d0=: -:&(/:~) 

Are x and y permutations of each other?

m1=: /:~-:i.@#

Is y a permutation vector?

m2=: -:-@|:

Is y antisymmetric?

m3=: -:|:

Is y symmetric?

m4=: [:+./[:*./]=/0 1"_

Are all atoms of Boolean list y equal?

m5=: *./ .= +./

Are all atoms of Boolean list y equal?

m6=: *./ .= *./

Are all atoms of Boolean list y equal?

d7=: -.@(] <:/ .>: >.@] , [)"1

Is y in the half open on the right interval x and is it an integer?

d8=: e.

Is list x a row of array y?

m9=: *./@(= >./\)

Are columns of y in ascending order?

m10=: *./@(= <./\)

Are columns of y in descending order?

m11=: >./=<./

Are atoms of numerical list y equal?

m12=: *./ +. -.@(+./)

Are atoms of Boolean list y equal?

m13=: *./ = +./

Are atoms of Boolean list y equal?

m14=: *./@(= {.)

Are atoms of list y equal?

m15=: 0:=#|+/

Are atoms of Boolean list y equal?

m16=: *./@(#1&|.)

Are atoms of Boolean list y equal?

m17=: ([:,:0:,#)-: v19"_ rxmatch ]

Is y a legal J name?

d18=: rxmatch=: 17!:0

'' to get rxmatch

v19=: '[[:alpha:]][[:alnum:]_]* '"_

'regex' to get alpha: and alnum: