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20
OrderSorted Algebra I: Equational Deduction for Multiple Inheritance, Overloading, Exceptions and Partial Operations
 Theoretical Computer Science
, 1992
"... This paper generalizes manysorted algebra (hereafter, MSA) to ordersorted algebra (hereafter, OSA) by allowing a partial ordering relation on the set of sorts. This supports abstract data types with multiple inheritance (in roughly the sense of objectoriented programming), several forms of pol ..."
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Cited by 208 (33 self)
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This paper generalizes manysorted algebra (hereafter, MSA) to ordersorted algebra (hereafter, OSA) by allowing a partial ordering relation on the set of sorts. This supports abstract data types with multiple inheritance (in roughly the sense of objectoriented programming), several forms of polymorphism and overloading, partial operations (as total on equationally defined subsorts), exception handling, and an operational semantics based on term rewriting. We give the basic algebraic constructions for OSA, including quotient, image, product and term algebra, and we prove their basic properties, including Quotient, Homomorphism, and Initiality Theorems. The paper's major mathematical results include a notion of OSA deduction, a Completeness Theorem for it, and an OSA Birkhoff Variety Theorem. We also develop conditional OSA, including Initiality, Completeness, and McKinseyMalcev Quasivariety Theorems, and we reduce OSA to (conditional) MSA, which allows lifting many known MSA results to OSA. Retracts, which intuitively are left inverses to subsort inclusions, provide relatively inexpensive runtime error handling. We show that it is safe to add retracts to any OSA signature, in the sense that it gives rise to a conservative extension. A final section compares and contrasts many different approaches to OSA. This paper also includes several examples demonstrating the flexibility and applicability of OSA, including some standard benchmarks like STACK and LIST, as well as a much more substantial example, the number hierarchy from the naturals up to the quaternions.
A Hidden Agenda
 Theoretical Computer Science
, 2000
"... This paper publicly reveals, motivates, and surveys the results of an ambitious hidden agenda for applying algebra to software engineering. The paper reviews selected literature, introduces a new perspective on nondeterminism, and features powerful hidden coinduction techniques for proving behaviora ..."
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Cited by 110 (23 self)
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This paper publicly reveals, motivates, and surveys the results of an ambitious hidden agenda for applying algebra to software engineering. The paper reviews selected literature, introduces a new perspective on nondeterminism, and features powerful hidden coinduction techniques for proving behavioral properties of concurrent systems, especially renements; some proofs are given using OBJ3. We also discuss where modularization, bisimulation, transition systems and combinations of the object, logic, constraint and functional paradigms t into our hidden agenda. 1 Introduction Algebra can be useful in many dierent ways in software engineering, including specication, validation, language design, and underlying theory. Specication and validation can help in the practical production of reliable programs, advances in language design can help improve the state of the art, and theory can help with building new tools to increase automation, as well as with showing correctness of the whole e...
How to Declare an Imperative
, 1995
"... How can we integrate interaction into a purely declarative language? This tutorial describes a solution to this problem based on a monad. The solution has been implemented in the functional language Haskell and the declarative language Escher. Comparisons are given to other approaches to interaction ..."
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Cited by 96 (3 self)
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How can we integrate interaction into a purely declarative language? This tutorial describes a solution to this problem based on a monad. The solution has been implemented in the functional language Haskell and the declarative language Escher. Comparisons are given to other approaches to interaction based on synchronous streams, continuations, linear logic, and side effects.
Forwarding in attribute grammars for modular language design
 In Proc. 11th Intl. Conf. on Compiler Construction, volume 2304 of LNCS
, 2002
"... Abstract. Forwarding is a technique for providing default attribute definitions in attribute grammars that is helpful in the modular implementation of programming languages. It complements existing techniques such as default copy rules. This paper introduces forwarding, and shows how it is but a sma ..."
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Cited by 41 (14 self)
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Abstract. Forwarding is a technique for providing default attribute definitions in attribute grammars that is helpful in the modular implementation of programming languages. It complements existing techniques such as default copy rules. This paper introduces forwarding, and shows how it is but a small extension of standard higherorder attribute grammars. The usual tools for manipulating higherorder attribute grammars, including the circularity check (which tests for cyclic dependencies between attribute values), carry over without modification. The closure test (which checks that each attribute has a defining equation) needs modification, however, because the resulting higherorder attribute grammars may contain spurious attributes that are never evaluated, and indeed that need not be defined. 1
An ImplementationOriented Semantics for Module Composition
, 1997
"... This paper describes an approach to module composition by executing "module expressions" to build systems out of component modules; the paper also gives a novel semantics intended to aid implementers. The semantics is based on set theoretic notions of tuple set, partial signature, and institution, t ..."
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Cited by 32 (14 self)
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This paper describes an approach to module composition by executing "module expressions" to build systems out of component modules; the paper also gives a novel semantics intended to aid implementers. The semantics is based on set theoretic notions of tuple set, partial signature, and institution, thus avoiding more difficult mathematics theory. Language features include information hiding, both vertical and horizontal composition, and views for binding modules to interfaces. Vertical composition refers to the hierarchical structuring of a system into layers, while horizontal composition refers to the structure of a given layer. Modules may involve information hiding, and views may involve behavioral satisfaction of a theory by a module. Several "Laws of Software Composition" are given, which show how the various module composition operations relate. Taken together, this gives foundations for an algebraic approach to software engineering. 1.1 Introduction The approach to module compos...
