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101
Homology of Higher Dimensional Automata
, 1992
"... . Higher dimensional automata can model concurrent computations. The topological structure of the higher dimensional automata determines certain properties of the concurrent computation. We introduce bicomplexes as an algebraic tool for describing these automata and develop a simple homology theory ..."
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Cited by 43 (11 self)
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. Higher dimensional automata can model concurrent computations. The topological structure of the higher dimensional automata determines certain properties of the concurrent computation. We introduce bicomplexes as an algebraic tool for describing these automata and develop a simple homology theory for higher dimensional automata. We then show how the homology of automata has applications in the study of branchingtime equivalences of processes such as bisimulation. 1 Introduction Geometry has been suggested as a tool for modeling concurrency using higher dimensional objects to describe the concurrent execution of processes. This contrasts with earlier models based on the interleaving of computation steps to capture all possible behaviours of a concurrent system. Interleaving models must necessarily commit themselves to a specific choice of atomic action which makes them unable to distinguish between the execution of two truly concurrent actions and two mutually exclusive actions as t...
Deciding Containment for Queries with Complex Objects and Aggregations
, 1997
"... We address the problem of query containment and query equivalence for complex objects. We show that for a certain conjunctive query language for complex objects, query containment and weak query equivalence are decidable. Our results have two consequences. First, when the answers of the two queries ..."
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Cited by 41 (5 self)
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We address the problem of query containment and query equivalence for complex objects. We show that for a certain conjunctive query language for complex objects, query containment and weak query equivalence are decidable. Our results have two consequences. First, when the answers of the two queries are guaranteed not to contain empty sets, then weak equivalence coincides with equivalence, and our result answers partially an open problem about the equivalence of nest; unnest queries for complex objects [GPG90]. Second, we derive an NPcomplete algorithm for checking the equivalence of certain conjunctive queries with grouping and aggregates. Our results rely on a translation of the containment and equivalence conditions for complex objects into novel conditions on conjunctive queries, which we call simulation and strong simulation. These conditions are more complex than containment of conjunctive queries, because they involve arbitrary numbers of quantifier alternations. We prove that c...
Operational Properties of Lily, a Polymorphic Linear Lambda Calculus with Recursion
"... Plotkin has advocated the combination of linear lambda calculus, polymorphism and fixed point recursion as an expressive semantic metalanguage. We study its expressive power from an operational point of view. We show that the naturally callbyvalue operators of linear lambda calculus can be given a ..."
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Cited by 35 (1 self)
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Plotkin has advocated the combination of linear lambda calculus, polymorphism and fixed point recursion as an expressive semantic metalanguage. We study its expressive power from an operational point of view. We show that the naturally callbyvalue operators of linear lambda calculus can be given a callbyname semantics without affecting termination at exponential types and hence without affecting ground contextual equivalence. This result is used to prove properties of a logical relation that provides a new extensional characterisation of ground contextual equivalence and relational parametricity properties of polymorphic types.
Action Structures
, 1992
"... Action structures are proposed as a variety of algebra to underlie concrete models of concurrency and interaction. An action structure is equipped with composition and product of actions, together with two other ingredients: an indexed family of abstractors to allow parametrisation of actions, a ..."
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Cited by 34 (1 self)
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Action structures are proposed as a variety of algebra to underlie concrete models of concurrency and interaction. An action structure is equipped with composition and product of actions, together with two other ingredients: an indexed family of abstractors to allow parametrisation of actions, and a reaction relation to represent activity. The eight axioms of an action structure make it an enriched strict monoidal category; however, the work is presented algebraically rather than in category theory. The notion of action structure is developed mathematically, and examples are studied ranging from the evaluation of expressions to the statics and dynamics of Petri nets. For algebraic process calculi in particular, it is shown how they may be defined by a uniform superposition of process structure upon an action structure specific to each calculus. This allows a common treatment of bisimulation congruence. The theory of action structures emphasizes the notion of effect; that ...
