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10
A TypeTheoretic Approach to HigherOrder Modules with Sharing
, 1994
"... The design of a module system for constructing and main taining large programs is a difficult task that raises a number of theoretical and practical issues. A fundamental issue is the management of the flow of information between program units at compile time via the notion of an interface. Experie ..."
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Cited by 268 (23 self)
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The design of a module system for constructing and main taining large programs is a difficult task that raises a number of theoretical and practical issues. A fundamental issue is the management of the flow of information between program units at compile time via the notion of an interface. Experience has shown that fully opaque interfaces are awkward to use in practice since too much information is hidden, and that fully transparent interfaces lead to excessive interdependencies, creating problems for maintenance and separate compilation. The "sharing" specifications of Standard ML address this issue by allowing the programmer to specify equational relationships between types in separate modules, but are not expressive enough to allow the programmer com plete control over the propagation of type information be tween modules.
Using Typed Lambda Calculus to Implement Formal Systems on a Machine
 Journal of Automated Reasoning
, 1992
"... this paper and the LF. In particular the idea of having an operator T : Prop ! Type appears already in De Bruijn's earlier work, as does the idea of having several judgements. The paper [24] describes the basic features of the LF. In this paper we are going to provide a broader illustration of its a ..."
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Cited by 83 (14 self)
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this paper and the LF. In particular the idea of having an operator T : Prop ! Type appears already in De Bruijn's earlier work, as does the idea of having several judgements. The paper [24] describes the basic features of the LF. In this paper we are going to provide a broader illustration of its applicability and discuss to what extent it is successful. The analysis (of the formal presentation) of a system carried out through encoding often illuminates the system itself. This paper will also deal with this phenomenon.
Explicit Polymorphism and CPS Conversion
 IN TWENTIETH ACM SYMPOSIUM ON PRINCIPLES OF PROGRAMMING LANGUAGES
, 1992
"... We study the typing properties of CPS conversion for an extension of F ! with control operators. Two classes of evaluation strategies are considered, each with callbyname and callbyvalue variants. Under the "standard" strategies, constructor abstractions are values, and constructor applications ..."
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Cited by 69 (9 self)
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We study the typing properties of CPS conversion for an extension of F ! with control operators. Two classes of evaluation strategies are considered, each with callbyname and callbyvalue variants. Under the "standard" strategies, constructor abstractions are values, and constructor applications can lead to nontrivial control effects. In contrast, the "MLlike" strategies evaluate beneath constructor abstractions, reflecting the usual interpretation of programs in languages based on implicit polymorphism. Three continuation passing style sublanguages are considered, one on which the standard strategies coincide, one on which the MLlike strategies coincide, and one on which all the strategies coincide. Compositional, typepreserving CPS transformation algorithms are given for the standard strategies, resulting in terms on which all evaluation strategies coincide. This has as a corollary the soundness and termination of welltyped programs under the standard evaluation strategies. A similar result is obtained for the MLlike callbyname strategy. In contrast, such results are obtained for the callby value MLlike strategy only for a restricted sublanguage in which constructor abstractions are limited to values.
Inductive Families
 Formal Aspects of Computing
, 1997
"... A general formulation of inductive and recursive definitions in MartinLof's type theory is presented. It extends Backhouse's `DoItYourself Type Theory' to include inductive definitions of families of sets and definitions of functions by recursion on the way elements of such sets are generated. Th ..."
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Cited by 65 (13 self)
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A general formulation of inductive and recursive definitions in MartinLof's type theory is presented. It extends Backhouse's `DoItYourself Type Theory' to include inductive definitions of families of sets and definitions of functions by recursion on the way elements of such sets are generated. The formulation is in natural deduction and is intended to be a natural generalization to type theory of MartinLof's theory of iterated inductive definitions in predicate logic. Formal criteria are given for correct formation and introduction rules of a new set former capturing definition by strictly positive, iterated, generalized induction. Moreover, there is an inversion principle for deriving elimination and equality rules from the formation and introduction rules. Finally, there is an alternative schematic presentation of definition by recursion. The resulting theory is a flexible and powerful language for programming and constructive mathematics. We hint at the wealth of possible applic...
Type Checking with Universes
, 1991
"... Various formulations of constructive type theories have been proposed to serve as the basis for machineassisted proof and as a theoretical basis for studying programming languages. Many of these calculi include a cumulative hierarchy of "universes," each a type of types closed under a collectio ..."
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Cited by 24 (6 self)
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Various formulations of constructive type theories have been proposed to serve as the basis for machineassisted proof and as a theoretical basis for studying programming languages. Many of these calculi include a cumulative hierarchy of "universes," each a type of types closed under a collection of typeforming operations. Universes are of interest for a variety of reasons, some philosophical (predicative vs. impredicative type theories), some theoretical (limitations on the closure properties of type theories), and some practical (to achieve some of the advantages of a type of all types without sacrificing consistency.) The Generalized Calculus of Constructions (CC ! ) is a formal theory of types that includes such a hierarchy of universes. Although essential to the formalization of constructive mathematics, universes are tedious to use in practice, for one is required to make specific choices of universe levels and to ensure that all choices are consistent. In this pa...
