[FoRK] 125 years of map-reduce (or, Elementarzahlung vom höheren Standpunkt aus)

Dave Long dave.long at bluewin.ch
Sun Aug 31 06:58:09 PDT 2014

> Dedekind's Bedingung II is (at least with the benefit of post-1931  
> hindsight) the mapping; his III (pointlessly: ψS=θψ), the  
> reduction.

We also have an anticipation of functional programming in axiomatic  
set theory.

Zermelo (the Z in ZF) had, ca. 1900, the Ausonderungsaxiom (given a  
set and a predicate, we can construct a subset) and the  
Vereinigungsaxiom (given a set of sets, we can construct the set of  
the contents of the subsets); to these Fraenkel (the F in ZF) added,  
ca. 1920, the Ersetzungsaxiom (given a set and a function, we can  
construct an image set).

With the benefit of hindsight we could now call these (specific  
instances of) filtering, reduction, and mapping.


Exercise: demonstrate that the Aussonderungsaxiom follows from the  
other two (alternatively, implement filter with join and map)

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