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How should one introduce subtyping into type theories with canonical objects such as Martin-Löf's type theory? It is known that the usual subsumptive subtyping is inadequate and it is understood, at least theoretically, that coercive subtyping should instead be employed. However, it has not been studied what the proper coercive subtyping mechanism is and how it should be used to capture intuitive notions of subtyping. In this paper, we introduce a type system with signatures where coercivedoi:10.4230/lipics.types.2016.13 dblp:conf/types/LunguL16 fatcat:cgf77i6v4bd7nen3up5kjuu5nq