Coprime To

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{-# LANGUAGE NoImplicitPrelude #-}
module CoprimeTo
  ( coprime, _test_coprime, main_coprime
  ) where

import Testing
import Booleans
import And
import NaturalNumbers
import Times
import DivisionAlgorithm
import Divides
import GreatestCommonDivisor

coprime :: (Natural n, Equal n) => n -> n -> Bool
coprime a b = eq (next zero) (gcd a b)

_test_coprime_euclids_lemma :: (Natural n, Equal n)
  => n -> Test (n -> n -> n -> Bool)
_test_coprime_euclids_lemma _ =
  testName "if coprime(a,b) and div(a,times(b,c)) then div(a,c)" $
  \a b c -> if and (coprime a b) (div a (times b c))
    then div a c
    else true

_test_coprime_gcd_quo :: (Natural n, Equal n)
  => n -> Test (n -> n -> Bool)
_test_coprime_gcd_quo _ =
  testName "coprime(quo(next(a),gcd(next(a),next(b))),quo(next(b),gcd(next(a),next(b))))" $
  \x y -> let
    a = next x
    b = next y
    u = quo a (gcd a b)
    v = quo b (gcd a b)
  in eq (coprime u v) true

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

  let args = testArgs size cases

  runTest args (_test_coprime_euclids_lemma n)
  runTest args (_test_coprime_gcd_quo n)

main_coprime :: IO ()
main_coprime = do
  _test_coprime 20 100 (zero :: Unary)