Here is what they say in the introduction of the second paper: Bidirectional propagation of type information allows the types of parameters of anonymous functi

Here is what they say in the introduction of the second paper: Bidirectional propagation of type information allows the types of parameters of anonymous functions to be inferred. When an anonymous function appears as an argument to another function, the expected domain type is used as the expected type for the anonymous abstraction, allowing the type annotations on its parameters to be omitted. A similar, but even simpler, technique infers type annotations on local variable bindings. From this I gather it means syntactically bidirectional. (But I don't understand this really, so someone should correct me :P)