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Ran 20 Jan 2020 01:50AM UTC

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Committed 20 Jan 2020 01:40AM UTC coverage: 92.761% (+20.1%) from 72.636%

Job # 1219.2

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push

travis-ci-com

Committed by

mergify[bot]

Commit Message

Generic `Reduced` handling in parallel reduce (#172)

Previously, `Reduced` did not have a meaningful behavior in parallel
`reduce` when the reducing function is not `right`:

    julia> tcollect(TakeWhile(x -> x < 5), 1:10; basesize=1)
    Empty{Array{T,1} where T}()

    julia> tcollect(TakeWhile(x -> x < 5), 1:10; basesize=2)
    1-element Array{Int64,1}:
     4

    julia> tcollect(TakeWhile(x -> x < 5), 1:10; basesize=4)
    2-element Array{Int64,1}:
     3
     4

    julia> tcollect(TakeWhile(x -> x < 5), 1:10; basesize=5)
    4-element Array{Int64,1}:
     1
     2
     3
     4

This PR fixes it by properly formulating how to execute the reducing
function when combined with `Reduced`.  This is done by "augmenting"
the reducing function `*`:

Given a semigroup `*(::T, ::T) :: T` where `!(Reduced <: T)`, fold
functions in Transducers.jl act on an "augmented" semigroup
`*′(::T′, ::T′) :: T′` where `T′ = Union{T, Reduced{T}}` defined by

    *′(a::Reduced, _) = a
    *′(a::T, b::Reduced) = reduced(a * unreduced(b))
    *′(a::T, b::T) = a * b

If `*` is a monoid with the identity element `e`, the "augmented"
semigroup `*′` is also a monoid with the identity element `e′`.

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