-- Hoogle documentation, generated by Haddock -- See Hoogle, http://www.haskell.org/hoogle/ -- | generalize counter-examples of test properties -- -- Extrapolate is a tool able to provide generalized counter-examples of -- test properties where irrelevant sub-expressions are replaces with -- variables. -- -- For the incorrect property \xs -> nub xs == (xs::[Int]): -- -- @package extrapolate @version 0.3.2 -- | This module is part of Extrapolate, a library for generalization of -- counter-examples. -- -- This module re-exports some functionality from Test.Speculate.Expr, -- but instead of working on single expressions it works in lists of -- expressions (the choosen representation for counter-examples). module Test.Extrapolate.Exprs type Exprs = [Expr] canonicalizeWith :: Instances -> [Expr] -> [Expr] grounds :: Instances -> [Expr] -> [[Expr]] groundsAndBinds :: Instances -> [Expr] -> [(Binds, [Expr])] vassignments :: [Expr] -> [[Expr]] vars :: [Expr] -> [(TypeRep, String)] fold :: [Expr] -> Expr unfold :: Expr -> [Expr] isAssignmentTest :: Instances -> Int -> Expr -> Bool nameWith :: Typeable a => String -> a -> Instances -- | A quantified type representation. type TypeRep = SomeTypeRep canonicalWith :: Instances -> Expr -> Bool canonicalize :: Expr -> Expr ($$) :: Expr -> Expr -> Maybe Expr arity :: Expr -> Int atomicConstants :: Expr -> [Expr] compareComplexity :: Expr -> Expr -> Ordering compareComplexityThen :: Expr -> Expr -> Ordering -> Expr -> Expr -> Ordering constant :: Typeable a => String -> a -> Expr consts :: Expr -> [Expr] countHoles :: TypeRep -> Expr -> Int countVar :: TypeRep -> String -> Expr -> Int countVars :: Expr -> [(TypeRep, String, Int)] depthE :: Expr -> Int eqExprCommuting :: [Expr] -> Expr -> Expr -> Bool etyp :: Expr -> Either Expr TypeRep eval :: Typeable a => a -> Expr -> a evaluate :: Typeable a => Expr -> Maybe a falseE :: Expr hasVar :: Expr -> Bool hole :: (Listable a, Typeable a) => a -> Expr holeOfTy :: TypeRep -> Expr holes :: Expr -> [TypeRep] isAssignment :: Expr -> Bool isConstantNamed :: Expr -> String -> Bool isSub :: Expr -> Expr -> Bool isTuple :: Expr -> Bool lengthE :: Expr -> Int lexicompare :: Expr -> Expr -> Ordering lexicompareBy :: Expr -> Expr -> Ordering -> Expr -> Expr -> Ordering showConstant :: (Typeable a, Show a) => a -> Expr showExpr :: Expr -> String showOpExpr :: String -> Expr -> String showPrecExpr :: Int -> Expr -> String showsOpExpr :: String -> Expr -> String -> String showsPrecExpr :: Int -> Expr -> String -> String subexprs :: Expr -> [Expr] subexprsV :: Expr -> [Expr] typ :: Expr -> TypeRep typeCorrect :: Expr -> Bool unfoldApp :: Expr -> [Expr] unfoldTuple :: Expr -> [Expr] unrepeatedVars :: Expr -> Bool var :: (Listable a, Typeable a) => String -> a -> Expr comparisonLE :: Instances -> Expr -> Expr -> Maybe Expr comparisonLT :: Instances -> Expr -> Expr -> Maybe Expr conditionalComparisonLE :: Instances -> Expr -> Expr -> Expr -> Maybe Expr conditionalComparisonLT :: Instances -> Expr -> Expr -> Expr -> Maybe Expr conditionalEquation :: Instances -> Expr -> Expr -> Expr -> Maybe Expr equation :: Instances -> Expr -> Expr -> Maybe Expr implication :: Expr -> Expr -> Maybe Expr inequality :: Instances -> Expr -> Expr -> Maybe Expr isEquation :: Expr -> Bool phonyEquation :: Expr -> Expr -> Expr unComparison :: Expr -> (Expr, Expr) unConditionalComparison :: Expr -> (Expr, Expr, Expr) unConditionalEquation :: Expr -> (Expr, Expr, Expr) unEquation :: Expr -> (Expr, Expr) unImplication :: Expr -> (Expr, Expr) usefulConditionalEquation :: Expr -> Bool usefulEquation :: Expr -> Bool usefulImplication :: Expr -> Bool uselessEquation :: Expr -> Bool condEqual :: Instances -> Int -> Expr -> Expr -> Expr -> Bool condEqualM :: Instances -> Int -> Int -> Expr -> Expr -> Expr -> Bool equal :: Instances -> Int -> Expr -> Expr -> Bool false :: Instances -> Int -> Expr -> Bool groundAndBinds :: Instances -> Expr -> [(Binds, Expr)] groundBinds :: Instances -> Expr -> [Binds] inequal :: Instances -> Int -> Expr -> Expr -> Bool less :: Instances -> Int -> Expr -> Expr -> Bool lessOrEqual :: Instances -> Int -> Expr -> Expr -> Bool true :: Instances -> Int -> Expr -> Bool trueBinds :: Instances -> Int -> Expr -> [Binds] trueRatio :: Instances -> Int -> Expr -> Ratio Int defNames :: [String] eq :: (Typeable a, Eq a) => a -> Instances eqE :: Instances -> TypeRep -> Maybe Expr eqOrd :: (Typeable a, Eq a, Ord a) => a -> Instances eqWith :: (Typeable a, Eq a) => a -> a -> Bool -> Instances findInfo :: () => Instance -> Maybe a -> Instances -> Maybe a instanceType :: Instance -> TypeRep iqE :: Instances -> TypeRep -> Maybe Expr isEq :: Instances -> TypeRep -> Bool isEqE :: Instances -> Expr -> Bool isEqOrd :: Instances -> TypeRep -> Bool isEqOrdE :: Instances -> Expr -> Bool isListable :: Instances -> TypeRep -> Bool isOrd :: Instances -> TypeRep -> Bool isOrdE :: Instances -> Expr -> Bool leE :: Instances -> TypeRep -> Maybe Expr listable :: (Typeable a, Show a, Listable a) => a -> Instances listableWith :: (Typeable a, Show a) => [[a]] -> Instances ltE :: Instances -> TypeRep -> Maybe Expr names :: Instances -> TypeRep -> [String] ord :: (Typeable a, Ord a) => a -> Instances ordWith :: (Typeable a, Ord a) => a -> a -> Bool -> Instances preludeInstances :: Instances tiersE :: Instances -> TypeRep -> [[Expr]] assign :: String -> Expr -> Expr -> Expr assigning :: Expr -> Binds -> Expr fill :: Expr -> [Expr] -> Expr hasCanonInstanceOf :: Expr -> Expr -> Bool hasInstanceOf :: Expr -> Expr -> Bool isCanonInstanceOf :: Expr -> Expr -> Bool isInstanceOf :: Expr -> Expr -> Bool match :: Expr -> Expr -> Maybe Binds match2 :: (Expr, Expr) -> (Expr, Expr) -> Maybe Binds matchWith :: Binds -> Expr -> Expr -> Maybe Binds renameBy :: String -> String -> Expr -> Expr sub :: Expr -> Expr -> Expr -> Expr unification :: Expr -> Expr -> Maybe Binds unify :: Expr -> Expr -> Maybe Expr boolTy :: TypeRep mkEqnTy :: TypeRep -> TypeRep data Expr Constant :: String -> Dynamic -> Expr Var :: String -> TypeRep -> Expr (:$) :: Expr -> Expr -> Expr data Instance Instance :: String -> TypeRep -> [Expr] -> Instance type Instances = [Instance] type Binds = [(String, Expr)] -- | This module is part of Extrapolate, a library for generalization of -- counter-examples. -- -- Some type binding operators that are useful when defining -- Generalizable instances. module Test.Extrapolate.TypeBinding argTy1of1 :: con a -> a argTy1of2 :: con a b -> a argTy2of2 :: con a b -> b argTy1of3 :: con a b c -> a argTy2of3 :: con a b c -> b argTy3of3 :: con a b c -> c argTy1of4 :: con a b c d -> a argTy2of4 :: con a b c d -> b argTy3of4 :: con a b c d -> c argTy4of4 :: con a b c d -> d argTy1of5 :: con a b c d e -> a argTy2of5 :: con a b c d e -> b argTy3of5 :: con a b c d e -> c argTy4of5 :: con a b c d e -> d argTy5of5 :: con a b c d e -> e argTy1of6 :: con a b c d e f -> a argTy2of6 :: con a b c d e f -> b argTy3of6 :: con a b c d e f -> c argTy4of6 :: con a b c d e f -> d argTy5of6 :: con a b c d e f -> e argTy6of6 :: con a b c d e f -> f -- | This module is part of Extrapolate, a library for generalization of -- counter-examples. -- -- Miscellaneous utility functions. -- -- This is not intended to be used by users of Extrapolate, only by -- modules of Extrapolate itself. Expect symbols exported here to come -- and go with every minor version. module Test.Extrapolate.Utils (+++) :: Ord a => [a] -> [a] -> [a] infixr 5 +++ nubMerge :: Ord a => [a] -> [a] -> [a] nubMergeOn :: Ord b => (a -> b) -> [a] -> [a] -> [a] nubMergeBy :: (a -> a -> Ordering) -> [a] -> [a] -> [a] foldr0 :: (a -> a -> a) -> a -> [a] -> a fromLeft :: Either a b -> a fromRight :: Either a b -> b elemBy :: (a -> a -> Bool) -> a -> [a] -> Bool listEq :: (a -> a -> Bool) -> [a] -> [a] -> Bool listOrd :: (a -> a -> Bool) -> [a] -> [a] -> Bool maybeEq :: (a -> a -> Bool) -> Maybe a -> Maybe a -> Bool maybeOrd :: (a -> a -> Bool) -> Maybe a -> Maybe a -> Bool eitherEq :: (a -> a -> Bool) -> (b -> b -> Bool) -> Either a b -> Either a b -> Bool eitherOrd :: (a -> a -> Bool) -> (b -> b -> Bool) -> Either a b -> Either a b -> Bool pairEq :: (a -> a -> Bool) -> (b -> b -> Bool) -> (a, b) -> (a, b) -> Bool pairOrd :: (a -> a -> Bool) -> (b -> b -> Bool) -> (a, b) -> (a, b) -> Bool tripleEq :: (a -> a -> Bool) -> (b -> b -> Bool) -> (c -> c -> Bool) -> (a, b, c) -> (a, b, c) -> Bool tripleOrd :: (a -> a -> Bool) -> (b -> b -> Bool) -> (c -> c -> Bool) -> (a, b, c) -> (a, b, c) -> Bool quadrupleEq :: (a -> a -> Bool) -> (b -> b -> Bool) -> (c -> c -> Bool) -> (d -> d -> Bool) -> (a, b, c, d) -> (a, b, c, d) -> Bool quadrupleOrd :: (a -> a -> Bool) -> (b -> b -> Bool) -> (c -> c -> Bool) -> (d -> d -> Bool) -> (a, b, c, d) -> (a, b, c, d) -> Bool minimumOn :: Ord b => (a -> b) -> [a] -> a maximumOn :: Ord b => (a -> b) -> [a] -> a takeBound :: Maybe Int -> [a] -> [a] nubMergeMap :: Ord b => (a -> [b]) -> [a] -> [b] -- | For a given type, return all *-kinded types. (all non-function types) -- -- 
--   typesIn (typeOf (undefined :: (Int -> Int) -> Int -> Bool))
--     == [Bool,Int]
--
typesIn :: TypeRep -> [TypeRep] argumentTy :: TypeRep -> TypeRep resultTy :: TypeRep -> TypeRep discard :: (a -> Bool) -> [a] -> [a] compareIndex :: Eq a => [a] -> a -> a -> Ordering (.:) :: (c -> d) -> (a -> b -> c) -> (a -> b -> d) -- | This module is part of Extrapolate, a library for generalization of -- counter-examples. -- -- This is the core of extrapolate. module Test.Extrapolate.Core -- | Takes as argument an integer length and tiers of element values; -- returns tiers of lists of element values of the given length. -- -- 
--   listsOfLength 3 [[0],[1],[2],[3],[4]...] =
--     [ [[0,0,0]]
--     , [[0,0,1],[0,1,0],[1,0,0]]
--     , [[0,0,2],[0,1,1],[0,2,0],[1,0,1],[1,1,0],[2,0,0]]
--     , ...
--     ]
--
listsOfLength :: () => Int -> [[a]] -> [[[a]]] -- | Takes as argument tiers of element values; returns tiers of -- size-ordered lists of elements without repetition. -- -- 
--   setsOf [[0],[1],[2],...] =
--     [ [[]]
--     , [[0]]
--     , [[1]]
--     , [[0,1],[2]]
--     , [[0,2],[3]]
--     , [[0,3],[1,2],[4]]
--     , [[0,1,2],[0,4],[1,3],[5]]
--     , ...
