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September 10, 2005 15:37Subject:

Hyper fmapMessage ID:

7ca3f01605091015376d8454ab@mail.gmail.comI think we should generalize the hyper stuff a little bit more. I want hyper operators serve as "fmap", or "functor map", rather than just list. This is a popular concept, and a pretty obvious generalization. A functor is any object $x on which you can do "fmap" such that it satisfies these laws: $x.fmap:{$_} eqv $x # identity maps to identity $x.fmap:{ f($_) }.fmap:{ g($_) } eqv $x.fmap:{ g(f($_)) } # transparent to composition Another way to think of a functor is just some sort of aggregate data structure, where "fmap" is what you use to do something to each of its elements. In order to do this, I want to desymmetricalize hyper operators again. That is, you put the arrows on the side of the operator you have the list (now functor). This is so that if you have a functor on either side of a hyper operator, it knows which side to map. Here's how it works: $x >>+ $y # $x.fmap:{ $_ + $y } $x +<< $y # $y.fmap:{ $x + $_ } +<< $x # $x.fmap:{ +$_ } foo(1, >>$x<<, 2) # $x.fmap:{ foo(1, $_, 2) } etc. For the current hyper semantics where (1,2,3) >>+<< (4,5,6) eqv (5,7,9), there is also a "binary functor". I call the mapping function fmap2 (but maybe we can find a better name). fmap2($a, $b, { $^x + $^y }) It takes a two argument function and two functors and returns the appropriate combination. Not all functors have to be binary functors (it's not clear that binary functors have to be regular functors either). $x >>+<< $y # fmap2($x, $y, &infix:<+>) Luke

**Hyper fmap**by Luke Palmer

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