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Constructor subtyping in the Calculus of Inductive Constructions
 Proceedings of FOSSACS'00, LNCS 1784
, 2000
"... The Calculus of Inductive Constructions (CIC) is a powerful type system, featuring dependent types and inductive definitions, that forms the basis of proofassistant systems such as Coq and Lego. We extend CIC with constructor subtyping, a basic form of subtyping in which an inductive type &sigm ..."
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Cited by 6 (0 self)
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The Calculus of Inductive Constructions (CIC) is a powerful type system, featuring dependent types and inductive definitions, that forms the basis of proofassistant systems such as Coq and Lego. We extend CIC with constructor subtyping, a basic form of subtyping in which an inductive type &sigma; is viewed as a subtype of another inductive type &tau; if &tau; has more elements than &sigma;. It is shown that the calculus is wellbehaved and provides a suitable basis for formalizing natural semantics in proofdevelopment systems.
Weak Transitivity in Coercive Subtyping
 TYPES FOR PROOFS AND PROGRAMS, VOLUME 2646 OF LNCS
, 2001
"... Coercive subtyping is a general approach to subtyping, inheritance and abbreviation in dependent type theories. A vital requirement for coercive subtyping is that of coherence which essentially says that coercions between any two types must be unique. Another important task for coercive subtyping is ..."
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Cited by 4 (4 self)
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Coercive subtyping is a general approach to subtyping, inheritance and abbreviation in dependent type theories. A vital requirement for coercive subtyping is that of coherence which essentially says that coercions between any two types must be unique. Another important task for coercive subtyping is to prove the admissibility or elimination of transitivity and substitution. In this paper, we propose and study the notion of Weak Transitivity, consider suitable subtyping rules for certain parameterised inductive types and prove its coherence and the admissibility of substitution and weak transitivity in the coercive subtyping framework.
Combining Incoherent Coercions for Σtypes
"... Coherence is a vital requirement for the correct use of coercive subtyping for abbreviation and other applications. However, some coercions are incoherent, although very useful. A typical example of such is the subtyping rules for types: the componentwise rules and the rule of the rst projecti ..."
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Coherence is a vital requirement for the correct use of coercive subtyping for abbreviation and other applications. However, some coercions are incoherent, although very useful. A typical example of such is the subtyping rules for types: the componentwise rules and the rule of the rst projection. Both of these groups of rules are often used in practice (and coherent themselves), but they are incoherent when put together directly. In this paper, we study this case for types by introducing a new subtyping relation and the resulting system enjoys the properties of coherence and admissibility of substitution and transitivity.
Under consideration of Math. Struct. in Comp. Science Structural subtyping for inductive types with functorial equality rules ∗
, 2006
"... Subtyping for inductive types in dependent type theories is studied in the framework of coercive subtyping. General structural subtyping rules for parameterised inductive types are formulated based on the notion of inductive schemata. Certain extensional equality rules play an important role in prov ..."
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Subtyping for inductive types in dependent type theories is studied in the framework of coercive subtyping. General structural subtyping rules for parameterised inductive types are formulated based on the notion of inductive schemata. Certain extensional equality rules play an important role in proving some of the crucial properties of the type system with these subtyping rules. In particular, it is shown that the structural subtyping rules are coherent and that transitivity is admissible in the presence of the functorial rules of computational equality. 1.
Generic H A SKELL, SPECIFICALLY
"... SKELL exploits the promising new incarnation of generic programming due to Hinze. Apart from extending the programming language Haskell, Hinzestyle polytypism offers a simple approach to defining generic functions which are applicable to types of all kinds. Here we explore a number of simple but si ..."
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SKELL exploits the promising new incarnation of generic programming due to Hinze. Apart from extending the programming language Haskell, Hinzestyle polytypism offers a simple approach to defining generic functions which are applicable to types of all kinds. Here we explore a number of simple but significant extensions to Hinze’s ideas which make generic programming both more expressive and easier to use. We illustrate our ideas with examples.
Constructor Subtyping (extended Version)
, 1999
"... Constructor subtyping is a form of subtyping in which an inductive type sigma is viewed as a subtype of another inductive type tau if tau has more constructors than sigma. As suggested in [5, 12], its (potential) uses include proof assistants and functional programming languages. In this report, we ..."
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Constructor subtyping is a form of subtyping in which an inductive type sigma is viewed as a subtype of another inductive type tau if tau has more constructors than sigma. As suggested in [5, 12], its (potential) uses include proof assistants and functional programming languages. In this report, we introduce and study the properties of a simply typed lambdacalculus with record types and datatypes, and which supports record subtyping and constructor subtyping. We show that the calculus is conuent and strongly normalizing. We also show that the typechecking is decidable.