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Modular typechecking for hierarchically extensible datatypes and functions
 In Proceedings of the International Conference on Functional Programming
, 2002
"... One promising approach for adding objectoriented (OO) facilities to functional languages like ML is to generalize the existing datatype and function constructs to be hierarchical and extensible, so that datatype variants simulate classes and function cases simulate methods. This approach allows exi ..."
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Cited by 38 (6 self)
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One promising approach for adding objectoriented (OO) facilities to functional languages like ML is to generalize the existing datatype and function constructs to be hierarchical and extensible, so that datatype variants simulate classes and function cases simulate methods. This approach allows existing datatypes to be easily extended with both new operations and new variants, resolving a longstanding conflict between the functional and OO styles. However, previous designs based on this approach have been forced to give up modular typechecking, requiring wholeprogram checks to ensure type safety. We describe Extensible ML (EML), an MLlike language that supports hierarchical, extensible datatypes and functions while preserving purely modular typechecking. To achieve this result, EMLâ€™s type system imposes a few requirements on datatype and function extensibility, but EML is still able to express both traditional functional and OO idioms. We have formalized a core version of EML and proven the associated type system sound, and we have developed a prototype
On Behavioural Abstraction and Behavioural Satisfaction in HigherOrder Logic
, 1996
"... The behavioural semantics of specifications with higherorder logical formulae as axioms is analyzed. A characterization of behavioural abstraction via behavioural satisfaction of formulae in which the equality symbol is interpreted as indistinguishability, which is due to Reichel and was recently g ..."
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Cited by 25 (4 self)
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The behavioural semantics of specifications with higherorder logical formulae as axioms is analyzed. A characterization of behavioural abstraction via behavioural satisfaction of formulae in which the equality symbol is interpreted as indistinguishability, which is due to Reichel and was recently generalized to the case of firstorder logic by Bidoit et al, is further generalized to this case. The fact that higherorder logic is powerful enough to express the indistinguishability relation is used to characterize behavioural satisfaction in terms of ordinary satisfaction, and to develop new methods for reasoning about specifications under behavioural semantics. 1 Introduction An important ingredient in the use of algebraic specifications to describe data abstractions is the concept of behavioural equivalence between algebras, which seems to appropriately capture the "black box" character of data abstractions, see e.g. [GGM76], [GM82], [ST87] and [ST95]. Roughly speaking (since there ...
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 23 (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.
Towards a Second Generation of Formal Description Techniques  Rationale for the Design of ELOTOS
 University of Nantes
, 1998
"... Process algebras are often advocated as suitable formalisms for the specification of telecommunication protocols and distributed systems. However, despite their mathematical basis, despite standardization attempts (most notably the Formal Description Technique Lotos), and despite an ever growing ..."
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Cited by 14 (2 self)
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Process algebras are often advocated as suitable formalisms for the specification of telecommunication protocols and distributed systems. However, despite their mathematical basis, despite standardization attempts (most notably the Formal Description Technique Lotos), and despite an ever growing number of successful casestudies, process algebras have not yet reached a wide acceptance in industry. On the other hand, description languages such as Promela or Sdl are quite popular, although they lack a formal semantics, which should prohibit their use for safetycritical systems. In this paper, we seek to merge the "best of both worlds" by attempting to define a "second generation Formal Description Technique" that would combine the strong theoretical foundations of process algebras with language features suitable for a wider industrial dissemination of formal methods. Taking the international standard Lotos as a basis, we suggest several enhancements, which fall into three ...
Protective interface specifications
 Iowa State University, Department of Computer Science
, 1997
"... Abstract The interface specification of a procedure describes the procedure's behavior using pre and postconditions. These pre and postconditions are written using various functions. If some of these functions are partial, or underspecified, then the procedure specification may not be wellde ..."
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Abstract The interface specification of a procedure describes the procedure's behavior using pre and postconditions. These pre and postconditions are written using various functions. If some of these functions are partial, or underspecified, then the procedure specification may not be welldefined. We show how to write pre and postcondition specifications that avoid such problems, by having the precondition "protect " the postcondition from the effects of partiality and underspecification. We formalize the notion of protection from partiality in the context of specification languages like VDMSL and COLDK. We also formalize the notion of protection from underspecification for the Larch family of specification languages, and for Larch show how one can prove that a procedure specification is protected from the effects of underspecification.
An ML Editor Based on ProofsasPrograms
, 1999
"... . C Y NTHIA is a novel editor for the functional programming language ML in which each function definition is represented as the proof of a simple specification. Users of C Y NTHIA edit programs by applying sequences of highlevel editing commands to existing programs. These commands make ch ..."
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Cited by 9 (2 self)
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. C Y NTHIA is a novel editor for the functional programming language ML in which each function definition is represented as the proof of a simple specification. Users of C Y NTHIA edit programs by applying sequences of highlevel editing commands to existing programs. These commands make changes to the proof representation from which a new program is then extracted. The use of proofs is a sound framework for analysing ML programs and giving useful feedback about errors. Amongst the properties analysed within C Y NTHIA at present is termination. C Y NTHIA has been successfully used in the teaching of ML in two courses at Napier University. 1 Introduction Current programming environments for novice functional programming (FP) are inadequate. This paper describes ways of using mechanised theorem proving to improve the situation, in the context of the language ML [9]. ML is a stronglytyped FP language with type inference [4]. ML incorporates extensive use of pattern match...
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 8 (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 : : : :...
RZ: A tool for bringing constructive and computable mathematics closer to programming practice
 CiE 2007: Computation and Logic in the Real World, volume 4497 of LNCS
, 2007
"... Abstract. Realizability theory can produce code interfaces for the data structure corresponding to a mathematical theory. Our tool, called RZ, serves as a bridge between constructive mathematics and programming by translating specifications in constructive logic into annotated interface code in Obje ..."
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Cited by 6 (3 self)
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Abstract. Realizability theory can produce code interfaces for the data structure corresponding to a mathematical theory. Our tool, called RZ, serves as a bridge between constructive mathematics and programming by translating specifications in constructive logic into annotated interface code in Objective Caml. The system supports a rich input language allowing descriptions of complex mathematical structures. RZ does not extract code from proofs, but allows any implementation method, from handwritten code to code extracted from proofs by other tools. 1
Specification Refinement with System F
 In Proc. CSL'99, volume 1683 of LNCS
, 1999
"... . Essential concepts of algebraic specification refinement are translated into a typetheoretic setting involving System F and Reynolds' relational parametricity assertion as expressed in Plotkin and Abadi's logic for parametric polymorphism. At first order, the typetheoretic setting ..."
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. Essential concepts of algebraic specification refinement are translated into a typetheoretic setting involving System F and Reynolds' relational parametricity assertion as expressed in Plotkin and Abadi's logic for parametric polymorphism. At first order, the typetheoretic setting provides a canonical picture of algebraic specification refinement. At higher order, the typetheoretic setting allows future generalisation of the principles of algebraic specification refinement to higher order and polymorphism. We show the equivalence of the acquired typetheoretic notion of specification refinement with that from algebraic specification. To do this, a generic algebraicspecification strategy for behavioural refinement proofs is mirrored in the typetheoretic setting. 1 Introduction This paper aims to express in type theory certain essential concepts of algebraic specification refinement. The benefit to algebraic specification is that inherently firstorder concepts are tra...