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module StdQTest
/* Test module StdQTest
Voor werken met Gast:
(*) gebruik Environment 'Gast'
(*) zet Project Options op 'Basic Values Only'
*/
import StdQ
import StdEnv
import gast
Start
= testn 1000
(\ a b c ->
let qa = fromInt a
in zero_is_neutral_for_addition qa /\
zero_is_neutral_for_subtraction qa /\
one_is_neutral_for_multiplication qa /\
one_is_neutral_for_division qa /\
negation_is_idempotent qa /\
add_then_subtract_yields_identity qa /\
subtract_then_add_yields_identity qa /\
abs_is_positive qa /\
isInt_holds_for_Ints qa /\
toQ_yields_rational a b c /\
True
)
zero_is_neutral_for_addition :: Q -> Property
zero_is_neutral_for_addition a = name "zero_is_neutral_for_addition"
(zero + a == a && a == a + zero)
zero_is_neutral_for_subtraction :: Q -> Property
zero_is_neutral_for_subtraction a = name "zero_is_neutral_for_subtraction"
(a - zero == a && a == ~ (zero - a))
one_is_neutral_for_multiplication :: Q -> Property
one_is_neutral_for_multiplication a = name "one_is_neutral_for_multiplication"
(one * a == a && a == a * one)
zero_is_zero_for_multiplication :: Q -> Property
zero_is_zero_for_multiplication a = name "zero_is_zero_for_multiplication"
(zero * a == zero && zero == a * zero)
one_is_neutral_for_division :: Q -> Property
one_is_neutral_for_division a = name "one_is_neutral_for_division"
(a / one == a)
negation_is_idempotent :: Q -> Property
negation_is_idempotent a = name "negation_is_idempotent"
(~ (~ a) == a)
add_then_subtract_yields_identity :: Q -> Property
add_then_subtract_yields_identity a = name "add then subtract" ((a + a) - a == a)
subtract_then_add_yields_identity :: Q -> Property
subtract_then_add_yields_identity a = name "subtract then add" ((zero - a - a) + a + a == zero)
abs_is_positive :: Q -> Property
abs_is_positive a = name "abs is positive" (abs a >= zero)
isInt_holds_for_Ints :: Q -> Property
isInt_holds_for_Ints a = name "isInt holds for Ints" (isInt a && (a == zero || not (isInt (a / (a+a)))))
toQ_yields_rational :: Int Int Int -> Property
toQ_yields_rational a b c = name "toQ yields rational"
( (abs a > 2^30 || abs b > 2^30 || a*b == zero || toQ (a,b) * toQ b == toQ a)
&&
(abs a > 2^30 || abs b > 2^30 || abs c > 2^30 || a*b*c == zero || (toQ (c,a,b) - toQ c) * toQ b == toQ a)
)
instance fromInt Q where fromInt i = toQ i
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