Programming in Martin-Lo¨f's type theory: an introduction
Programming in Martin-Lo¨f's type theory: an introduction
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
Some Algorithmic and Proof-Theoretical Aspects of Coercive Subtyping
TYPES '96 Selected papers from the International Workshop on Types for Proofs and Programs
Coercive Subtyping in Type Theory
CSL '96 Selected Papers from the10th International Workshop on Computer Science Logic
Transitivity in coercive subtyping
Information and Computation
Weak transitivity in coercive subtyping
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
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Coercive subtyping is a general approach to subtyping, inheritance and abbreviation in dependent type theories. A vital requirement for coercive subtypingis that of coherence - computational uniqueness of coercions between any two types. In this paper, we develop techniques useful in proving coherence and its related result on admissibility of transitivity and substitution. In particular, we consider suitable subtyping rules for Π-types and Σ-types and prove its coherence and the admissibility of substitution and transitivity rules at the type level in the coercive subtyping framework.