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25
Essential Concepts of Algebraic Specification and Program Development
, 1996
"... The main ideas underlying work on the modeltheoretic foundations of algebraic specification and formal program development are presented in an informal way. An attempt is made to offer an overall view, rather than new results, and to focus on the basic motivation behind the technicalities presente ..."
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Cited by 55 (15 self)
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The main ideas underlying work on the modeltheoretic foundations of algebraic specification and formal program development are presented in an informal way. An attempt is made to offer an overall view, rather than new results, and to focus on the basic motivation behind the technicalities presented elsewhere.
The definition of Extended ML: a gentle introduction
 THEORETICAL COMPUTER SCIENCE
, 1995
"... Extended ML (EML) is a framework for the formal development of modular Standard ML (SML) software systems. Development commences with a specification of the behaviour required and proceeds via a sequence of partial solutions until a complete solution, an executable SML program, is obtained. All s ..."
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Cited by 34 (12 self)
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Extended ML (EML) is a framework for the formal development of modular Standard ML (SML) software systems. Development commences with a specification of the behaviour required and proceeds via a sequence of partial solutions until a complete solution, an executable SML program, is obtained. All stages in this development process are expressed in the EML language, an extension of SML with axioms for describing properties of module components. This is an overview of the formal definition of the EML language. To complement the full technical details presented elsewhere, it provides an informal explanation of the main ideas, gives the rationale for certain design decisions, and outlines some of the technical issues involved. EML is unusual in being built around a "real" programming language having a formallydefined syntax and semantics. Interesting and complex problems arise both from the nature of this relationship and from interactions between the features of the language.
A module calculus for Pure Type Systems
, 1996
"... Several proofassistants rely on the very formal basis of Pure Type Systems. However, some practical issues raised by the development of large proofs lead to add other features to actual implementations for handling namespace management, for developing reusable proof libraries and for separate verif ..."
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Cited by 24 (3 self)
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Several proofassistants rely on the very formal basis of Pure Type Systems. However, some practical issues raised by the development of large proofs lead to add other features to actual implementations for handling namespace management, for developing reusable proof libraries and for separate verification of distincts parts of large proofs. Unfortunately, few theoretical basis are given for these features. In this paper we propose an extension of Pure Type Systems with a module calculus adapted from SMLlike module systems for programming languages. Our module calculus gives a theoretical framework addressing the need for these features. We show that our module extension is conservative, and that type inference in the module extension of a given PTS is decidable under some hypotheses over the considered PTS.
Extended ML: Past, present and future
 PROC. 7TH WORKSHOP ON SPECIFICATION OF ABSTRACT DATA TYPES, WUSTERHAUSEN. SPRINGER LNCS 534
, 1991
"... An overview of past, present and future work on the Extended ML formal program development framework is given, with emphasis on two topics of current active research: the semantics of the Extended ML specification language, and tools to support formal program development. ..."
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Cited by 22 (8 self)
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An overview of past, present and future work on the Extended ML formal program development framework is given, with emphasis on two topics of current active research: the semantics of the Extended ML specification language, and tools to support formal program development.
An applicative module calculus
 In Theory and Practice of Software Development 97, Lecture Notes in Computer Science
, 1997
"... Abstract. The SMLlike module systems are small typed languages of their own. As is, one would expect a proof of their soundness following from a proof of subject reduction. Unfortunately, the subjectreduction property and the preservation of type abstraction seem to be incompatible. As a consequen ..."
