Exponentiation

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{-# LANGUAGE NoImplicitPrelude #-}
module Exponentiation
  ( power, _test_power, main_power
  ) where

import Testing
import Booleans
import NaturalNumbers
import SimpleRecursion
import Plus
import Times

power :: (Natural n) => n -> n -> n
power a b = simpleRec phi mu b a
  where
    phi _     = next zero
    mu  _ c d = times d c

_test_power_zero_right :: (Natural n, Equal n)
  => n -> Test (n -> Bool)
_test_power_zero_right _ =
  testName "power(a,zero) == next(zero)" $
  \a -> eq (power a zero) (next zero)


_test_power_next_right :: (Natural n, Equal n)
  => n -> Test (n -> n -> Bool)
_test_power_next_right _ =
  testName "power(a,next(b)) == times(power(a,b),a)" $
  \a b -> eq (power a (next b)) (times (power a b) a)

_test_power_one_right :: (Natural n, Equal n)
  => n -> Test (n -> Bool)
_test_power_one_right _ =
  testName "power(a,1) == a" $
  \a -> eq (power a (next zero)) a


_test_power_zero_left :: (Natural n, Equal n)
  => n -> Test (n -> Bool)
_test_power_zero_left _ =
  testName "power(zero,next(a)) == zero" $
  \a -> eq (power zero (next a)) zero


_test_power_one_left :: (Natural n, Equal n)
  => n -> Test (n -> Bool)
_test_power_one_left _ =
  testName "power(next(zero),a) == next(zero)" $
  \a -> eq (power (next zero) a) (next zero)

_test_power_plus_right :: (Natural n, Equal n)
  => n -> Test (n -> n -> n -> Bool)
_test_power_plus_right _ =
  testName "power(a,plus(b,c)) == times(power(a,b),power(a,c))" $
  \a b c -> eq (power a (plus b c)) (times (power a b) (power a c))


_test_power_times_right :: (Natural n, Equal n)
  => n -> Test (n -> n -> n -> Bool)
_test_power_times_right _ =
  testName "power(a,times(b,c)) == power(power(a,b),c)" $
  \a b c -> eq (power a (times b c)) (power (power a b) c)


_test_power_times_left :: (Natural n, Equal n)
  => n -> Test (n -> n -> n -> Bool)
_test_power_times_left _ =
  testName "power(times(a,b),c) == times(power(a,c),power(b,c))" $
  \a b c -> eq (power (times a b) c) (times (power a c) (power b c))

_test_power ::
  ( TypeName n, Natural n, Equal n, Arbitrary n, Show n
  ) => Int -> Int -> n -> IO ()
_test_power size cases n = do
  testLabel1 "power" n

  let args = testArgs size cases

  runTest args (_test_power_zero_right n)
  runTest args (_test_power_next_right n)
  runTest args (_test_power_one_right n)
  runTest args (_test_power_zero_left n)
  runTest args (_test_power_one_left n)
  runTest args (_test_power_plus_right n)
  runTest args (_test_power_times_right n)
  runTest args (_test_power_times_left n)

main_power :: IO ()
main_power = do
  _test_power 4 30 (zero :: Unary)