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The `TypeInference` dialect provides three operations. The operation `TypeInference.propagate_downwards` respresents a type barrier, which is supposed to forward the type of its operand as its result type during type inference. The operation `TypeInference.propagate_upwards` also respresents a type barrier, but is supposed to forward the type of its result as the type for its operand during type inference. The operation `TypeInference.unresolved_conflict` can be used as a marker when two different types have beed inferred for a value (e.g., one type during forward dataflow analysis and the other during backward dataflow analysis)