--     ]
--
-- -- Can be used in the constructor of specialized Listable -- instances. For Set (from Data.Set), we would have: -- -- 
--   instance Listable a => Listable (Set a) where
--     tiers = mapT fromList $ setsOf tiers
--
setsOf :: () => [[a]] -> [[[a]]] -- | Takes as argument tiers of element values; returns tiers of -- size-ordered lists of elements possibly with repetition. -- -- 
--   bagsOf [[0],[1],[2],...] =
--     [ [[]]
--     , [[0]]
--     , [[0,0],[1]]
--     , [[0,0,0],[0,1],[2]]
--     , [[0,0,0,0],[0,0,1],[0,2],[1,1],[3]]
--     , [[0,0,0,0,0],[0,0,0,1],[0,0,2],[0,1,1],[0,3],[1,2],[4]]
--     , ...
--     ]
--
bagsOf :: () => [[a]] -> [[[a]]] -- | Takes as argument tiers of element values; returns tiers of lists with -- no repeated elements. -- -- 
--   noDupListsOf [[0],[1],[2],...] ==
--     [ [[]]
--     , [[0]]
--     , [[1]]
--     , [[0,1],[1,0],[2]]
--     , [[0,2],[2,0],[3]]
--     , ...
--     ]
--
noDupListsOf :: () => [[a]] -> [[[a]]] -- | Normalizes tiers by removing up to 12 empty tiers from the end of a -- list of tiers. -- -- 
--   normalizeT [xs0,xs1,...,xsN,[]]     =  [xs0,xs1,...,xsN]
--   normalizeT [xs0,xs1,...,xsN,[],[]]  =  [xs0,xs1,...,xsN]
--
-- -- The arbitrary limit of 12 tiers is necessary as this function would -- loop if there is an infinite trail of empty tiers. normalizeT :: () => [[a]] -> [[a]] -- | Delete the first occurence of an element in a tier. -- -- For normalized lists-of-tiers without repetitions, the following -- holds: -- -- 
--   deleteT x = normalizeT . (`suchThat` (/= x))
--
deleteT :: Eq a => a -> [[a]] -> [[a]] -- | Takes the product of N lists of tiers, producing lists of length N. -- -- Alternatively, takes as argument a list of lists of tiers of elements; -- returns lists combining elements of each list of tiers. -- -- 
--   products [xss] = mapT (:[]) xss
--   products [xss,yss] = mapT (\(x,y) -> [x,y]) (xss >< yss)
--   products [xss,yss,zss] = product3With (\x y z -> [x,y,z]) xss yss zss
--
products :: () => [[[a]]] -> [[[a]]] -- | Takes as argument tiers of element values; returns tiers of lists of -- elements. -- -- 
--   listsOf [[]] == [[[]]]
--
-- -- 
--   listsOf [[x]] == [ [[]]
--                    , [[x]]
--                    , [[x,x]]
--                    , [[x,x,x]]
--                    , ...
--                    ]
--
-- -- 
--   listsOf [[x],[y]] == [ [[]]
--                        , [[x]]
--                        , [[x,x],[y]]
--                        , [[x,x,x],[x,y],[y,x]]
--                        , ...
--                        ]
--
listsOf :: () => [[a]] -> [[[a]]] -- | Take the product of lists of tiers by a function returning a -- Maybe value discarding Nothing values. productMaybeWith :: () => a -> b -> Maybe c -> [[a]] -> [[b]] -> [[c]] -- | Like productWith, but over 3 lists of tiers. product3With :: () => a -> b -> c -> d -> [[a]] -> [[b]] -> [[c]] -> [[d]] -- | Given a constructor that takes a list with no duplicate elements, -- return tiers of applications of this constructor. noDupListCons :: Listable a => [a] -> b -> [[b]] -- | Given a constructor that takes a map of elements (encoded as a list), -- lists tiers of applications of this constructor -- -- So long as the underlying Listable enumerations have no -- repetitions, this will generate no repetitions. -- -- This allows defining an efficient implementation of tiers that -- does not repeat maps given by: -- -- 
--   tiers = mapCons fromList
--
mapCons :: (Listable a, Listable b) => [(a, b)] -> c -> [[c]] -- | Given a constructor that takes a set of elements (as a list), lists -- tiers of applications of this constructor. -- -- A naive Listable instance for the Set (of -- Data.Set) would read: -- -- 
--   instance Listable a => Listable (Set a) where
--     tiers = cons0 empty \/ cons2 insert
--
-- -- The above instance has a problem: it generates repeated sets. A more -- efficient implementation that does not repeat sets is given by: -- -- 
--   tiers = setCons fromList
--
