Results 11  20
of
31
Effective Applicative Structures
 In: Proceedings of the 6th biennial conference on Category Theory in Computer Science (CTCS'95). SpringerVerlag Lecture Notes in Computer Science 953 8195
, 1995
"... S. All local authors can be reached viaemail at theaddress lastname@cs.unibo.it. Written requests and comments should be addressed to tradmin@cs.unibo.it. UBLCS Technical Report Series 9320 An Information Flow Security Property for CCS, R. Focardi, R. Gorrieri, October 1993. 9321 A Classifica ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
S. All local authors can be reached viaemail at theaddress lastname@cs.unibo.it. Written requests and comments should be addressed to tradmin@cs.unibo.it. UBLCS Technical Report Series 9320 An Information Flow Security Property for CCS, R. Focardi, R. Gorrieri, October 1993. 9321 A Classification of Security Properties, R. Focardi, R. Gorrieri, October 1993. 9322 Real Time Systems: A Tutorial, F. Panzieri, R. Davoli, October 1993. 9323 A Scalable Architecture for Reliable Distributed Multimedia Applications, F. Panzieri, M. Roccetti, October 1993. 9324 WideArea Distribution Issues in Hypertext Systems, C. Maioli, S. Sola, F. Vitali, October 1993. 9325 On Relating Some Models for Concurrency, P. Degano, R. Gorrieri, S. Vigna, October 1993. 9326 Axiomatising ST Bisimulation Equivalence, N. Busi, R. van Glabbeek, R. Gorrieri, December 1993. 9327 A Theory of Processeswith Durational Actions, R. Gorrieri, M. Roccetti, E. Stancampiano, December1993. 941 Further Modifications t...
Denotational Semantics of Object Specification
 ACTA INFORMATICA
, 1998
"... From an arbitrary temporal logic institution we show how to set up the corresponding institution of objects. The main properties of the resulting institution are studied and used in establishing a categorial, denotational semantics of several basic constructs of object specification, namely aggre ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
From an arbitrary temporal logic institution we show how to set up the corresponding institution of objects. The main properties of the resulting institution are studied and used in establishing a categorial, denotational semantics of several basic constructs of object specification, namely aggregation (parallel composition), interconnection, abstraction (interfacing) and monotonic specialization. A duality is established between the category of theories and the category of objects, as a corollary of the Galois correspondence between these concrete categories. The special case of linear temporal logic is analysed in detail in order to show that categorial products do reflect interleaving and reducts may lead to internal nondeterminism.
Type Theory via Exact Categories (Extended Abstract)
 In Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science LICS '98
, 1998
"... Partial equivalence relations (and categories of these) are a standard tool in semantics of type theories and programming languages, since they often provide a cartesian closed category with extended definability. Using the theory of exact categories, we give a categorytheoretic explanation of why ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
Partial equivalence relations (and categories of these) are a standard tool in semantics of type theories and programming languages, since they often provide a cartesian closed category with extended definability. Using the theory of exact categories, we give a categorytheoretic explanation of why the construction of a category of partial equivalence relations often produces a cartesian closed category. We show how several familiar examples of categories of partial equivalence relations fit into the general framework. 1 Introduction Partial equivalence relations (and categories of these) are a standard tool in semantics of programming languages, see e.g. [2, 5, 7, 9, 15, 17, 20, 22, 35] and [6, 29] for extensive surveys. They are usefully applied to give proofs of correctness and adequacy since they often provide a cartesian closed category with additional properties. Take for instance a partial equivalence relation on the set of natural numbers: a binary relation R ` N\ThetaN on th...
Graphical reasoning in compact closed categories for quantum computation
 AMAI
, 2009
"... Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning about such graphs and develop this into a generic proof sys ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning about such graphs and develop this into a generic proof system with a fixed logical kernel for reasoning about compact closed categories. A salient feature of our system is that it provides a formal and declarative account of derived results that can include ‘ellipses’style notation. We illustrate the framework by instantiating it for a graphical language of quantum computation and show how this can be used to perform symbolic computation.
Concrete Data Structures and Functional Parallel Programming
, 1997
"... We present a framework for designing parallel programming languages whose semantics is functional and where communications are explicit. To this end, we specialize Brookes and Geva's generalized concrete data structures with a notion of explicit data layout and obtain a CCC of distributed struc ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
We present a framework for designing parallel programming languages whose semantics is functional and where communications are explicit. To this end, we specialize Brookes and Geva's generalized concrete data structures with a notion of explicit data layout and obtain a CCC of distributed structures called arrays. We find that arrays' symmetric replicated structures, suggested by the dataparallel SPMD paradigm, are incompatible with sum types. We then outline a functional language with explicitlydistributed (monomorphic) concrete types, including higherorder, sum and recursive ones. In this language, programs can be as large as the network and can observe communication events in other programs. Such flexibility is missing from current dataparallel languages and amounts to a fusion with their socalled annotations, directives or metalanguages. 1 Explicit communications and functional programming Faced with the mismatch between parallel programming languages and the requirements o...
