Betarte, G. (1998). Dependent record types and algebraic structures in type theory. Ph.D. thesis, PMG, Dept. of Computing Science, University of Goteborg and Chalmers University of Technology.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a relation between types that allows to lift every element of A into an element of B whenever A B. Thus, subtyping makes it possible to apply a function f : B C to a : A and thus provides a limited form of reusability. Specic forms of subtyping connected to reusability include record subtyping [10] and constructor subtyping [7] but these forms of subtyping are too specialised to provide a general solution to the problem of reusability. Implicit coercions and coercive subtyping These paradigms [3, 5, 28, 35] provide a very powerful mechanism that subsumes a variety of previous and seemingly ....

G. Betarte. Dependent Record Types and Algebraic Structures in Type Theory. PhD thesis, Department of Computer Science, Chalmers Tekniska H#gskola, 1998.

....to nat and NatPreorder. to le nat, while NatPreorder.trans will be considered a normal form. Therefore the type checker will accept 0 NatPreorder. 0. 8 This manifest eld feature makes MC 2 depart fundamentally from formalisms implementing packages as record types [Bet00b, Tas97, Bet98, Pol97] Indeed, in these formalisms, there is no middle way: given a record expression e, either it reduces to an explicit record whose value of all elds are known or it reduces to a variable (possibly applied to some arguments) and none of its elds can be known. On the contrary in MC 2 a ....

....same reasons as for IMPS, we believe MC 2 more suited to PTS based proof assistants. 6.1. 4 Betarte s dependently typed records Gustavo Betarte and Alvaro Tasistro have proposed to add dependently typed records to type theory in order to formalize some body of abstract algebra [Bet00b, Bet00a, Bet98] One advantage of their system over ours is that records are rst class expressions and functors are ordinary functions working over record types. However, we believe the lack of manifest elds for their record types has serious drawbacks from our point of vue: this prevents them from building ....

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Gustavo Betarte. Dependent Record Types and Algebraic Structures in Type Theory. PhD thesis, PMG, Dept. of Computing Science, University of Goteborg and Chalmers University of Technology, 1998.

....isomorphisms. However, our work ts in a series of eoeorts to lay theoretical foundations for proof reuse in dependent type theory. Subtyping Subtyping [16, 17] is a basic mechanism to enhance proof reuse in type systems. Specic forms of subtyping connected to reusability include record subtyping [11] and constructor subtyping [8] but these forms of subtyping are too specialised to provide a general solution to the problem of reusability. Implicit coercions Implicit coercions [3, 5, 28, 36] provide a very powerful mechanism that subsumes a variety of previous and seemingly unrelated proposals ....

G. Betarte. Dependent Record Types and Algebraic Structures in Type Theory. PhD thesis, Department of Computer Science, Chalmers Tekniska H#gskola, 1998.

....the record. The second name is not part of the type and can clearly be ff converted when necessary. To avoid cluttering the typing rules even more we will not introduce any notation for this in the rules, instead we assume that the problem can be handled if needed. A similar solution is used in [Bet98] 4.3 Type checking Type checking of Cayenne is basically simple, just because it is type checking rather than type deductions, like e.g. Haskell uses. Type checking proceeds in a single traversal of the syntax tree. On the way down the environment ( Gamma ) is extended with the types (and ....

....Since types and values are combined, a partial evaluator would serve both as a type specializer (as used in, e.g. Aug93,PJ93] and a traditional partial evaluator. To make the record types more useful, subtyping could be added. Subtyping in the presence of dependent types has been studied in [Bet98] As a proof of concept the Cayenne compiler should, of course, be rewritten in Cayenne. 9 Acknowledgments A big thanks to Jessica for improving my English. The programming logic group at Chalmers has over the years provided me with enough background material to nally try to make a programming ....

Gustavo Betarte. Dependent Record Types and Algebraic Structures in Type Theory. PhD thesis, Department of Computing Science, University of G#teborg, G#teborg, Sweden, February 1998.

.... and to enforce a subsumption rule a : A A B a : B This basic mechanism of subtyping is powerful enough to capture a variety of concepts in computer science, see e.g. 9] and its use is spreading both in functional programming languages, see e.g. 23, 28, 29] and in proof assistants, see e.g. [7, 22, 30]. Constructor subtyping is a basic form of subtyping, suggested in [12] and developed in [5] in which an inductive type is viewed as a subtype of another inductive type if has more constructors than . As such, constructor subtyping captures in a type theoretic context the ubiquitous use ....

G. Betarte. Dependent Record Types and Algebraic Structures in Type Theory. PhD thesis, Department of Computer Science, Chalmers Tekniska Hogskola, 1998.

.... and to enforce a subsumption rule a : A A B a : B This basic mechanism of subtyping is powerful enough to capture a variety of concepts in computer science, see e.g. 9] and its use is spreading both in functional programming languages, see e.g. 25, 30, 31] and in proof assistants, see e.g. [7, 24, 32]. Constructor subtyping is a basic form of subtyping, suggested in [12] and developed in [5] in which an inductive type oe is viewed as a subtype of another inductive type if has more constructors than oe. As such, constructor subtyping captures in a type theoretic context the ubiquitous use ....

G. Betarte. Dependent Record Types and Algebraic Structures in Type Theory. PhD thesis, Department of Computer Science, Chalmers Tekniska Hogskola, 1998.