-- -- Alternatively, you can use setsOf direclty. setCons :: Listable a => [a] -> b -> [[b]] -- | Given a constructor that takes a bag of elements (as a list), lists -- tiers of applications of this constructor. -- -- For example, a Bag represented as a list. -- -- 
--   bagCons Bag
--
bagCons :: Listable a => [a] -> b -> [[b]] -- | Derives a Listable instance for a given type Name -- cascading derivation of type arguments as well. deriveListableCascading :: Name -> DecsQ -- | Derives a Listable instance for a given type Name. -- -- Consider the following Stack datatype: -- -- 
--   data Stack a = Stack a (Stack a) | Empty
--
-- -- Writing -- -- 
--   deriveListable ''Stack
--
-- -- will automatically derive the following Listable instance: -- -- 
--   instance Listable a => Listable (Stack a) where
--     tiers = cons2 Stack \/ cons0 Empty
--
-- -- Needs the TemplateHaskell extension. deriveListable :: Name -> DecsQ -- | Adds to the weight of tiers of a constructor -- -- addWeight is closely related to delay. addWeight :: () => [[a]] -> Int -> [[a]] -- | Resets the weight of a constructor (or tiers) Typically used as an -- infix constructor when defining Listable instances: -- -- 
--   cons<N> `ofWeight` <W>
--
-- -- Be careful: do not apply ofWeight 0 to recursive data -- structure constructors. In general this will make the list of size 0 -- infinite, breaking the tier invariant (each tier must be finite). -- -- ofWeight is closely related to reset. ofWeight :: () => [[a]] -> Int -> [[a]] cons12 :: (Listable a, Listable b, Listable c, Listable d, Listable e, Listable f, Listable g, Listable h, Listable i, Listable j, Listable k, Listable l) => a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> k -> l -> m -> [[m]] cons11 :: (Listable a, Listable b, Listable c, Listable d, Listable e, Listable f, Listable g, Listable h, Listable i, Listable j, Listable k) => a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> k -> l -> [[l]] cons10 :: (Listable a, Listable b, Listable c, Listable d, Listable e, Listable f, Listable g, Listable h, Listable i, Listable j) => a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> k -> [[k]] cons9 :: (Listable a, Listable b, Listable c, Listable d, Listable e, Listable f, Listable g, Listable h, Listable i) => a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> [[j]] cons8 :: (Listable a, Listable b, Listable c, Listable d, Listable e, Listable f, Listable g, Listable h) => a -> b -> c -> d -> e -> f -> g -> h -> i -> [[i]] cons7 :: (Listable a, Listable b, Listable c, Listable d, Listable e, Listable f, Listable g) => a -> b -> c -> d -> e -> f -> g -> h -> [[h]] cons6 :: (Listable a, Listable b, Listable c, Listable d, Listable e, Listable f) => a -> b -> c -> d -> e -> f -> g -> [[g]] -- | Boolean implication operator. Useful for defining conditional -- properties: -- -- 
--   prop_something x y = condition x y ==> something x y
--
(==>) :: Bool -> Bool -> Bool infixr 0 ==> -- | There exists an assignment of values that satisfies a property -- up to a number of test values? -- -- 
--   exists 1000 $ \x -> x > 10
--
exists :: Testable a => Int -> a -> Bool -- | Does a property fail for a number of test values? -- -- 
--   fails 1000 $ \xs -> xs ++ ys == ys ++ xs
--
fails :: Testable a => Int -> a -> Bool -- | Does a property hold up to a number of test values? -- -- 
--   holds 1000 $ \xs -> length (sort xs) == length xs
--
holds :: Testable a => Int -> a -> Bool -- | Up to a number of tests to a property, returns Just the first -- witness or Nothing if there is none. witness :: Testable a => Int -> a -> Maybe [String] -- | Lists all witnesses up to a number of tests to a property, witnesses :: Testable a => Int -> a -> [[String]] -- | Take a tiered product of lists of tiers. -- -- 
--   [t0,t1,t2,...] >< [u0,u1,u2,...] =
--   [ t0**u0
--   , t0**u1 ++ t1**u0
--   , t0**u2 ++ t1**u1 ++ t2**u0
--   , ...       ...       ...       ...
--   ]
--   where xs ** ys = [(x,y) | x <- xs, y <- ys]
--
-- -- Example: -- -- 
--   [[0],[1],[2],...] >< [[0],[1],[2],...]
