Abstract
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.
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Luo, Y., Luo, Z., Soloviev, S. (2003). Weak Transitivity in Coercive Subtyping. In: Geuvers, H., Wiedijk, F. (eds) Types for Proofs and Programs. TYPES 2002. Lecture Notes in Computer Science, vol 2646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39185-1_13
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DOI: https://doi.org/10.1007/3-540-39185-1_13
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