173 lines
3.7 KiB
AppleScript
173 lines
3.7 KiB
AppleScript
on run
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take(25, weirds())
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-- Gets there, but takes about 6 seconds on this system,
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-- (logging intermediates through the Messages channel, for the impatient :-)
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end run
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-- weirds :: Gen [Int]
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on weirds()
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script
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property x : 1
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property v : 0
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on |λ|()
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repeat until isWeird(x)
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set x to 1 + x
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end repeat
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set v to x
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log v
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set x to 1 + x
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return v
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end |λ|
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end script
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end weirds
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-- isWeird :: Int -> Bool
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on isWeird(n)
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set ds to descProperDivisors(n)
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set d to sum(ds) - n
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0 < d and not hasSum(d, ds)
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end isWeird
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-- hasSum :: Int -> [Int] -> Bool
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on hasSum(n, xs)
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if {} ≠ xs then
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set h to item 1 of xs
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set t to rest of xs
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if n < h then
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hasSum(n, t)
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else
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n = h or hasSum(n - h, t) or hasSum(n, t)
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end if
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else
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false
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end if
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end hasSum
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-- GENERIC ------------------------------------------------
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-- descProperDivisors :: Int -> [Int]
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on descProperDivisors(n)
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if n = 1 then
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{1}
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else
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set realRoot to n ^ (1 / 2)
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set intRoot to realRoot as integer
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set blnPerfect to intRoot = realRoot
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-- isFactor :: Int -> Bool
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script isFactor
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on |λ|(x)
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n mod x = 0
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end |λ|
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end script
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-- Factors up to square root of n,
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set lows to filter(isFactor, enumFromTo(1, intRoot))
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-- and cofactors of these beyond the square root,
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-- integerQuotient :: Int -> Int
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script integerQuotient
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on |λ|(x)
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(n / x) as integer
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end |λ|
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end script
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set t to rest of lows
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if blnPerfect then
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set xs to t
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else
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set xs to lows
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end if
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map(integerQuotient, t) & (reverse of xs)
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end if
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end descProperDivisors
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-- enumFromTo :: (Int, Int) -> [Int]
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on enumFromTo(m, n)
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if m ≤ n then
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set lst to {}
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repeat with i from m to n
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set end of lst to i
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end repeat
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return lst
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else
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return {}
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end if
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end enumFromTo
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-- filter :: (a -> Bool) -> [a] -> [a]
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on filter(f, xs)
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tell mReturn(f)
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set lst to {}
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set lng to length of xs
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repeat with i from 1 to lng
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set v to item i of xs
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if |λ|(v, i, xs) then set end of lst to v
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end repeat
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return lst
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end tell
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end filter
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-- foldl :: (a -> b -> a) -> a -> [b] -> a
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on foldl(f, startValue, xs)
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tell mReturn(f)
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set v to startValue
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set lng to length of xs
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repeat with i from 1 to lng
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set v to |λ|(v, item i of xs, i, xs)
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end repeat
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return v
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end tell
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end foldl
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-- map :: (a -> b) -> [a] -> [b]
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on map(f, xs)
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tell mReturn(f)
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set lng to length of xs
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set lst to {}
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repeat with i from 1 to lng
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set end of lst to |λ|(item i of xs, i, xs)
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end repeat
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return lst
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end tell
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end map
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-- sum :: [Num] -> Num
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on sum(xs)
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script add
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on |λ|(a, b)
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a + b
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end |λ|
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end script
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foldl(add, 0, xs)
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end sum
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-- take :: Int -> Gen [a] -> [a]
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on take(n, xs)
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set ys to {}
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repeat with i from 1 to n
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set v to xs's |λ|()
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if missing value is v then
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return ys
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else
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set end of ys to v
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end if
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end repeat
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return ys
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end take
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-- Lift 2nd class handler function into 1st class script wrapper
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-- mReturn :: First-class m => (a -> b) -> m (a -> b)
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on mReturn(f)
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if script is class of f then
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f
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else
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script
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property |λ| : f
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end script
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end if
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end mReturn
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