Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
Inheritance as implicit coercion
Information and Computation
Computation and reasoning: a type theory for computer science
Computation and reasoning: a type theory for computer science
Typing algorithm in type theory with inheritance
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
An Implementation of LF with Coercive Subtyping & Universes
Journal of Automated Reasoning
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Coercive Subtyping in Type Theory
CSL '96 Selected Papers from the10th International Workshop on Computer Science Logic
Weak transitivity in coercive subtyping
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Coherence and Transitivity in Coercive Subtyping
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
Coercions in a polymorphic type system
Mathematical Structures in Computer Science
Coercive subtyping in lambda-free logical frameworks
Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice
A theory of typed coercions and its applications
Proceedings of the 14th ACM SIGPLAN international conference on Functional programming
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Coercive subtyping is a general approach to abbreviation and subtyping in dependent type theories with inductive types. Coherence and admissibility of transitivity are important both for understanding of the framework and for its correct implementation. In this paper, we study the issue of transitivity in the context of subtyping for parameterised inductive types. In particular, we propose and study the notion of weak transitivity and show that, for a large class of parameterised inductive types, the natural subtyping rules are coherent and weak transitivity is admissible in an intensional type theory. A possible extension of type theory with certain extensional computation rules is also discussed for achieving admissibility of transitivity in general.