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Subtyping Parametric and Dependent Types
, 1996
"... A type may be a subtype of another type. The intuition about this should be clear: a type is a type of data, some data then may live in a given type as well as in a larger one, up to a simple "transformation". The advantage is that those data may be "seen" or used in different contexts. The formal ..."
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A type may be a subtype of another type. The intuition about this should be clear: a type is a type of data, some data then may live in a given type as well as in a larger one, up to a simple "transformation". The advantage is that those data may be "seen" or used in different contexts. The formal treatment of this intuition, though, is not so obvious, in particular when data may be programs. In Object Oriented Programming, where the issue of "reusing data" is crucial, there has been a longlasting discussion on "inheritance" and ... little agreement. There are several ways to understand and formalize inheritance, which depend on the specific programming environment used. Since early work of Cardelli and Wegner, there has been a large amount of papers developing several possible functional approaches to inheritance, as subtyping. Indeed, functional subtyping captures only one point of view on inheritance, yet this notion largely motivated most of that work. Whethe
TYPE THEORY AND FUNCTIONAL PROGRAMMING A WORK PROPOSAL Gustavo Betarte
"... We propose a series of work areas related to type theory and functional programming. By type theory we mean the formulation of MartinLof's set theory using the theory of types as logical framework, extended with record types and subtyping. The areas presented are: the implementation of an environme ..."
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We propose a series of work areas related to type theory and functional programming. By type theory we mean the formulation of MartinLof's set theory using the theory of types as logical framework, extended with record types and subtyping. The areas presented are: the implementation of an environment for carrying out constructions in type theory, the systematic development of programming in type theory as a formal discipline and the formalization in type theory of the theory of functional programming languages. We also give a succint introduction to a theory of specifications and programs in which programs and their correctness proofs are separated but still can be built up simultaneously; we propose the implementation of a programming system for this theory too. The group of people presenting this work proposal is defined by their common interest to work together in at least one of the areas proposed. There will be people working in each of these areas in the Plata region. 1. Introdu...
TECHNICAL ANNEX LOGCOMP Logic and Computation
"... 2 3 Objectives 2 4 Background and State of the Art 3 5 Project Organization 6 5.1 Technical Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . 6 5.1.1 Logical Representation of the Specification Paradigms . . . . 6 5.1.2 Integration with the Proof Assistant Systems . . . . . . . . . 8 ..."
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2 3 Objectives 2 4 Background and State of the Art 3 5 Project Organization 6 5.1 Technical Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . 6 5.1.1 Logical Representation of the Specification Paradigms . . . . 6 5.1.2 Integration with the Proof Assistant Systems . . . . . . . . . 8 5.1.3 Publications and Cooperation . . . . . . . . . . . . . . . . . . 8 5.2 Task Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 6 Work Planning 13 7 Deliverables 14 8 Project Management 14 9 Publication of Results 14 10 Ethical, Social and Environmental Impact 14 11 Team Member Experience 15 12 Available and Requested Resources 19 Research and Development medium size project proposal submitted to the PRAXIS XXI Program, in the area of Information Technology and Telecommunications, in August 1995 1 1 Title LOGCOMP Logic and Computation Integration of Proof Assistants with Symbolic Systems for Specification and Prototyping. 2 Abstract The project aims to integra...
Generalised Simultaneous InductiveRecursive Definitions and their Application to Programming in Type Theory
"... In this work we present a generalisation of Dybjer's schema for simultaneous inductiverecursive definitions for the cases where we have several mutually recursive predicates defined simultaneously with several functions which, in turn, are defined by recursion on those predicates. ..."
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In this work we present a generalisation of Dybjer's schema for simultaneous inductiverecursive definitions for the cases where we have several mutually recursive predicates defined simultaneously with several functions which, in turn, are defined by recursion on those predicates.
Subtyping Parametric and Dependent Types  An introduction
, 1996
"... A type may be a subtype of another type. The intuition about this should be clear: a type is a type of data, some data then may live in a given type as well as in a larger one, up to a simple "transformation". The advantage is that those data may be "seen" or used in different contexts. The formal ..."
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A type may be a subtype of another type. The intuition about this should be clear: a type is a type of data, some data then may live in a given type as well as in a larger one, up to a simple "transformation". The advantage is that those data may be "seen" or used in different contexts. The formal treatment of this intuition, though, is not so obvious, in particular when data may be programs. In Object Oriented Programming, where the issue of "reusing data" is crucial, there has been a longlasting discussion on "inheritance" and ... little agreement. There are several ways to understand and formalize inheritance, which depend on the specific programming environment used. Since early work of Cardelli and Wegner, there has been a large amount of papers developing several possible functional approaches to inheritance, as subtyping. Indeed, functional subtyping captures only one point of view on inheritance, yet this notion largely motivated most of that work. Whethe
Dependent Type System with Subtyping  Type Level Transitivity Elimination
, 1996
"... Dependent type systems have been the basis of many proof development enviroments. In [AC96], a system P is proposed as a subtyping extension of the dependent type system P[Bar92] (also called \Pi[Dow95]). P has nice metatheoretic properties including subject reduction and decidability, but transit ..."
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Dependent type systems have been the basis of many proof development enviroments. In [AC96], a system P is proposed as a subtyping extension of the dependent type system P[Bar92] (also called \Pi[Dow95]). P has nice metatheoretic properties including subject reduction and decidability, but transitivity elimination is restricted to the fi 2 normalized types. In this report, we propose a system \Pi , which is equivalent to P , but it has type level transitivity eliminatioin property. This feature distinguishes our approach from the existing subtyping systems with reduction relations in types. e.g. P[AC96], F ! [SP94], F ! [Com94], where transitivity elimination only holds for normalized types. Metatheoretic properties including subject reduction and decidability are established. The system is shown to be equivalent with P in typing, kinding and context formation. The type checking algorithm is more clear and efficient than P . The technique is suitable for future extensions and...