Source code in the applescript programming language

-- f :: Int -> Int
on f(x)
    if x = 0 then
        1
    else
        x - m(f(x - 1))
    end if
end f

-- m :: Int -> Int
on m(x)
    if x = 0 then
        0
    else
        x - f(m(x - 1))
    end if
end m


-- TEST
on run
    set xs to range(0, 19)
    
    {map(f, xs), map(m, xs)}
end run


-- GENERIC FUNCTIONS

-- 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 lambda(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 lambda : f
        end script
    end if
end mReturn

-- range :: Int -> Int -> [Int]
on range(m, n)
    if n < m 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 range


{{1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 12}, 
 {0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12}}