Z. Luo. An Extended Calculus of Constructions. PhD thesis, University of Edinburgh, 1990. Also as Report CST-65-90/ECS-LFCS-90-118, Department of Computer Science, University of Edinburgh. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Program Specification and Data Refinement in Type Theory - Luo (1991) (15 citations) Self-citation (Luo) (Correct)
....and data refinement and show that a type theory with nice structural mechanisms provides an adequate formalism for both modular design by data refinement and structured specification. The type theory that we work with in this paper is the Extended Calculus of Constructions (ECC) Luo89, Luo90a] As a formal system, ECC extends the calculus of constructions [CH88] with predicative type universes and Sigma types (strong sum) it may also be seen as an extension of Martin Lof s type theory with universes [ML75] by an impredicative universe (higher order logic) However, different from ....
....specifications and their implementations are discussed in section 5. The work reported here is in progress; several further research topics are discussed in the conclusion. 2 The Extended Calculus of Constructions As we have mentioned in the introduction, the type theory ECC [Luo89, Luo90a] is a natural combination of Martin Lof s type theory [ML75] and the calculus of constructions [CH88] based on the idea that there should be clear distinction between the notion of sets (data types) and that of logical formulae. The type system has good proof theoretic properties (Church Rosser, ....
[Article contains additional citation context not shown here]
Z. Luo. An Extended Calculus of Constructions. PhD thesis, University of Edinburgh, 1990. Also as Report CST-65-90/ECS-LFCS-90-118, Department of Computer Science, University of Edinburgh.
Inductive Data Types: Well-ordering Types Revisited - Goguen, Luo (1992) (4 citations) Self-citation (Luo) (Correct)
....extensionality, the filling up rules provide sufficient uniqueness conditions (perhaps called weak extensionality) so that the representations of inductive types by W types are faithful. Based on this observation, we consider incorporating W types into the Extended Calculus of Constructions [Luo90a] and show that a large class of inductive data types can be faithfully represented by W types with the help of filling up rules. Filling up equality rules are not viewed as computational (or definitional) Their introduction may have certain side effects: in particular, some metatheoretic ....
....particular approach we have taken in developing type theories for this is based on the idea that, even in type theory, there should be a distinction between the notions of logical formula and data type. This idea has been reflected in the development of the Extended Calculus of Constructions (ECC) [Luo90a], where higher order logical propositions reside in the impredicative universe (c.f. the calculus of constructions [CH88] while the data types (or sets) reside in the predicative universes. As in Martin Lof s type theory, the predicative universes are supposed to be open in the sense that new ....
[Article contains additional citation context not shown here]
Z. Luo. An Extended Calculus of Constructions. PhD thesis, University of Edinburgh, 1990. Also as Report CST-65-90/ECS-LFCS-90118, Department of Computer Science, University of Edinburgh.
Coercive Subtyping - Luo (1995) (2 citations) Self-citation (Luo) (Correct)
....in the presence of subtyping, the usual elimination rules for inductive types become inadequate since they do not take into the account (the forms of) the canonical objects in the subtypes. For instance, subtyping between two Sigma types as found in the Extended Calculus of Constructions (ECC) [25, 26] is not quite compatible with the general elimination rules as found in Martin Lof s type theory and UTT. A simple combination would lead to a system for which the subject reduction property fails to hold (see Section 4.3) In general, there are two notions of subtyping that have been studied in ....
....can then be generalised to other (structured) types. Judgements and their meaning explanation When subtyping is introduced, a type theory does not have the property of unique typing (type uniqueness) anymore. Instead, a notion of principal typing is the best that one can expect (see, eg, [26] for a definition of the notion of principal type for ECC) Intuitively, K is a principal kind of object k if and only if k is of kind K and, for any kind K 0 , k is of kind K 0 if and only if K is a subkind of K 0 . Note that being a principal kind is more than just being a minimal or ....
[Article contains additional citation context not shown here]
Z. Luo. An Extended Calculus of Constructions. PhD thesis, University of Edinburgh, 1990. Also as Report CST-65-90/ECS-LFCS-90-118, Department of Computer Science, University of Edinburgh.
Coercive Subtyping in Type Theory - Luo (1996) (8 citations) Self-citation (Luo) (Correct)
....presence of subtyping, the usual elimination rules for inductive types become inadequate since they do not take into the account (the forms of) the canonical objects in the subtypes. For instance, subtyping between two Sigma types as found in the Extended Calculus of Constructions (ECC) Luo89, Luo90] is not quite compatible with the general elimination rules as found in Martin Lof s type theory and UTT. A simple combination would lead to a system for which the subject reduction property fails to hold (see Section 4.3) 3.1.2 Coercive subtyping: informal explanation There are two basic ....
....will then be generalised to other (structured) types. Judgements and their meaning explanation When subtyping is introduced, a type theory does not have the property of unique typing (type uniqueness) anymore. Instead, a notion of principal typing is the best that one can expect (see, eg, Luo90] for a definition of the notion of principal type for ECC) Intuitively, K is a principal kind of object k if and only if k is of kind K and, for any kind K 0 , k is of kind K 0 if and only if K is a subkind of K 0 . Note that being a principal kind is more than just being a minimal or ....
[Article contains additional citation context not shown here]
Z. Luo. An Extended Calculus of Constructions. PhD thesis, University of Edinburgh, 1990. Also as Report CST-65-90/ECS-LFCS-90-118, Department of Computer Science, University of Edinburgh.
Online articles have much greater impact More about CiteSeer.IST Add search form to your site Submit documents Feedback
CiteSeer.IST - Copyright Penn State and NEC