Category theory for operational semantics
نویسندگان
چکیده
7 Abstract 9 We use the concept of a distributive law of a monad over a copointed endofunctor to define and develop a reformulation and mild generalisation of Turi and Plotkin's notion of an abstract operational 11 rule. We make our abstract definition and give a precise analysis of the relationship between it and Turi and Plotkin's definition. 13 with the notion of a set of GSOS-rules, allowing one to construct both an operational model and a canonical, internally fully abstract denotational model. Going beyond Turi and Plotkin, we construct 15 what might be seen as large-step operational semantics from small-step operational semantics and we show how our definition allows one to combine distributive laws, in particular accounting for the 17 combination of operational semantics with congruences.
منابع مشابه
Functorial semantics of topological theories
Following the categorical approach to universal algebra through algebraic theories, proposed by F.~W.~Lawvere in his PhD thesis, this paper aims at introducing a similar setting for general topology. The cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. We introduce t...
متن کاملDynamic Categorization of Semantics of Fashion Language: A Memetic Approach
Categories are not invariant. This paper attempts to explore the dynamic nature of semantic category, in particular, that of fashion language, based on the cognitive theory of Dawkins’ memetics, a new theory of cultural evolution. Semantic attributes of linguistic memes decrease or proliferate in replication and spreading, which involves a dynamic development of semantic category. More specific...
متن کاملGuarded Computational Type Theory
We develop a computational interpretation of guarded dependent type theory with clocks called CTT which enjoys a straightforward operational semantics and immediate canonicity result for base types. Our realizability-style presentation of guarded type theory is a computational and syntactic alternative to category-theoretic accounts of guarded recursion, emphasizing type theory’s role as the ul...
متن کاملOperational Theories of Physics as Categories
We introduce a new approach to the study of operational theories of physics using category theory. We define a generalisation of the (causal) operational-probabilistic theories of Chiribella et al. and establish their correspondence with our new notion of an operational category. Our work is based on effectus theory, a recently developed area of categorical logic, to which we give an operationa...
متن کاملTensors of Comodels and Models for Operational Semantics
In seeking a unified study of computational effects, in particular in order to give a general operational semantics agreeing with the standard one for state, one must take account of the coalgebraic structure of state. Axiomatically, one needs a countable Lawvere theory L, a comodel C, typically the final one, and a model M , typically free; one then seeks a tensor C ⊗ M of the comodel with the...
متن کاملDomain equations for probabilistic processes
In this paper we consider Milner’s calculus CCS enriched by a probabilistic choice operator. The calculus is given operational semantics based on probabilistic transition systems. We define operational notions of preorder and equivalence as probabilistic extensions of the simulation preorder and the bisimulation equivalence respectively. We extend existing category-theoretic techniques for solv...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Theor. Comput. Sci.
دوره 327 شماره
صفحات -
تاریخ انتشار 2004