--   == [  [(0,0)]
--      ,  [(1,0),(0,1)]
--      ,  [(2,0),(1,1),(0,2)]
--      ,  [(3,0),(2,1),(1,2),(0,3)]
--      ...
--      ]
--
(><) :: () => [[a]] -> [[b]] -> [[(a, b)]] infixr 8 >< -- | Interleave tiers --- sum of two tiers enumerations. When in doubt, use -- \/ instead. -- -- 
--   [xs,ys,zs,...] \/ [as,bs,cs,...] = [xs+|as,ys+|bs,zs+|cs,...]
--
(\\//) :: () => [[a]] -> [[a]] -> [[a]] infixr 7 \\// -- | Append tiers --- sum of two tiers enumerations. -- -- 
--   [xs,ys,zs,...] \/ [as,bs,cs,...] = [xs++as,ys++bs,zs++cs,...]
--
(\/) :: () => [[a]] -> [[a]] -> [[a]] infixr 7 \/ -- | Lazily interleaves two lists, switching between elements of the two. -- Union/sum of the elements in the lists. -- -- 
--   [x,y,z] +| [a,b,c] == [x,a,y,b,z,c]
--
(+|) :: () => [a] -> [a] -> [a] infixr 5 +| -- | Tiers of values that follow a property -- -- 
--   cons<N> `suchThat` condition
--
suchThat :: () => [[a]] -> a -> Bool -> [[a]] -- | Resets any delays in a list-of tiers. Conceptually this -- function makes a constructor "weightless", assuring the first tier is -- non-empty. Typically used when defining Listable instances: -- -- 
--   reset (cons<N> <Constr>)
--
-- -- Be careful: do not apply reset to recursive data structure -- constructors. In general this will make the list of size 0 infinite, -- breaking the tiers invariant (each tier must be finite). reset :: () => [[a]] -> [[a]] -- | Delays the enumeration of tiers. Conceptually this function -- adds to the weight of a constructor. Typically used when defining -- Listable instances: -- -- 
--   delay (cons<N> <Constr>)
--
delay :: () => [[a]] -> [[a]] -- | Returns tiers of applications of a 5-argument constructor. -- -- Test.LeanCheck.Basic defines cons6 up to cons12. -- Those are exported by default from Test.LeanCheck, but are -- hidden from the Haddock documentation. cons5 :: (Listable a, Listable b, Listable c, Listable d, Listable e) => a -> b -> c -> d -> e -> f -> [[f]] -- | Returns tiers of applications of a 4-argument constructor. cons4 :: (Listable a, Listable b, Listable c, Listable d) => a -> b -> c -> d -> e -> [[e]] -- | Returns tiers of applications of a 3-argument constructor. cons3 :: (Listable a, Listable b, Listable c) => a -> b -> c -> d -> [[d]] -- | Given a constructor with two Listable arguments, return -- tiers of applications of this constructor. By default, returned -- values will have size/weight of 1. cons2 :: (Listable a, Listable b) => a -> b -> c -> [[c]] -- | Given a constructor with one Listable argument, return -- tiers of applications of this constructor. By default, returned -- values will have size/weight of 1. cons1 :: Listable a => a -> b -> [[b]] -- | Given a constructor with no arguments, returns tiers of all -- possible applications of this constructor. Since in this case there is -- only one possible application (to no arguments), only a single value, -- of size/weight 0, will be present in the resulting list of tiers. cons0 :: () => a -> [[a]] -- | concatMap over tiers concatMapT :: () => a -> [[b]] -> [[a]] -> [[b]] -- | concat tiers of tiers concatT :: () => [[[[a]]]] -> [[a]] -- | filter tiers filterT :: () => a -> Bool -> [[a]] -> [[a]] -- | map over tiers mapT :: () => a -> b -> [[a]] -> [[b]] -- | Tiers of Fractional values. This can be used as the -- implementation of tiers for Fractional types. tiersFractional :: Fractional a => [[a]] -- | Tiers of Integral values. Can be used as a default -- implementation of list for Integral types. listIntegral :: (Enum a, Num a) => [a] -- | Takes a list of values xs and transform it into tiers on -- which each tier is occupied by a single element from xs. -- -- To convert back to a list, just concat. toTiers :: () => [a] -> [[a]] -- | A type is Listable when there exists a function that is able to -- list (ideally all of) its values. -- -- Ideally, instances should be defined by a tiers function that -- returns a (potentially infinite) list of finite sub-lists (tiers): the -- first sub-list contains elements of size 0, the second sub-list -- contains elements of size 1 and so on. Size here is defined by the -- implementor of the type-class instance. -- -- For algebraic data types, the general form for tiers is -- -- 
--   tiers = cons<N> ConstructorA
--        \/ cons<N> ConstructorB
--        \/ ...