.... and to enforce a subsumption rule a : A A B a : B This basic mechanism of subtyping is powerful enough to capture a variety of concepts in computer science, see e.g. 9] and its use is spreading both in functional programming languages, see e.g. 25, 30, 31] and in proof assistants, see e.g. [7, 24, 32]. Constructor subtyping is a basic form of subtyping, suggested in [12] and developed in [5] in which an inductive type oe is viewed as a subtype of another inductive type if has more constructors than oe. As such, constructor subtyping captures in a type theoretic context the ubiquitous use ....

G. Betarte. Dependent Record Types and Algebraic Structures in Type Theory. PhD thesis, Department of Computer Science, Chalmers Tekniska Hogskola, 1998.

.... b) has sketched a revision of the view of information states presented in Cooper (1996) and Cooper and Ginzburg (1996) which involves using ideas from Martin L#f s type theory, in particular the notion of dependent record types introduced by Betarte and Tasistro (forthcoming) Tasistro (1997) Betarte (1998). The results are similar in spirit to other work using type theory for natural language semantics such as Ranta (1994) Ahn (1995) amd Ahn and Borghuis (1998) In this paper, I will suggest that this blend of situation theory and type theory gives us a tractable way of characterizing information ....

....the kind of information states we need in dialogue exchange, that is, information states which relate semantic content to speech events. 2 Records and Record Types The presentation in this section takes as its starting point the work of Betarte and Tasistro (forthcoming) Tasistro (1997) and Betarte (1998). The reader should consult these works for an exact formulation within Martin L#f type theory. The basic idea is represented informally as follows: If a 1 : T 1 ; a 2 : T 2 (a 1 ) an : Tn (a 1 ; a 2 ; an Gamma1 ) the record: 2 6 6 4 l 1 = a 1 l 2 = a 2 . l n = an 3 7 ....

Betarte, Gustavo (1998) Dependent Record Types and Algebraic Structures in Type Theory , Ph.D. thesis, Department of Computing Science, G#teborg University and Chalmers University of Technology.

.... see [NPS90, Chapter 6] would provide a framework in which to formalize typed languages with subtyping, including the various typed object calculi considered in [AC96a] Finally it would be interesting to combine the approach suggested in this paper with other approaches to subtyping, see e.g. [Bet98, Luo98]. Acknowledgements The author is grateful to the anonymous referees for their remarks and suggestions. Earlier versions of the paper were written while the author was working at the Center for Mathematics and Computer Science (CWI) Amsterdam, and Chalmers University, Goteborg. The author ....

G. Betarte. Dependent Record Types and Algebraic Structures in Type Theory. PhD thesis, Department of Computer Science, Chalmers Tekniska Hogskola, 1998.

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Betarte, G. (1998). Dependent record types and algebraic structures in type theory. Ph.D. thesis, PMG, Dept. of Computing Science, University of Goteborg and Chalmers University of Technology.

....in section 2.1. The mechanism of subtyping or type inclusion introduced is, in the first place, the one naturally induced by record types. However, once record inclusion is formally stipulated it is also required that rules of subtyping have to be given for the rest of the type formers. In [Bet98] we have investigated an alternative formulation of the extended theory. In that formulation we make use of parameters, in the sense of [Coq91, Pol94b] to stand for generic objects of the various types. The introduction of the notion of parameter allows us to give a solution to the problems posed ....

....we make use of parameters, in the sense of [Coq91, Pol94b] to stand for generic objects of the various types. The introduction of the notion of parameter allows us to give a solution to the problems posed by the manipulation of free names in the presence of dependent types. We also present in [Bet98] the procedures for the mechanical verification of the forms of judgement of that variant Date: September 12, 2000. THIS PAPER IS AN ENHANCED VERSION OF [Bet97] 1 2 of the extension. In [Bet00] we make a detailed presentation of the investigations concerned with the design, specification ....

[Article contains additional citation context not shown here]

G. Betarte. Dependent Record Types and Algebraic Structures in Type Theory. PhD thesis, PMG, Dept. of Computing Science, University of Goteborg and Chalmers University of Technology, 1998.

....of the record object. The mechanism of subtyping or type inclusion introduced is, in the first place, the one naturally induced by record types. However, once record inclusion is formally stipulated it is also required that rules of subtyping have to be given for the rest of the type formers. In [Bet98] we have investigated an alternative formulation of the extended theory. In that formulation we make use of parameters, in the sense of [Coq91, Pol94b] to stand for generic objects of the various types. The introduction of the notion of parameter allows to give a solution to the problems posed by ....

....we make use of parameters, in the sense of [Coq91, Pol94b] to stand for generic objects of the various types. The introduction of the notion of parameter allows to give a solution to the problems posed by the manipulation of free names in the presence of dependent types. We also present in [Bet98] the procedures for the mechanical verification of the forms of judgement of that variant of the extension. In this paper we are mainly concerned with the design and specification of those procedures. The plan for the rest of the article is as follows. In the next section we start by giving a ....

[Article contains additional citation context not shown here]

G. Betarte. Dependent Record Types and Algebraic Structures in Type Theory. PhD thesis, PMG, Dept. of Computing Science, University of Goteborg and Chalmers University of Technology, 1998.

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