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Cited by 15 (1 self)
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Abstract. The SMLlike module systems are small typed languages of their own. As is, one would expect a proof of their soundness following from a proof of subject reduction. Unfortunately, the subjectreduction property and the preservation of type abstraction seem to be incompatible. As a consequence, in relevant module systems, the theoretical study of reductions is meaningless, and for instance, the question of normalization of module expressions can not even be considered. In this paper, we analyze this problem as a misunderstanding of the notion of module definition. We build a variant of the SML module system — inspired from recent works by Leroy, Harper, and Lillibridge — which enjoys the subject reduction property. Type abstraction — achieved through an explicit declaration of the signature of a module at its definition — is preserved. This was the initial motivation. Besides our system enjoys other typetheoretic properties: the calculus is strongly normalizing, there are no syntactic restrictions on module paths, it enjoys a purely applicative semantics, every module has a principal type, and type inference is decidable. Neither Leroy’s system nor Harper and Lillibridge’s system has all of them. 1
Structuring Specifications intheLarge and intheSmall: HigherOrder Functions, Dependent Types and Inheritance in SPECTRAL
 PROC. COLLOQ. ON COMBINING PARADIGMS FOR SOFTWARE DEVELOPMENT, JOINT CONF. ON THEORY AND PRACTICE OF SOFTWARE DEVELOPMENT (TAPSOFT
"... ..."
The Definition of Extended ML
, 1994
"... This document formally defines the syntax and semantics of the Extended ML language. It is based directly on the published semantics of Standard ML in an attempt to ensure compatibility between the two languages. LFCS, Department of Computer Science, University of Edinburgh, Edinburgh, Scotland. ..."
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Cited by 9 (4 self)
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This document formally defines the syntax and semantics of the Extended ML language. It is based directly on the published semantics of Standard ML in an attempt to ensure compatibility between the two languages. LFCS, Department of Computer Science, University of Edinburgh, Edinburgh, Scotland. y Institute of Informatics, Warsaw University, and Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland. ii CONTENTS Contents 1 Introduction 1 1.1 Behavioural equivalence : : : : : : : : : : : : : : : : : : : : : : : : 3 1.2 Metalanguage : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2 Syntax of the Core 8 2.1 Reserved Words : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 2.2 Special constants : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 2.3 Comments : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.4 Identifiers : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.5 Lexical analysis : : : :...
Algebraic specification and program development by stepwise refinement (Extended Abstract)
 9th international workshop, LOPSTR ’99
, 1999
"... . Various formalizations of the concept of "refinement step" as used in the formal development of programs from algebraic specifications are presented and compared. 1 Introduction Algebraic specification aims to provide a formal basis to support the systematic development of correct programs fro ..."
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Cited by 6 (0 self)
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. Various formalizations of the concept of "refinement step" as used in the formal development of programs from algebraic specifications are presented and compared. 1 Introduction Algebraic specification aims to provide a formal basis to support the systematic development of correct programs from specifications by means of verified refinement steps. Obviously, a central piece of the puzzle is how best to formalize concepts like "specification", "program" and "refinement step". Answers are required that are simple, elegant and general and which enjoy useful properties, while at the same time taking proper account of the needs of practice. Here I will concentrate on the last of these concepts, but first I need to deal with the other two. For "program", I take the usual approach of algebraic specification whereby programs are modelled as manysorted algebras consisting of a collection of sets of data values together with functions over those sets. This level of abstraction is commens...
A Theory of Program Refinement
, 1998
"... We give a canonical program refinement calculus based on the lambda calculus and classical firstorder predicate logic, and study its proof theory and semantics. The intention is to construct a metalanguage for refinement in which basic principles of program development can be studied. The idea is t ..."
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Cited by 6 (1 self)
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We give a canonical program refinement calculus based on the lambda calculus and classical firstorder predicate logic, and study its proof theory and semantics. The intention is to construct a metalanguage for refinement in which basic principles of program development can be studied. The idea is that it should be possible to induce a refinement calculus in a generic manner from a programming language and a program logic. For concreteness, we adopt the simplytyped lambda calculus augmented with primitive recursion as a paradigmatic typed functional programming language, and use classical firstorder logic as a simple program logic. A key feature is the construction of the refinement calculus in a modular fashion, as the combination of two orthogonal extensions to the underlying programming language (in this case, the simplytyped lambda calculus). The crucial observation is that a refinement calculus is given by extending a programming language to allow indeterminate expressions (or ‘stubs’) involving the construction ‘some program x such that P ’. Factoring this into ‘some x...’