Haar wavelet transform in Factor

Here is the Haar wavelet transform implemented in Factor. This is only the 1-dimensional version:

: averages ( seq -- seq )
    [ first2 + 2 / ] map ;

: differences ( seq averages -- differences )
    >r 0 <column> r> [ - ] 2map ;

: haar-step ( seq -- differences averages )
    2 group dup averages [ differences ] keep ;

: haar ( seq -- seq )
    dup length 1 <= [ haar-step haar swap append ] unless ;