Coherence and Transitivity in Coercive Subtyping

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.

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