Axioms for Definability and Full Completeness
 in Proof, Language and Interaction: Essays in Honour of Robin
, 2000
"... ion problem for PCF (see [BCL86, Cur93, Ong95] for surveys). The importance of full abstraction for the semantics of programming languages is that it is one of the few quality filters we have. Specifically, it provides a clear criterion for assessing how definitive a semantic analysis of some langu ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
ion problem for PCF (see [BCL86, Cur93, Ong95] for surveys). The importance of full abstraction for the semantics of programming languages is that it is one of the few quality filters we have. Specifically, it provides a clear criterion for assessing how definitive a semantic analysis of some language is. It must be admitted that to date the quest for fully abstract models has not yielded many obvious applications; but it has generated much of the deepest work in semantics. Perhaps it is early days yet. Recently, game semantics has been used to give the first syntaxindependent constructions of fully abstract models for a number of programming languages, including PCF [AJM96, HO96, Nic94], richer functional languages [AM95, McC96b, McC96a, HY97], and languages with nonfunctional features such as reference types and nonlocal control constructs [AM97c, AM97b, AM97a, Lai97]. A noteworthy feature is that the key definability results for the richer languages are proved by a reduction to...
Lifting of Operations in Modular Monadic Semantics
, 2009
"... Monads have become a fundamental tool for structuring denotational semantics and programs by abstracting a wide variety of computational features such as sideeffects, input/output, exceptions, continuations and nondeterminism. In this setting, the notion of a monad is equipped with operations that ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Monads have become a fundamental tool for structuring denotational semantics and programs by abstracting a wide variety of computational features such as sideeffects, input/output, exceptions, continuations and nondeterminism. In this setting, the notion of a monad is equipped with operations that allow programmers to manipulate these computational effects. For example, a monad for sideeffects is equipped with operations for setting and reading the state, and a monad for exceptions is equipped with operations for throwing and handling exceptions. When several effects are involved, one can employ the incremental approach to modular monadic semantics, which uses monad transformers to build up the desired monad one effect at a time. However, a limitation of this approach is that the effectmanipulating operations need to be manually lifted to the resulting monad, and consequently, the lifted operations are nonuniform. Moreover, the number of liftings needed in a system grows as the product of the number of monad transformers and operations involved. This dissertation proposes a theory of uniform lifting of operations that extends the incremental approach to modular monadic semantics with a principled technique for lifting operations. Moreover the theory is generalized from monads to monoids in a monoidal category, making it possible to apply it to structures other than monads. The extended theory is taken to practice with the implementation of a new extensible monad transformer library in Haskell, and with the use of modular monadic semantics to obtain modular operational semantics. i No hay ejercicio intelectual que no sea finalmente inútil. Una doctrina es al principio una descripción verosímil del universo; giran los años y es un mero capítulo—cuando no un párrafo o un nombre—de la historia de la filosofía. There is no exercise of the intellect which is not, in the final analysis, useless. A philosophical doctrine begins as a plausible description of the universe; with the passage of the years it becomes a mere chapter—if not a paragraph or a name—in the history of philosophy.
Extending graphical representations for compact closed categories with applications to symbolic quantum computation
, 2008
"... Graphbased formalisms of quantum computation provide an abstract and symbolic way to represent and simulate computations. However, manual manipulation of such graphs is slow and error prone. We present a formalism, based on compact closed categories, that supports mechanised reasoning about such g ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Graphbased formalisms of quantum computation provide an abstract and symbolic way to represent and simulate computations. However, manual manipulation of such graphs is slow and error prone. We present a formalism, based on compact closed categories, that supports mechanised reasoning about such graphs. This gives a compositional account of graph rewriting that preserves the underlying categorical semantics. Using this representation, we describe a generic system with a fixed logical kernel that supports reasoning about models of compact closed category. A salient feature of the system is that it provides a formal and declarative account of derived results that can include ‘ellipses’style notation. We illustrate the framework by instantiating it for a graphical language of quantum computation and show how this can be used to perform symbolic computation. Key words: graph rewriting, quantum computing, categorical logic, interactive theorem proving, graphical calculi.
An Introduction to Category Theory, Category Theory Monads, and Their Relationship to Functional Programming
"... Incorporating imperative features into a purely functional language has become an active area of research within the functional programming community [10, 7, 12]. One of the techniques gaining widespread acceptance as a model for imperative functional programming is monads [13, 9]. The purpose of th ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Incorporating imperative features into a purely functional language has become an active area of research within the functional programming community [10, 7, 12]. One of the techniques gaining widespread acceptance as a model for imperative functional programming is monads [13, 9]. The purpose of this technical report is to give a category theoretic introduction to monads, and to explore the relationship to what functional programmers term a monad. Keywords: Monads; Category theory; Kleisli triple; Imperative functional programming. 1 Motivation This paper stems from the desire for an understanding of Moggi's work on the computational calculus and Monads [9, 8]. The presentation here owes much to the papers of Wadler [13, 14], and the basic texts on category theory [11, 1, 4, 6, 2]. 2 Basic category theory and monads Category theory is concerned with the observation that many of the properties from algebra can be simplified by a presentation in terms of diagrams containing arrows....
Prototype Proofs in Type Theory
, 2000
"... The proofs of universally quantified statements, in mathematics, are given as "schemata" or as "prototypes" which may be applied to each specific instance of the quantified variable. Type Theory allows to turn into a rigorous notion this informal intuition described by many, i ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The proofs of universally quantified statements, in mathematics, are given as "schemata" or as "prototypes" which may be applied to each specific instance of the quantified variable. Type Theory allows to turn into a rigorous notion this informal intuition described by many, including Herbrand. In this constructive approach where propositions are types, proofs are viewed as terms of \Gammacalculus and act as "proofschemata", as for universally quantified types. We examine here the critical case of Impredicative Type Theory, i.e. Girard's system F, where typequantification ranges over all types. Coherence and decidability properties are proved for prototype proofs in this impredicative context.