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Abstract: We propose and study coercive subtyping, a formal extension with subtyping of dependent type theories such as Martin-Lof's type theory [38] and the type theory UTT [30]. In this approach, subtyping with specified implicit coercions is treated as a feature at the level of the logical framework; in particular, the meaning of an object being in a supertype is given by coercive definition rules for the definitional equality. This provides a conceptually simple and uniform framework to understand... (Update)
Context of citations to this paper: More
.... The use of implicit coercions or subtyping in proof checking has been considered by several authors (see [1, 3, 4] for the former and [2, 5, 14, 15] for the latter) In [4] the author reports on a medium scale example of formalisation of mathematics using implicit coercions....
...test is made, k] is a valid path in the graph, but the path [h; k] is ignored. Another difference is that in [5] and also [10]) the theory is extended by adding coercions related inference rules, and a new computation rule for insertion of coercions. They then study the...
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Typing Algorithm in Type Theory with Inheritance - Saïbi (Correct)
Implicit Coercions in Type Systems - Barthe (1995) (Correct)
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BibTeX entry: (Update)
Z. Luo. Coercive subtyping. Draft, 1995. http://citeseer.ist.psu.edu/luo95coercive.html More
@article{ luo99coercive,
author = "Zhaohui Luo",
title = "Coercive Subtyping",
journal = "Journal of Logic and Computation",
volume = "9",
number = "1",
pages = "105-130",
year = "1999",
url = "citeseer.ist.psu.edu/luo95coercive.html" }
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434 A framework for defining logics - Harper, Honsell et al. - 1987
382 Lambda calculi with types - Barendregt - 1992
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266 Information and Computation (context) - Coquand, Huet et al. - 1988
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191 LEGO Proof Development System: User's Manual (context) - Luo, Pollack - 1992
143 Foundations of Constructive Mathematics (context) - Beeson - 1985
95 an extended calculus of constructions - Luo - 1989
85 The ALF proof editor and its proof engine (context) - Magnusson, Nordstrom - 1994
84 Computation and Reasoning: A Type Theory for Computer Scienc.. (context) - Luo - 1994
81 Information and Computation (context) - Bruce, Longo et al. - 1990
79 Pattern matching with dependent types (context) - Coquand - 1992
72 The Theory of LEGO: A Proof Checker for the Extended Calculu.. - Pollack - 1994
62 Programming in Martin-Lof's Type Theory: An Introduction (context) - Nordstrom, Petersson et al. - 1990
41 Inductive sets and families in Martin-Lof's type theory and .. - Dybjer - 1991
40 Subtyping dependent types - Aspinall, Compagnoni - 1996
39 A Typed Operational Semantics for Type Theory (context) - Goguen - 1994
33 Deliverables: a categorical approach to program development .. - Burstall, McKinna - 1992
25 Program specification and data refinement in type theory - Luo - 1993
25 The Machine-checked Literate Formalisation of Algebra in Typ.. (context) - Bailey - 1998
24 A higher-order calculus and theory abstraction - Luo - 1991
23 Typing algorithm in type theory with inheritance (context) - Saibi - 1997
18 Analytic and synthetic judgements in type theory (context) - Martin-Lof - 1994
17 record types and subtyping in type theory (context) - Tasistro - 1997
17 Lecture Notes in Computer Science (context) - Coquand, Paulin-Mohring et al. - 1990
16 Mathematical vernacular and conceptual wellformedness in mat.. - Luo, Callaghan - 1997
15 Some proof-theoretic and algorithmic aspects of coercive sub.. (context) - Jones, Luo et al. - 1997
15 A logic of subtyping - Longo, Milsted et al. - 1995
14 Lego with implicit coercions (context) - Bailey - 1996
14 Type-checking dependent types and subtypes (context) - Cardelli - 1988
11 A unifying theory of dependent types: the schematic approach (context) - Luo - 1992
9 The undecidability of typability in the lambda-Pi calculus (context) - Dowek - 1993
9 Information and Computation (context) - Breazu-Tannen, Coquand et al. - 1991
9 Simple overloading for type theories (context) - Aczel - 1994
6 The Coq Proof Assistent: User's Guide (context) - Dowek - 1991
4 Also as Report CST-65-90/ECS-LFCS-90-118 (context) - Luo, Calculus et al. - 1990
3 FME'97: Industrial Applications and Strengthened Foundations.. (context) - Yu, Luo et al. - 1997
2 Extended Calculus of Constructions as a specification langua.. (context) - Burstall - 1993
2 TAPSOFT'97: Theory and Practice of Software Development (context) - Schreiber, recursive - 1997
2 Preliminary Proceedings of BRA Workshop on Types and Proofs (context) - Pfenning, for - 1993
2 Developing reuse technology in proof engineering - Luo - 1995
1 Implicit coercions in type systems (context) - Barthes - 1996
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