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Reduces value from tff.CLIENTS to tff.SERVER using a reduction op.


This method reduces a set of member constituents of a value of federated type T@CLIENTS for some T, using a given zero in the algebra (i.e., the result of reducing an empty set) of some type U, and a reduction operator op with type signature (<U,T> -> U) that incorporates a single T-typed member constituent of value into the U-typed result of partial reduction. In the special case of T equal to U, this corresponds to the classical notion of reduction of a set using a commutative associative binary operator. The generalized reduction (with T not equal to U) requires that repeated application of op to reduce a set of T always yields the same U-typed result, regardless of the order in which elements of T are processed in the course of the reduction.


  • value: A value of a TFF federated type placed at the tff.CLIENTS.
  • zero: The result of reducing a value with no constituents.
  • op: An operator with type signature (<U,T> -> U), where T is the type of the constituents of value and U is the type of zero to be used in performing the reduction.


A representation on the tff.SERVER of the result of reducing the set of all member constituents of value using the operator op into a single item.


  • TypeError: if the arguments are not of the types specified above.