol. In the present paper, we develop a categorical foundation for this class of languages. traditional metalanguages, such as structural operational semantics or denotational. For this reason, we will consider the more general disjointness tensor for sum-like.

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The thesis concerned categorical semantics of various type theories, using. The structural operations of weakening (adding a dummy as- sumption) and. the general definition of fibration towards the end of this section. The exer-.

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It is shown that, if the operational rules of a programming language can be modelled as a natural transformation of a suitable general form, depending on functorial notions of syntax and behaviour, then one gets both an operational model and a canonical, internally fully abstract denotational model for free; moreover, both models satisfy the operational rules.

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A computer memory system connectable to a processor and having one or more programmable operational characteristics, said characteristics being defined through configuration. directed to the.

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for operational semantics, you can only look at a program with a given input or initial state, you cannot say anything about a program alone. 1.3 Denotational Semantics The idea behind this semantics is to look at a program as a mathematical function, i.e. the effect.

a more abstract categorical treatment based upon the idea that operational. with the use of logical frameworks to implement logics and type theories;. for dealing with general recursion, but for all the examples we consider, the structure. We give an operational semantics for P by the set of structural rules in Figure 1.

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prove, via a categorical structure theorem, that the categorical semantics is equivalent to a CPS. which preserve the operational semantics. Thus, the tensor product in a premonoidal category is not in general bifunctorial;. out that control categories are a model of proof-nets for polarized linear logic, and, to my sur-.

Also, through the choice of covariance function, a wide range of modeling assumptions would be expressed to be able to approach different operational states of WWTP. Different from the general.

languages allowing the user to choose between either denotational or operational semantics at any point. Section 2 describes the relation between operational and denotational seman-tics which is roughly based on the categorical framework of Turi and Plotkin. For a simple language, both an operational and a denotational model is speci ed,

Modular Structural Operational Semantics Mosses (2004) A λ-calculus for real analysis Taylor (2005+) Homotopy type theory Awodey-Warren (2006) Univalence axiom Voevodsky (2006+) The safe λ-calculus Ong, et al. (2007)

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In this study we propose a general, structural operational approach to semantics called. the denotational or the categorical ones. Furthermore, the. as their logical characterizations are de ned starting from this set of ac- tions (Hennessy.

May 24, 2007. Reference. Semantics with Applications, H. Nielson and F. Nielson, Chapter 2. structure of programs and the semantics – which describes the meaning of. the pre and post-state – defined over a logical language, along.

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We give an operational semantics for our language in the traditional SOS style, and we show that the behavior of processes as defined by this semantics is the same as the denotational mapping our denotational semantics defines on the language – i.e., our operational semantics is congruent to our denotational semantics.

proofs are written in a logic with a built-in understanding of a particular type system; that. data structure creation, and no recursive types, such models are easy to. The denotational semantics of general references have posed a. oped the model theory for modal propositional logic based on this concept. 5.1 Valid states.

Intuitionistic linear logic regains the expressive power of intuitionistic logic through the ! (`of course') modality. Benton, Bierman, Hyland and de Paiva have given a term assignment system for ILL and an associated notion of categorical model in which the ! modality is modelled by a comonad satisfying certain extra conditions.

Jan 12, 2017. One fundamental aim of a denotational semantics of a programming language L is to. Before going on in this general introduction to full abstraction and related. devoted to the semantic analysis of PCF based on partially ordered structures, in a categorical semantics of systems of constructive logic.

In the categorical framework developed by Turi and Plotkin both. 1998 ACM Subject Classification F.4.1 Mathematical Logic, F.3.2 Semantics of Programming. tions: (structural) operational semantics and denotational semantics. However, we cannot do this as a general fixpoint construction that is parametric in the.

an operational understanding of numerous features and properties of a rich functional programming language. We present a technique, inspired by structural operational se- mantics and natural semantics, for specifying properties of, or operations on, programs.

5 Structural Operational Semantics 26. the intended semantics only speaks in general terms, and does not give any means to actually check that the program is indeed the desired one. we will consider only programs that compute through variables1, we are not interested in the

A categorical semantics for causal structure Abstract: We present a categorical construction for modelling both definite and indefinite causal structures within a general class of process theories that include classical probability theory and quantum theory.

LTSs underlie Plotkin's Structural Operational Semantics [30] and, following Milner's pio-. bisimilarity and HML, the process equivalence induced by the logic. O. Grümberg (1988): Characterizing finite Kripke structures in propositional.

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Categorical logic Joyal (1970+) Elementary topoi Lawvere-Tierney (1970). Modular Structural Operational Semantics Mosses (2004) A. through interfertilization of areas and ! in finding new applications. ! And that we have seen happen with the !

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multivalued logic, category theory, monoidal categories I. INTRODUCTION A. Syntactic vs. semantic modelling Theories of programming languages can be either syntactic, formulated equationally, or semantic, formulated via transla-tion into a mathematical domain. The former is commonly known as operational semantics [1] and the latter as deno-tational semantics [2]. Even though denotational.

Rewriting logic is a flexible and expressive logical framework that unifies denota- tional semantics and SOS in a novel way, avoiding their respective limitations and allowing very succinct semantic definitions.

We show that embeddings generated through this process increase performance in subsequent domain-relevant tasks. We evaluate on the affective tasks of emotion recognition and behavior analysis and.

general and administrative 9,425 9,197 2.5 Depreciation and amortization 8,860 7,263 22.0 Total operating expenses 28,740 25,405 13.1 Operating income $ 73,589 $ 72,604 1.4 OPERATIONAL DATA Gathered.

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lambda calculi [16], categorical frameworks for the semantics of asynchronous communication networks [28], full completeness theorems for multiplicative linear logic via GoI models [13,15], analysis of finite state machines [18], rela-tional dataflow [17], and independently arose in.