QuickCheck

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???????? ? QuickCheck

• ??????? ????????
• 13 ??????? 2007 ?.
• ?????-????????????? ?????? ????????????? Haskell

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????????? ? ??????

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• ?????? ????????? ???????? ?????, ???????
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• ?????? ? ?????? ?????? ?????????
• ??? ?????? ?????????? ?????? ????????????.

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• ??? ???????? ??????? ?????? ? ?? ???????????
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???????????? ? Haskell

• REPL
• Hat
• Debug.Trace, print, unsafePerformIO
• HUnit
• QuickCheck

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QuickCheck

• ????????? ????????? ???????? ?????? ??? ??????
  ????? ??????.
• ????????????? ?????????? ??????.
• ???????????? ??????????? ??????? ????? Haskell.

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???????? ???????

• QuickCheck ?????????? ???????? ?????? ?
  ?????????, ??????????? ?? ????????? ????????.
• ???????????? ?????? ?? ????????????

• prop_RevRev xs reverse (reverse xs) xs
• where types xsInt
• gt quickCheck prop_RevRev
• OK, passed 100 tests.

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prop_RevRev
prop_RevRev xs reverse (reverse xs)
xs where types xsInt
??????? ??? ???? ??????? ?????????? ??????????
reverse ?????????? ???????? ??????.
??? ?????? ? ???????? ???????? ?????? ?????
?????????????? ????????? ?????? ????? ?????.
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??????? ??????? ???????

• ???????? ??? ???????, ???????????? ????????
  ???? Bool.
• ???????? ?????? ????? ??????????? ??? ??????????
  ???????????? ???????? ?????? ???????????? ????.

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???? ???????

• ???????? ????????
• lt???????gt gt lt????????gt

ordered xs and (zipWith (lt) xs (drop 1
xs)) insert x x insert x (yys)
x lt y x y ys otherwise y insert x
ys prop_Insert x xs ordered xs gt ordered
(insert x xs) where types xInt
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???? ???????

• ?????????????????? ????????
• forAll lt?????????gt \x -gt lt????????gt

prop_Insert2 x forAll orderedList \xs -gt
ordered (insert x xs) where types xInt

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• QuickCheck ?????????? ??????????? ?????????? ???
  ???????? ????? ??????.
• ??? ???? ?? ????? ?????? ????? ?????? ???????????
  ??????????.
• ????? ?????????? ???? ?????????? ??? ????? ?????
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• ????????? ??? ???? a ?????? Gen a.
• choose Random a gt (a, a) -gt Gen a
• choose (0, n) gtgt \i -gt return (list !! i)

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???????????

• oneof lt?????? ???????????gt
• oneof Gen a -gt Gen a
• oneof return a, return b, return c
• ?????????? ?????????? ?????????????.
• frequency lt?????? ???????????gt
• frequency (Int, Gen a) -gt Gen a
• frequency (2, return a), (3, return b)
• ?????????? ?????????? ? ????????? ????????.

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???????????

• sized ?????????? ???????? ??????
• sized (Int -gt Gen a) -gt Gen a
• resize ????????? ??????? ???????? ??????
• resize Int -gt Gen a -gt Gen a
• ??? ???????????????? ?????? ?????? ????
  ????????????.

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????????? ???????? ??????

• ????????? ???????????? ? ?????? Gen.

data IntList Nil Cons Int IntList listGen
oneof return Nil, liftM2 Cons arbitrary
listGen

• ????? ??????? ? ??????? ??????.
• ??????????? ??????????
• two, three, four, vector

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Arbitrary
class Arbitrary a where arbitrary Gen
a coarbitrary a -gt Gen b -gt Gen b

• arbitrary ????????? ????????? ????????
• coarbitrary ???????????? ??? ????????? ?????????
  ???????

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?????? ??????-?????? ???????

• ????????????? ???????? ? ??????? ??????-??????
  ????????
• ?????????? Chris Okasaki, 1993 (Functional
  Pearls)

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  ?, ??? ?????????, ????????????? ??????

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??????????
import Data.List hiding (insert) import
Control.Monad import Test.QuickCheck data Color
R B deriving (Eq, Show) data Tree elt E T
Color (Tree elt) elt (Tree elt) deriving
Show type Set elt Tree elt empty Set
elt empty E member Ord elt gt elt -gt Set
elt -gt Bool member x E False member x (T _ a y
b) x lt y member x a x y True x
gt y member x b
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??????????
insert Ord elt gt elt -gt Set elt -gt Set
elt insert x s makeBlack (ins s) where ins E
T R E x E ins (T color a
y b) x lt y balance color (ins a) y b
x y T
color a y b
x gt y balance color a y (ins
b) makeBlack (T _ a y b) T B a y
b balance Ord elt gt Color -gt Tree elt -gt elt
-gt Tree elt -gt Tree elt balance B (T R (T R a x
b) y c) z d T R (T B a x b) y (T B c z
d) balance B (T R a x (T R b y c)) z d T R (T B
a x b) y (T B c z d) balance B a x (T R (T R b y
c) z d) T R (T B a x b) y (T B c z d) balance B
a x (T R b y (T R c z d)) T R (T B a x b) y (T
B c z d) balance color a x b T color a x b
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??????????????? ???????
setFromList Ord elt gt elt -gt Set
elt setFromList empty setFromList (xxs)
insert x setFromList xs listFromSet Ord elt
gt Set elt -gt elt listFromSet E
listFromSet (T _ a y b) listFromSet a y
listFromSet b
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Arbitrary Tree
instance (Arbitrary a, Ord a) gt Arbitrary (Tree
a) where arbitrary sized \n -gt
liftM setFromList arbitrary
coarbitrary tree coarbitrary (listFromSet tree)
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???????? ????????????????????-?????????

• prop_listConvert Int -gt Bool
• prop_listConvert list
• (listFromSet . setFromList) list (nub
  . sort) list
• -- ??????? ???????? ???? ????????????
• prop_listConvertBad Int -gt Bool
• prop_listConvertBad list
• (listFromSet . setFromList) list sort
  list
• gt quickCheck prop_listConvert
• Falsifiable, after 10 tests
• 2,2

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???????? ??????
prop_blackRoot Tree Int -gt Bool prop_blackRoot
E True prop_blackRoot (T color _ _ _) color
B -- All children of a red node must be
black prop_blackChildren Tree Int -gt
Bool prop_blackChildren E True prop_blackChildre
n (T color left _ right) color R
isNotBlack left isNotBlack right False
otherwise prop_blackChildren left
prop_blackChildren right where
isNotBlack Tree Int -gt Bool isNotBlack
(T R _ _ _) True isNotBlack _ False
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