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## B.1 Pairwise

This `silly` code fragment is mentioned in Reduce, in the discussion of `reduce`, and is provided as an example of a solution to equations E1 to E3. It is written in the style of a higher order function, in that it takes a function `f` as an argument and returns another function, [[`pairwise`]] `f` as a result.

    self     = left
    argument = right
    head     = left
    tail     = right

    pairwise =

    compose(
       refer,
       compose(
          bu(
             conditional,
             conditional(argument,compose(tail,argument),constant nil)),
          couple(
             (hired couple)(
                (hired compose)(
                   identity,
                   constant (hired fan head)(
                      argument,
                      compose(tail,argument))),
                constant (hired meta)(
                   self,
                   compose(tail,compose(tail,argument)))),
             constant argument)))

To see how this works, one should evaluate it symbolically with an unknown `f`, which will result in some `silly` pseudocode, and then evaluate that symbolically with some sample lists.

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