The exclusion of tautologies as "a bit meta" points
to the definition of "natural" as "what John is used to" ;-)
It not surprising that [ and ] etc. occur often in forks,
because many functions are not symmetric wrt the
left and right arguments. For example, suppose
you want to model x|.y where x is a single number.
You'd expect the function to treat x and y differently,
and for that different treatment it'd have to first select
x and select y . Thus:
rot=: ] {~ #...@] | (+ i...@#@])
3 rot 'abcdefghij'
defghijabc
_2 rot 'abcdefghij'
ijabcdefgh
To find examples of the required forks, look for functions
that are symmetric (commutative).
----- Original Message -----
From: John Randall <[email protected]>
Date: Wednesday, February 4, 2009 5:31
Subject: Re: [Jprogramming] Examples of dyadic forks
To: Programming forum <[email protected]>
> Tracy Harms wrote:
>
> > [: would also be excluded; I'm sure John left it out only as
> an oversight.
> >
> > What John's looking for, I think, are "natural" examples where the
> > dyadic fork applies.
>
> This is right on the money. It is very easy to come up
> with monadic
> forks. Most dyadic forks seem degenerate, in that one of
> the tines is
> only applied to one argument. For example:
>
> cap=:e. # [
>
> 1 2 3 4 cap 4 3 5 6
> 3 4
>
> This is the intersection of two lists, in the order of the
> LHA. The fork
> is of the form (x f y ) g (y).
>
> The verb proj defines the projection of y onto x:
>
> mp=:+/ .*
> norm=:[: %: mp~
> proj=:mp % n...@[
>
> 3 4 proj 1 1
> 1.4
>
> Here proj has the form (x f y) g (h x).
>
> What I was trying to get at is that most dyadic forks one can
> think of do
> not use the full generality (x f y) g (x h y), and I was seeking
> "natural"examples which do.
>
> Best wishes,
>
> John
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