--        \/ cons<N> ConstructorZ
--
-- -- where N is the number of arguments of each constructor -- A...Z. -- -- Instances can be alternatively defined by list. In this case, -- each sub-list in tiers is a singleton list (each succeeding -- element of list has +1 size). -- -- The function deriveListable from Test.LeanCheck.Derive -- can automatically derive instances of this typeclass. -- -- A Listable instance for functions is also available but is not -- exported by default. Import Test.LeanCheck.Function if you need -- to test higher-order properties. class Listable a tiers :: Listable a => [[a]] list :: Listable a => [a] -- | Extrapolate can generalize counter-examples of any types that are -- Generalizable. -- -- The core (and only required functions) of the generalizable typeclass -- are the expr and instances functions. -- -- The following example shows a datatype and its instance: -- -- 
--   data Stack a = Stack a (Stack a) | Empty
--
-- -- 
--   instance Generalizable a => Generalizable (Stack a) where
--   name _ = "s"
--   expr s@(Stack x y) = constant "Stack" (Stack ->>: s) :$ expr x :$ expr y
--   expr s@Empty       = constant "Empty" (Empty   -: s)
--   instances s = this s $ instances (argTy1of1 s)
--
-- -- To declare instances and expr it may be useful to use: -- -- class (Listable a, Typeable a, Show a) => Generalizable a -- | Transforms a value into an manipulable expression tree. See -- constant and :$. expr :: Generalizable a => a -> Expr -- | Common name for a variable, defaults to "x". name :: Generalizable a => a -> String -- | List of symbols allowed to appear in side-conditions. Defaults to -- []. See constant. background :: Generalizable a => a -> [Expr] -- | Computes a list of reified instances. See this. instances :: Generalizable a => a -> Instances -> Instances this :: Generalizable a => a -> (Instances -> Instances) -> Instances -> Instances backgroundWith :: Typeable a => [Expr] -> a -> Instances (+++) :: Ord a => [a] -> [a] -> [a] infixr 5 +++ backgroundOf :: Generalizable a => a -> [Expr] bgEq :: (Eq a, Generalizable a) => a -> [Expr] bgOrd :: (Ord a, Generalizable a) => a -> [Expr] bgEqWith1 :: (Generalizable a, Generalizable b) => ((b -> b -> Bool) -> a -> a -> Bool) -> [Expr] bgEqWith2 :: (Generalizable a, Generalizable b, Generalizable c) => ((b -> b -> Bool) -> (c -> c -> Bool) -> a -> a -> Bool) -> [Expr] data Option MaxTests :: Int -> Option ExtraInstances :: Instances -> Option MaxConditionSize :: Int -> Option MinFailures :: (Ratio Int) -> Option MaxSpeculateSize :: (Maybe Int) -> Option ConditionBound :: (Maybe Int) -> Option ConstantBound :: (Maybe Int) -> Option DepthBound :: (Maybe Int) -> Option data WithOption a With :: a -> Option -> WithOption a [property] :: WithOption a -> a [option] :: WithOption a -> Option maxTests :: Testable a => a -> Int extraInstances :: Testable a => a -> Instances maxConditionSize :: Testable a => a -> Int hasEq :: Generalizable a => a -> Bool (*==*) :: Generalizable a => a -> a -> Bool (*/=*) :: Generalizable a => a -> a -> Bool (*<=*) :: Generalizable a => a -> a -> Bool (*<*) :: Generalizable a => a -> a -> Bool tBackground :: Testable a => a -> [Expr] counterExamples :: Testable a => Int -> a -> [[Expr]] counterExampleGen :: Testable a => Int -> a -> Maybe ([Expr], Maybe [Expr]) counterExampleGens :: Testable a => Int -> a -> Maybe ([Expr], [[Expr]]) generalizations :: Instances -> [Expr] -> [[Expr]] generalizationsCE :: Testable a => Int -> a -> [Expr] -> [[Expr]] generalizationsCEC :: Testable a => a -> [Expr] -> [(Expr, [Expr])] generalizationsCounts :: Testable a => Int -> a -> [Expr] -> [([Expr], Int)] atoms :: Testable a => a -> [[Expr]] theoryAndReprExprs :: Testable a => a -> (Thy, [Expr]) theoryAndReprConds :: Testable a => a -> (Thy, [Expr]) candidateConditions :: Testable a => (Thy, [Expr]) -> a -> [Expr] -> [Expr] validConditions :: Testable a => (Thy, [Expr]) -> a -> [Expr] -> [(Expr, Int)] weakestCondition :: Testable a => (Thy, [Expr]) -> a -> [Expr] -> Expr getBackground :: Instances -> [Expr] fullInstances :: Testable a => a -> Instances -- | List matches of lists of expressions if possible -- -- 
