109 lines
2.4 KiB
AppleScript
109 lines
2.4 KiB
AppleScript
-- PERFECT NUMBERS -----------------------------------------------------------
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-- perfect :: integer -> bool
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on perfect(n)
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-- isFactor :: integer -> 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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-- quotient :: number -> number
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script quotient
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on |λ|(x)
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n / x
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end |λ|
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end script
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-- sum :: number -> number -> number
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script sum
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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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-- Integer factors of n below the square root
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set lows to filter(isFactor, enumFromTo(1, (n ^ (1 / 2)) as integer))
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-- low and high factors (quotients of low factors) tested for perfection
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(n > 1) and (foldl(sum, 0, (lows & map(quotient, lows))) / 2 = n)
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end perfect
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-- TEST ----------------------------------------------------------------------
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on run
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filter(perfect, enumFromTo(1, 10000))
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--> {6, 28, 496, 8128}
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end run
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-- GENERIC FUNCTIONS ---------------------------------------------------------
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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 d to -1
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else
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set d to 1
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end if
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set lst to {}
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repeat with i from m to n by d
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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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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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-- Lift 2nd class handler function into 1st class script wrapper
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-- mReturn :: Handler -> Script
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on mReturn(f)
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if class of f is script 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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