Binding Time Analysis: A New PERspective
 In Proceedings of the ACM Symposium on Partial Evaluation and SemanticsBased Program Manipulation (PEPM'91
, 1991
"... Given a description of the parameters in a program that will be known at partial evaluation time, a binding time analysis must determine which parts of the program are dependent solely on these known parts (and therefore also known at partial evaluation time). In this paper a binding time analysis f ..."
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Cited by 33 (5 self)
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Given a description of the parameters in a program that will be known at partial evaluation time, a binding time analysis must determine which parts of the program are dependent solely on these known parts (and therefore also known at partial evaluation time). In this paper a binding time analysis for the simply typed lambda calculus is presented. The analysis takes the form of an abstract interpretation and uses a novel formalisation of the problem of binding time analysis, based on the use of partial equivalence relations. A simple proof of correctness is achieved by the use of logical relations. 1 Introduction Given a description of the parameters in a program that will be known at partial evaluation time, a binding time analysis must determine which parts of the program are dependent solely on these known parts (and therefore also known at partial evaluation time). A binding time analysis performed prior to the partial evaluation process can have several practical benefits (see [...
Feature Logics
 HANDBOOK OF LOGIC AND LANGUAGE, EDITED BY VAN BENTHEM & TER MEULEN
, 1994
"... Feature logics form a class of specialized logics which have proven especially useful in classifying and constraining the linguistic objects known as feature structures. Linguistically, these structures have their origin in the work of the Prague school of linguistics, followed by the work of Chom ..."
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Cited by 33 (0 self)
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Feature logics form a class of specialized logics which have proven especially useful in classifying and constraining the linguistic objects known as feature structures. Linguistically, these structures have their origin in the work of the Prague school of linguistics, followed by the work of Chomsky and Halle in The Sound Pattern of English [16]. Feature structures have been reinvented several times by computer scientists: in the theory of data structures, where they are known as record structures, in artificial intelligence, where they are known as frame or slotvalue structures, in the theory of data bases, where they are called "complex objects", and in computati
Computational Comonads and Intensional Semantics
, 1991
"... We explore some foundational issues in the development of a theory of intensional semantics. A programming language may be given a variety of semantics, differing in the level of abstraction; one generally chooses the semantics at an abstraction level appropriate for reasoning about a particular kin ..."
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Cited by 27 (1 self)
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We explore some foundational issues in the development of a theory of intensional semantics. A programming language may be given a variety of semantics, differing in the level of abstraction; one generally chooses the semantics at an abstraction level appropriate for reasoning about a particular kind of program property. Extensional semantics are typically appropriate for proving properties such as partial correctness, but an intensional semantics at a lower abstraction level is required in order to reason about computation strategy and thereby support reasoning about intensional aspects of behavior such as order of evaluation and efficiency. It is obviously desirable to be able to establish sensible relationships between two semantics for the same language, and we seek a general categorytheoretic framework that permits this. Beginning with an "extensional" category, whose morphisms we can think of as functions of some kind, we model a notion of computation as a comonad with certain e...
Abstract Interpretation of Functional Languages: From Theory to Practice
, 1991
"... Abstract interpretation is the name applied to a number of techniques for reasoning about programs by evaluating them over nonstandard domains whose elements denote properties over the standard domains. This thesis is concerned with higherorder functional languages and abstract interpretations with ..."
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Cited by 25 (0 self)
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Abstract interpretation is the name applied to a number of techniques for reasoning about programs by evaluating them over nonstandard domains whose elements denote properties over the standard domains. This thesis is concerned with higherorder functional languages and abstract interpretations with a formal semantic basis. It is known how abstract interpretation for the simply typed lambda calculus can be formalised by using binary logical relations. This has the advantage of making correctness and other semantic concerns straightforward to reason about. Its main disadvantage is that it enforces the identification of properties as sets. This thesis shows how the known formalism can be generalised by the use of ternary logical relations, and in particular how this allows abstract values to deno...