We present a domain-independent model of hierarchical software system design and construction that is based on interchangeable software components and largescale reuse. The model unifies the conceptualizations of two independent projects, Genesis and Avoca, that are successful examples of software component/building-block technologies and domain modeling. Building-block technologies exploit large-scale reuse, rely on open architecture software, and elevate the granularity of programming to the subsystem level. Domain modeling formalizes the similarities and differences among systems of a domain. We believe our model is a blue-print for achieving software component technologies in many domains.

This paper generalizes many-sorted algebra (hereafter, MSA) to order-sorted 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 object-oriented 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 McKinsey-Malcev 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 run-time 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.

Standard ML is one of a number of new programming languages developed in the 1980s that are seen as suitable vehicles for serious systems and applications programming. It offers an excellent ratio of expressiveness to language complexity, and provides competitive efficiency. Because of its type and module system, Standard ML manages to combine safety, security, and robustness with much of the flexibility of dynamically typed languages like Lisp. It is also has the most well-developed scientific foundation of any major language. Here I review the strengths and weaknesses of Standard ML and describe some of what we have learned through the design, implementation, and use of the language.

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This is an introduction to the philosophy and use of OBJ, emphasizing its operational semantics, with aspects of its history and its logical semantics. Release 2 of OBJ3 is described in detail, with many examples. OBJ is a wide spectrum first-order functional language that is rigorously based on (order sorted) equational logic and parameterized programming, supporting a declarative style that facilitates verification and allows OBJ to be used as a theorem prover.

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...

GenVoca generators synthesize software systems by composing components from reuse libraries. GenVoca components are designed to export and import standardized interfaces, and thus be plugcompatible, interchangeable, and interoperable with other components. In this paper, we examine two different but important issues in software system synthesis. First, not all syntactically correct compositions of components are semantically correct. We present simple, efficient, and domainindependent algorithms for validating compositions of GenVoca components. Second, components that export and import immutable interfaces are too restrictive for software system synthesis. We show that the interfaces and bodies of GenVoca components are subjective, i.e., they mutate and enlarge upon instantiation. This mutability enables software systems with customized interfaces to be composed from components with “standardized ” interfaces. 1

Two major obstacles hindering the wider acceptance of multi-methods are concerns over the lack of encapsulation and modularity and the absence of static typechecking in existing multi-method-based languages. This paper addresses both of these problems. We present a polynomial-time static typechecking algorithm that checks the conformance, completeness, and consistency of a group of method implementations with respect to declared message signatures. This algorithm improves on previous algorithms by handling separate type and inheritance hierarchies, abstract classes, and graph-based method lookup semantics. We also present a module system that enables independently-developed code to be fully encapsulated and statically typechecked on a per-module basis. To guarantee that potential conflicts between independently-developed modules have been resolved, a simple well-formedness condition on the modules comprising a program is checked at link-time. The typechecking algorithm and module system are applicable to a range of multi-method-based languages, but the paper uses the Cecil language as a concrete example of how they can be applied.

This paper surveys our current state of knowledge (and ignorance) on the use of hidden sorted algebra as a foundation for the object paradigm. Our main goal is to support equational reasoning about properties of concurrent systems of objects, because of its simple and ecient mechanisation. We show how equational speci cations can describe objects, inheritance and modules; our treatment of the latter topic emphasises the importance of reuse, and the r^ole of the so-called Satisfaction Condition. We then consider how to prove things about objects, how to unify the object and logic paradigms by using logical variables that range over objects, and how to connect objects into concurrent systems.

Generic programming centers around the idea of abstracting from concrete, efficient algorithms to obtain generic algorithms that can be combined with different data representations to produce a wide variety of useful software. For example, a class of generic sorting algorithms can be defined which work with finite sequences but which can be instantiated in different ways to produce algorithms working on arrays or linked lists. Four kinds of abstraction---data, algorithmic, structural, and representational--- are discussed, with examples of their use in building an Ada library of software components. The main topic discussed is generic algorithms and an approach to their formal specification and verification, with illustration in terms of a partitioning algorithm such as is used in the quicksort algorithm. It is argued that generically programmed software component libraries offer important advantages for achieving software productivity and reliability. This paper was presented at the...