'''First-class functions'''

from math import (acos, cos, asin, sin)
from inspect import signature


# main :: IO ()
def main():
    '''Composition of several functions.'''

    pwr = flip(curry(pow))

    fs = [sin, cos, pwr(3.0)]
    ifs = [asin, acos, pwr(1 / 3.0)]

    print([
        f(0.5) for f in
        zipWith(compose)(fs)(ifs)
    ])


# GENERIC FUNCTIONS ------------------------------


# compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
def compose(g):
    '''Right to left function composition.'''
    return lambda f: lambda x: g(f(x))


# curry :: ((a, b) -> c) -> a -> b -> c
def curry(f):
    '''A curried function derived
       from an uncurried function.'''
    return lambda a: lambda b: f(a, b)


# flip :: (a -> b -> c) -> b -> a -> c
def flip(f):
    '''The (curried or uncurried) function f with its
       two arguments reversed.'''
    if 1 < len(signature(f).parameters):
        return lambda a, b: f(b, a)
    else:
        return lambda a: lambda b: f(b)(a)


# zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
def zipWith(f):
    '''A list constructed by zipping with a
       custom function, rather than with the
       default tuple constructor.'''
    return lambda xs: lambda ys: [
        f(a)(b) for (a, b) in zip(xs, ys)
    ]


if __name__ == '__main__':
    main()