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# tff.federated_reduce

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.

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