If we apply some simple definitions to terms, HTML is a valid language to use for this. (i.e. Program: Series of instructions to be executed. HTML thusly instructs the interpreter to write the code.)
code segment ; Start of the code
assume cs:code ; Load code segment register
org 100h ; and set program up as a .COM file
start:
assume cs:code
mov ax, 1 ; Start at 1
loop:
call outdec ; Output the AX register
inc ax ; next value
cmp ax, 10 ; Above 10 yet?
jle loop
mov al, 0
mov ah, 4Ch
int 21h ; Exit
; ******************************** ;
outdec:
push ax ; save AX
mov bx, 10 ; divisor
mov cx, 3 ; # characters
convloopd:
mov dx, 0 ; zero high word for div
div bx ; divide by 10
add dl, 30h ; convert remainder to char
push dx ; Save character
loop convloopd ; do it til cx = 0
mov cx, 3 ; start another loop
outloopd:
pop dx ; get the character
mov ah, 02h ; output character fcn
int 21h ; output it
loop outloopd
mov ah, 02h
mov dl, ' '
int 21h ; output 2 spaces
int 21h
pop ax ; restore original number
ret
code ends
end start
First, let's implement a datatype for storing integers.
> data IntType = Zero
> | Succ IntType
> | Pred IntType
> deriving Eq
Then we'll want to implement comparison for integers.
> instance Ord IntType where
> compare (Pred xt) (Pred yt) = compare xt yt
> compare (Pred _) _ = LT
> compare _ (Pred _) = GT
> compare Zero Zero = EQ
> compare (Succ xt) (Succ yt) = compare xt yt
> compare (Succ _) _ = GT
> compare _ (Succ _) = LT
Integers should be enumerable too...
> instance Enum IntType where
> toEnum 0 = Zero
> toEnum n = accume n Zero
> where accume 0 k = k
> accume n k
> | n < 0 = accume (n+1) (Pred k)
> | n > 0 = accume (n-1) (Succ k)
> fromEnum k = adder 0 k
> where adder n Zero = n
> adder n (Pred kt) = adder (n-1) kt
> adder n (Succ kt) = adder (n+1) kt
> succ (Pred kt) = kt
> succ k = Succ k
> pred (Succ kt) = kt
> pred k = Pred k
> enumFrom x = iterate succ x
> enumFromTo x y
> | x == y = [x]
> | otherwise = x : enumFromTo (succ x) y
And we need to perform arithmetic.
> instance Num IntType where
> x + Zero = x
> Zero + y = y
> (Pred xt) + y = xt + pred y
> (Succ xt) + y = xt + succ y
> x - Zero = x
> x - (Pred yt) = succ x - yt
> x - (Succ yt) = pred x - yt
> Zero * y = Zero
> (Pred xt) * y = xt * y - y
> (Succ xt) * y = xt * y + y
> abs x@(Pred _) = Zero - x
> abs x = x
> signum (Pred _) = Pred Zero
> signum (Succ _) = Succ Zero
> signum Zero = Zero
> fromInteger n = accume n Zero
> where accume 0 k = k
> accume n k
> | n < 0 = accume (n+1) (Pred k)
> | n > 0 = accume (n-1) (Succ k)
They must be an instance of Real in order to be an instance of
Integral.
> instance Real IntType where
> toRational = toRational . toInteger
Our integers are indeed integral :-)
> instance Integral IntType where
> quotRem Zero _ = (Zero, Zero)
> quotRem n d = appsig (signum n * signum d) (foo n d)
> where appsig k (q,r) = (k*q, k*r)
> foo n d = countup (abs n) (abs d) Zero
> countup n@(Pred _) d c
> = (pred c, n + d)
> countup n d c
> = countup (n - d) d (succ c)
> toInteger k = acc 0 k
> where acc n Zero = n
> acc n (Pred kt) = acc (n-1) kt
> acc n (Succ kt) = acc (n+1) kt
Finally, implement an instance of the Show class, for converting
integers to strings.
> instance Show IntType where
> show n | n == Zero = "0"
> | n < Zero = '-' : show (negate n)
> | n > Zero = onshow n ""
> where ten = Succ $ Succ $ Succ $ Succ $ Succ five
> five = Succ $ Succ $ Succ $ Succ $ Succ Zero
> onshow Zero s = s
> onshow k s = let (q,r) = quotRem k ten
> in onshow q (charate r : s)
> charate Zero = '0'
> charate (Succ kt) = succ (charate kt)
Might as well show off that it works...
> greaterroot :: IntType -> IntType
> greaterroot n = head [k | k <- [Zero ..], k * k >= n]
Finally, our main function! Make a list of perfect squares from Zero
to (Succ (Succ (Succ ... (one hundred times) ... (Succ Zero) ... ))),
then find their square roots, and output them!
> main :: IO ()
> main =
> mapM_ (putStrLn . show) $ map greaterroot squares
> where squares = map (\x -> x*x) [one .. ten]
> one = Succ Zero
> two = one + one
> five = two + two + one
> ten = two * five
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