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 *~ /:~ 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 {./.~ #/.~ 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 (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^:_ @ stdarg subgroup generated by a set of permutations; see Symmetric Array

Contributed by RogerHui.

Essays/Reflexive (last edited 2010-02-08 23:58:40 by RogerHui)