160 lines
3.7 KiB
AppleScript
160 lines
3.7 KiB
AppleScript
-- ZECKENDORF NUMBERS --------------------------------------------------------
|
|
|
|
-- zeckendorf :: Int -> String
|
|
on zeckendorf(n)
|
|
script f
|
|
on |λ|(n, x)
|
|
if n < x then
|
|
[n, 0]
|
|
else
|
|
[n - x, 1]
|
|
end if
|
|
end |λ|
|
|
end script
|
|
|
|
if n = 0 then
|
|
{0} as string
|
|
else
|
|
item 2 of mapAccumL(f, n, |reverse|(just of tailMay(fibUntil(n)))) as string
|
|
end if
|
|
end zeckendorf
|
|
|
|
-- fibUntil :: Int -> [Int]
|
|
on fibUntil(n)
|
|
set xs to {}
|
|
set limit to n
|
|
|
|
script atLimit
|
|
property ceiling : limit
|
|
on |λ|(x)
|
|
(item 2 of x) > (atLimit's ceiling)
|
|
end |λ|
|
|
end script
|
|
|
|
script nextPair
|
|
property series : xs
|
|
on |λ|([a, b])
|
|
set nextPair's series to nextPair's series & b
|
|
[b, a + b]
|
|
end |λ|
|
|
end script
|
|
|
|
|until|(atLimit, nextPair, {0, 1})
|
|
return nextPair's series
|
|
end fibUntil
|
|
|
|
-- TEST ----------------------------------------------------------------------
|
|
on run
|
|
|
|
intercalate(linefeed, ¬
|
|
map(zeckendorf, enumFromTo(0, 20)))
|
|
|
|
end run
|
|
|
|
-- GENERIC FUNCTIONS ---------------------------------------------------------
|
|
|
|
-- enumFromTo :: Int -> Int -> [Int]
|
|
on enumFromTo(m, n)
|
|
if m > n then
|
|
set d to -1
|
|
else
|
|
set d to 1
|
|
end if
|
|
set lst to {}
|
|
repeat with i from m to n by d
|
|
set end of lst to i
|
|
end repeat
|
|
return lst
|
|
end enumFromTo
|
|
|
|
-- foldl :: (a -> b -> a) -> a -> [b] -> a
|
|
on foldl(f, startValue, xs)
|
|
tell mReturn(f)
|
|
set v to startValue
|
|
set lng to length of xs
|
|
repeat with i from 1 to lng
|
|
set v to |λ|(v, item i of xs, i, xs)
|
|
end repeat
|
|
return v
|
|
end tell
|
|
end foldl
|
|
|
|
-- 'The mapAccumL function behaves like a combination of map and foldl;
|
|
-- it applies a function to each element of a list, passing an
|
|
-- accumulating parameter from left to right, and returning a final
|
|
-- value of this accumulator together with the new list.' (see Hoogle)
|
|
|
|
-- mapAccumL :: (acc -> x -> (acc, y)) -> acc -> [x] -> (acc, [y])
|
|
on mapAccumL(f, acc, xs)
|
|
script
|
|
on |λ|(a, x)
|
|
tell mReturn(f) to set pair to |λ|(item 1 of a, x)
|
|
[item 1 of pair, (item 2 of a) & item 2 of pair]
|
|
end |λ|
|
|
end script
|
|
|
|
foldl(result, [acc, []], xs)
|
|
end mapAccumL
|
|
|
|
-- map :: (a -> b) -> [a] -> [b]
|
|
on map(f, xs)
|
|
tell mReturn(f)
|
|
set lng to length of xs
|
|
set lst to {}
|
|
repeat with i from 1 to lng
|
|
set end of lst to |λ|(item i of xs, i, xs)
|
|
end repeat
|
|
return lst
|
|
end tell
|
|
end map
|
|
|
|
-- Lift 2nd class handler function into 1st class script wrapper
|
|
-- mReturn :: Handler -> Script
|
|
on mReturn(f)
|
|
if class of f is script then
|
|
f
|
|
else
|
|
script
|
|
property |λ| : f
|
|
end script
|
|
end if
|
|
end mReturn
|
|
|
|
-- intercalate :: Text -> [Text] -> Text
|
|
on intercalate(strText, lstText)
|
|
set {dlm, my text item delimiters} to {my text item delimiters, strText}
|
|
set strJoined to lstText as text
|
|
set my text item delimiters to dlm
|
|
return strJoined
|
|
end intercalate
|
|
|
|
-- reverse :: [a] -> [a]
|
|
on |reverse|(xs)
|
|
if class of xs is text then
|
|
(reverse of characters of xs) as text
|
|
else
|
|
reverse of xs
|
|
end if
|
|
end |reverse|
|
|
|
|
-- tailMay :: [a] -> Maybe [a]
|
|
on tailMay(xs)
|
|
if length of xs > 1 then
|
|
{nothing:false, just:items 2 thru -1 of xs}
|
|
else
|
|
{nothing:true}
|
|
end if
|
|
end tailMay
|
|
|
|
-- until :: (a -> Bool) -> (a -> a) -> a -> a
|
|
on |until|(p, f, x)
|
|
set mp to mReturn(p)
|
|
set v to x
|
|
|
|
tell mReturn(f)
|
|
repeat until mp's |λ|(v)
|
|
set v to |λ|(v)
|
|
end repeat
|
|
end tell
|
|
return v
|
|
end |until|
|