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.
A Natural Deduction Approach to Dynamic Logic
 Proceedings of TYPES'95, LNCS 1158
, 1996
"... . Natural Deduction style presentations of program logics are useful in view of the implementation of such logics in interactive proof development environments, based on type theory, such as LEGO, Coq, etc. In fact, NDstyle systems are the kind of systems which can take best advantage of the possib ..."
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Cited by 13 (5 self)
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. Natural Deduction style presentations of program logics are useful in view of the implementation of such logics in interactive proof development environments, based on type theory, such as LEGO, Coq, etc. In fact, NDstyle systems are the kind of systems which can take best advantage of the possibility of reasoning "under assumptions" o#ered by proof assistants generated by Logical Frameworks. In this paper we introduce and discuss sound and complete proof systems in Natural Deduction style for representing various "truth" consequence relations of Dynamic Logic. We discuss the design decisions which lead to adequate encodings of these logics in Coq. We derive in Dynamic Logic a set of rules representing a NDstyle system for Hoare Logic.
Experiences with a mechanisation of MartinLöf's Theory of Types
, 1992
"... MartinLof's Theory of TypesMLTT can be used as a logical framework in which other theories can be defined. This paper describes ILF, a mechanisation of MLTT which allows definition of object theories, judgement checking, reduction of expressions and other facilities for its use. An example of how ..."
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MartinLof's Theory of TypesMLTT can be used as a logical framework in which other theories can be defined. This paper describes ILF, a mechanisation of MLTT which allows definition of object theories, judgement checking, reduction of expressions and other facilities for its use. An example of how a particular object theory  MartinLof's Monomorphic Theory of Sets  can be defined in ILF and used to develop correct programs is also presented. Keywords : Logical Framework, Programming Logic, MartinLof's Theory of Types. Both authors are partially supported by a PEDECIBA (Programa de Desarrollo de las Ciencias B'asicas) grant. 1 Introduction. During the last two decades, as direct result of the strive for the reliability of software there has appeared an increasing interest in methodologies for systematic reasoning about programs. The concept of type, as taken from well known works in foundations of mathematics, has arisen as a very useful tool for dealing with issues connected ...
Desiderata for Interactive Verification Systems
, 1994
"... What facilities should an interactive verification system provide? We take the pragmatic view that the particular logic underlying a proof system is not as important as the support that is provided. Although a plethora of logics have been implemented, we think that there is a common kernel of suppor ..."
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What facilities should an interactive verification system provide? We take the pragmatic view that the particular logic underlying a proof system is not as important as the support that is provided. Although a plethora of logics have been implemented, we think that there is a common kernel of support that a proof system ought to provide. Towards this end, we give detailed suggestions for verification support in three major areas: formalization, proof, and interface. Although our perspective comes from experience with highly expressive logics such as set theory, higher order logic, and type theory, we think our analyses apply more generally. Introduction Currently, theorem provers are used in the verification of both hardware and software [GM93, ORS92, BM90, HRS90, FFMH92], the formalization of informal mathematical proofs [FGT90, CH85, Pau90b], the teaching of logic[AMC84], and as tools of mathematical and metamathematical research [WWM + 90, CAB + 86]. 1 In this paper we describ...
Machine Assisted Proofs for Generic Semantics to Compiler Transformation Correctness Theorems
"... This thesis investigates the issues involved in the creation of a “general theory of operational semantics ” in LEGO, a typetheoretic theorem proving environment implementing a constructionist logic. Such a general theory permits the ability to manipulate and reason about operational semantics both ..."
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This thesis investigates the issues involved in the creation of a “general theory of operational semantics ” in LEGO, a typetheoretic theorem proving environment implementing a constructionist logic. Such a general theory permits the ability to manipulate and reason about operational semantics both individually and as a class. The motivation for this lies in the studies of semantics directed compiler generation in which a set of generic semantics transforming functions can help convert arbitrary semantic definitions to abstract machines. Such transformations require correctness theorems that quantify over the class of operational semantics. In implementation terms this indicates the need to ensure both the class of operational semantics and the means of inferring results thereon remain at the theorem prover level. The endeavour of this thesis can be seen as assessing both the requirements that general theories of semantics impose on proof assistants and the efficacy of proof assistants in modelling such theories. Acknowledgements First and foremost I would like to thank Kevin Mitchell who supervised me for my first four years, supplying me with many helpful hints and constructive criticisms. He also bore with me at a period of my life when my mental health deteriorated for which I am eternally grateful. Secondly I would like to thank Stuart Anderson an ever present of my life at the University since I first arrived in 1988, for taking over the supervision of my work when it was seemingly near its conclusion. The help and encouragement I received meant I was able to (finally!) complete this thesis. Special mention must go to Rod Burstall, my mentor through the entirety of my postgraduate studies. My all too brief encounters with him lifted my spirits at a time when they were desperately in need of a boost. I would also like to especially thank Thomas Kleymann (formerly Schreiber) for the many times he aided me in my Lego miseries. I also thank James Hugh McKinna, Randy Pollack and other members of the Lego club for their helpful ideas, various helpful officemates