Faulhaber's triangle: Difference between revisions

from itertools import (accumulate, chain, count, islice, starmap)

fs = faulhaberTriangle(9)

fTable(__doc__ + ':\n')(str)(

compose(concat)(fmap(showRatio(4)(3)))

)(

index(fs)

)(range(1, len(fs)))

# compose (<<<) :: (b -> c) -> (a -> b) -> a -> c

def compose(g):

'''Right to left function composition.'''

return lambda f: lambda x: g(f(x))

# concat :: [[a]] -> [a]

# concat :: [String] -> String

def concat(xs):

'''The concatenation of all the elements

in a list or iterable.'''

def f(ys):

zs = list(chain(*ys))

return ''.join(zs) if isinstance(ys[0], str) else zs

return (

f(xs) if isinstance(xs, list) else (

chain.from_iterable(xs)

)

) if xs else []

# fmap :: (a -> b) -> [a] -> [b]

def fmap(f):

'''fmap over a list.

f lifted to a function over a list.

'''

return lambda xs: list(map(f, xs))

# index (!!) :: [a] -> Int -> a

def index(xs):

'''Item at given (zero-based) index.'''

return lambda n: None if 0 > n else (

xs[n] if (

hasattr(xs, "__getitem__")

) else next(islice(xs, n, None))

)

# MAIN ---