{

An n-digit number which is the sum of the n-th powers of its digits is called an
n-narcissistic number.
The smallest example other than the trivial 1-digit numbers is (n=3)

    153 = 1*1*1 + 5*5*5 + 3*3*3

There are 88 known (and theoretically possible) n-narcissistic numbers, the
largest with n = 39. 

For a very nice descrition of narcissistic numbers see
    http://mathworld.wolfram.com/NarcissisticNumber.html

Here we present sample code to calculate all narcissistic numbers of 3 digits up
to 8 digits. It is easy to generalize the code to calculate all 88 numbers, but
beware the it can take VERY long time to calculate.

Sample query:
To calculate all 6 digit narcissistic numbers, run the query
    
    all  Narcissistic(6)

}

Digit = L[0..9]
DigitNZ = L[1..9]   //No leading zero


pred Narcissistic(n:<I[3..8]) iff
    if n = 3 then 
         Narcissistic3()
    elsif n = 4 then
         Narcissistic4()
    elsif n = 5 then
         Narcissistic5()
    elsif n = 6 then
         Narcissistic6()
    elsif n = 7 then
         Narcissistic7()
    elsif n = 8 then
         Narcissistic8()
    end

pred Narcissistic3() iff
    a::DigitNZ & b::Digit & c::Digit & 
    100*a + 
    10*b + 
    c = Pow(3,a) + Pow(3,b) + Pow(3,c) & 
    Print(a,b,c)


pred Narcissistic4() iff
    a::DigitNZ & b::Digit & c::Digit & d::Digit & 
    1000*a + 
    100*b + 
    10*c + 
    d = Pow(4,a) + Pow(4,b) + Pow(4,c) + Pow(4,d) &
    Print(a,b,c,d)


pred Narcissistic5() iff
    a::DigitNZ & b::Digit & c::Digit & d::Digit & e::Digit & 
    10000*a + 
    1000*b + 
    100*c + 
    10*d +
    e = Pow(5,a) + Pow(5,b) + Pow(5,c) + Pow(5,d) + Pow(5,e) &
    Print(a,b,c,d,e)

pred Narcissistic6() iff
    a::DigitNZ & b::Digit & c::Digit & d::Digit & e::Digit & f::Digit &
    100000*a + 
    10000*b + 
    1000*c + 
    100*d +
    10*e + 
    f = Pow(6,a) + Pow(6,b) + Pow(6,c) + Pow(6,d) + Pow(6,e) + Pow(6,f) &
    Print(a,b,c,d,e,f)

pred Narcissistic7()iff
    a::DigitNZ & b::Digit & c::Digit & d::Digit & e::Digit & f::Digit & g::Digit & 
    1000000*a + 
    100000*b + 
    10000*c + 
    1000*d +
    100*e + 
    10*f + 
    g = Pow(7,a) + Pow(7,b) + Pow(7,c) + Pow(7,d) + Pow(7,e) + Pow(7,f) + Pow(7,g) &
    Print(a,b,c,d,e,f,g)

pred Narcissistic8()iff
    a::DigitNZ & b::Digit & c::Digit & d::Digit & e::Digit & f::Digit & g::Digit & h::Digit &
    10000000*a + 
    1000000*b + 
    100000*c + 
    10000*d +
    1000*e + 
    100*f + 
    10*g + 
    h = Pow(8,a) + Pow(8,b) + Pow(8,c) + Pow(8,d) + Pow(8,e) + Pow(8,f) + Pow(8,g) + Pow(8,h) &
    Print(a,b,c,d,e,f,g,h)

// xout = xin**e
local proc Pow(e:<I,xin:<Digit,xout:>L) iff 
    if e = 1 then 
        xout = xin 
    else
        Pow(e-1,xin,xout1) & xout = xin*xout1
    end

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