Essays/Reflexive
< Essays
Jump to navigation
Jump to search
The monad f~ y is defined to be y f y . Such usage also occurs in natural languages, for example self-made billionaire in English or je m'appelle Roger in French. The following are some examples of the reflexive:
+~ double *~ square /:~ sort ?~ n random permutation of order n p}~i.#p the inverse of permutation p i.~ a more efficient form of self-classify; see Index in Nub {./.~ nub #/.~ frequencies corresponding to the nub; see Histogram i.@# = i.~ nub sieve (the monad ~:) i.~ = i:~ nub sieve #~ i.~ = i:~ unique items (nub) i.&>~@[ i.&|: i.&> index-of for an inverted table i.&>~ e.&|: i.&>~@] member-of for an inverted table ~:@|:@:(i.&>)~ nub sieve for an inverted table f/~ function table =/~ n$0 1 n by n checkerboard >:@#.~/.~&.q: sum of divisors (f g) y ↔ y (f g) y ↔ (f g)~ y fib=: 3 : 0 " 0
mp=. +/ .*
{.{: mp/ mp~^:(I.|.#:y) 2 2$0 1 1 1x
)the i-th Fibonacci number stdarg =: i.@{:@$ , ,:^:(1: -: #@$)
pvp =: ~. @ (,/) @ ({"1/~)
subgroup=: pvp^:_ @ stdargsubgroup generated by a set of permutations;
see Symmetric Array
Contributed by Roger Hui.