Abstract : Core calculi that model the essence of computations use full reductionsemantics to be built on solid grounds. Expressive type systems forthese calculi may use propositions to refine the notion of types, whichallows abstraction over possibly inconsistent hypotheses. To preservetype soundness, reduction must then be delayed until logical hypotheseson which the computation depends have been proved consistent. Whenlogical information is explicit inside terms, proposition variablesdelay the evaluation by construction. However, logical hypotheses may beleft implicit, for the user's convenience in a surface language orbecause they have been erased prior to computation in an internallanguage. It then becomes difficult to track the dependencies ofcomputations over possibly inconsistent hypotheses.We propose anexpressive type system with implicit coercions, consistent andinconsistent abstraction over coercions, and assumption hiding, whichprovides a fine-grained control of dependencies between computations andthe logical hypotheses they depend on. Assumption hiding opens acontinuum between explicit and implicit use of hypotheses, and restoresconfluence when full and weak reductions are mixed.