Matrix multiplication in FP

def MM = (applyall applyall IP) . (applyall distl) . distr . [1, trans.2]

def IP = (/+) . (applyall mul) . trans

where

( e is empty sequence, # is buttom)

trans:x == x = < e , .. e > -> e;
           x = <x1,..xn> -> <y1,..ym>; #
  where
  xi = <xi1,...xim> and yj = <x1j,..xnj>

distl:x == x = <y,e> -> e;
           x = <y,<z1,..zn>> -> <<y,z1>,...<y,zn>>; #

distr:x == x = <y,e> -> e;
           x = <<y1,..yn>,z> -> <<y1,z>,...<yn,z>>; #

example
trans:<<1,2,3>, <4,5,6>> = <<1,4>,<2,5>,<3,6>>
distl:<sq,<1,2,3>> = <<sq,1>,<sq,2>,<sq,3>>
distr:<<single,double,triple>,10> = <<single,10>,<double,10>,<triple,10>>