Explicit Graphs in a Functional Model for Spatial Databases
 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING
, 1994
"... Observing that networks are ubiquitous in applications for spatial databases, we define a new data model and query language that especially supports graph structures. This model integrates concepts of functional data modeling with ordersorted algebra. Besides object and data type hierarchies grap ..."
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Cited by 28 (9 self)
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Observing that networks are ubiquitous in applications for spatial databases, we define a new data model and query language that especially supports graph structures. This model integrates concepts of functional data modeling with ordersorted algebra. Besides object and data type hierarchies graphs are available as an explicit modeling tool, and graph operations are part of the query language. Graphs have three classes of components, namely nodes, edges, and explicit paths. These are at the same time object types within the object type hierarchy and can be used like any other type. Explicit paths are useful because “real world ” objects often correspond to paths in a network. Furthermore, a dynamic generalization concept is introduced to handle heterogeneous collections of objects in a query. In connection with spatial data types this leads to powerful modeling and querying capabilities for spatial databases, in particular for spatially embedded networks such as highways, rivers, public transport, and so forth. We use multilevel ordersorted algebra as a formal framework for the specification of our model. Roughly spoken, the first level algebra defines types and operations of the query language whereas the second level algebra defines kinds (collections of types) and type constructors as functions between kinds and so provides the types that can be used at the first level.
Categorybased Semantics for Equational and Constraint Logic Programming
, 1994
"... This thesis proposes a general framework for equational logic programming, called categorybased equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equation ..."
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Cited by 24 (10 self)
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This thesis proposes a general framework for equational logic programming, called categorybased equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equational deduction to an arbitrary category satisfying certain natural conditions; completeness is proved under a hypothesis of quantifier projectivity, using a semantic treatment that regards quantifiers as models rather than variables, and regards valuations as model morphisms rather than functions. This is used as a basis for a model theoretic categorybased approach to a paramodulationbased operational semantics for equational logic programming languages. Categorybased equational logic in conjunction with the theory of institutions is used to give mathematical foundations for modularisation in equational logic programming. We study the soundness and completeness problem for module imports i...
Program Tactics and Logic Tactics
 IN PROCEEDINGS 5TH INTNL. CONFERENCE ON LOGIC PROGRAMMING AND AUTOMATED REASONING (LPAR'94
, 1994
"... In this paper we present a first order classical metatheory, called MT, with the following properties: (1) tactics are terms of the language of MT (we call these tactics, Logic Tactics); (2) there exists a mapping between Logic Tactics and the tactics developed as programs within the GETFOL theor ..."
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Cited by 19 (10 self)
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In this paper we present a first order classical metatheory, called MT, with the following properties: (1) tactics are terms of the language of MT (we call these tactics, Logic Tactics); (2) there exists a mapping between Logic Tactics and the tactics developed as programs within the GETFOL theorem prover (we call these tactics, Program Tactics). MT is expressive enough to represent the most interesting tacticals, i.e. then, orelse, try, progress and repeat. repeat allows us to express Logic Tactics which correspond to Program Tactics which may not terminate. This work is part of a larger project which aims at the development and mechanization of a metatheory which can be used to reason about, extend and, possibly, modify the code implementing Program Tactics and the GETFOL basic inference rules.
Maude versus Haskell: an Experimental Comparison in Security Protocol Analysis
, 2000
"... We compare two executable languages: the rewriting logic based specification language Maude and the higherorder, lazy, functional programming language Haskell. We compare these languages experimentally on a problem in modeling and reasoning about a security protocol for authentication. We explore d ..."
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Cited by 9 (3 self)
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We compare two executable languages: the rewriting logic based specification language Maude and the higherorder, lazy, functional programming language Haskell. We compare these languages experimentally on a problem in modeling and reasoning about a security protocol for authentication. We explore differences in how models can be formalized and analyzed, as well as performance and tool use.
Maude's Module Algebra
, 2000
"... The reflective capabilities of rewriting logic and their efficient implementation in the Maude language can be exploited to endow a reflective language like Maude with a module algebra in which structured theories can be combined and transformed by means of a rich collection of module operations. We ..."
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Cited by 7 (4 self)
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The reflective capabilities of rewriting logic and their efficient implementation in the Maude language can be exploited to endow a reflective language like Maude with a module algebra in which structured theories can be combined and transformed by means of a rich collection of module operations. We have followed this approach and we have used the specification of such a module algebra as its implementation, including a user interface and an execution environment for it. The high level at which the specification of the module algebra has been given makes this approach particularly attractive when compared to conventional implementations, because of its shorter development time and the greater flexibility, maintainability, and extensibility that it affords. We explain the general principles of the reflective design of the module algebra and explain the categorical semantics of parameterized theories, modules and views and their instantiation, and the reflective algebraic specification of the different module and view operations.