--   [0,1]   `matchList` [x,y]   = Just [x=0, y=1]
--   [0,1+2] `matchList` [x,y+y] = Nothing
--
matchList :: [Expr] -> [Expr] -> Maybe Binds newMatches :: [Expr] -> [Expr] -> Maybe Binds class Testable a resultiers :: Testable a => a -> [[([Expr], Bool)]] ($-|) :: Testable a => a -> [Expr] -> Bool tinstances :: Testable a => a -> Instances options :: Testable a => a -> Options results :: Testable a => a -> [([Expr], Bool)] areInstancesOf :: [Expr] -> [Expr] -> Bool instance GHC.Show.Show Test.Extrapolate.Core.Option instance Test.Extrapolate.Core.Testable a => Test.Extrapolate.Core.Testable (Test.Extrapolate.Core.WithOption a) instance Test.Extrapolate.Core.Testable GHC.Types.Bool instance (Test.Extrapolate.Core.Testable b, Test.Extrapolate.Core.Generalizable a, Test.LeanCheck.Core.Listable a) => Test.Extrapolate.Core.Testable (a -> b) instance Test.Extrapolate.Core.Generalizable () instance Test.Extrapolate.Core.Generalizable GHC.Types.Bool instance Test.Extrapolate.Core.Generalizable GHC.Types.Int instance Test.Extrapolate.Core.Generalizable GHC.Integer.Type.Integer instance Test.Extrapolate.Core.Generalizable GHC.Types.Char instance Test.Extrapolate.Core.Generalizable a => Test.Extrapolate.Core.Generalizable (GHC.Base.Maybe a) instance (Test.Extrapolate.Core.Generalizable a, Test.Extrapolate.Core.Generalizable b) => Test.Extrapolate.Core.Generalizable (Data.Either.Either a b) instance (Test.Extrapolate.Core.Generalizable a, Test.Extrapolate.Core.Generalizable b) => Test.Extrapolate.Core.Generalizable (a, b) instance (Test.Extrapolate.Core.Generalizable a, Test.Extrapolate.Core.Generalizable b, Test.Extrapolate.Core.Generalizable c) => Test.Extrapolate.Core.Generalizable (a, b, c) instance (Test.Extrapolate.Core.Generalizable a, Test.Extrapolate.Core.Generalizable b, Test.Extrapolate.Core.Generalizable c, Test.Extrapolate.Core.Generalizable d) => Test.Extrapolate.Core.Generalizable (a, b, c, d) instance Test.Extrapolate.Core.Generalizable a => Test.Extrapolate.Core.Generalizable [a] instance Test.Extrapolate.Core.Generalizable GHC.Types.Ordering -- | This module is otherwise unused in the code. -- -- This is a stub of a new algorithm that is smarter and generalizes from -- several initial counter-examples rather than just one. -- -- When this gets finished, it should be moved into -- Test.Extrapolate.Core. module Test.Extrapolate.New generalizedCounterExamples :: Testable a => Int -> a -> [Exprs] lgg :: Exprs -> Exprs -> Exprs -- | Computes the least general generalization of two expressions -- -- 
--   lgg1 (expr [0,0]) (expr [1,1])
--
-- -- lgg1 :: Expr -> Expr -> Expr -- | This module is part of Extrapolate, a library for generalization of -- counter-examples. -- -- QuickCheck-like interface. module Test.Extrapolate.IO -- | Checks a property printing results on stdout -- -- 
--   > check $ \xs -> sort (sort xs) == sort (xs::[Int])
--   +++ OK, passed 360 tests.
--   
--   > check $ \xs ys -> xs `union` ys == ys `union` (xs::[Int])
--   *** Failed! Falsifiable (after 4 tests):
--   [] [0,0]
--   
--   Generalization:
--   [] (x:x:_)
--
check :: Testable a => a -> IO () -- | Check a property printing results on stdout and returning -- True on success. -- -- There is no option to silence this function: for silence, you should -- use holds. checkResult :: Testable a => a -> IO Bool -- | Use for to configure the number of tests performed by -- check. -- -- 
--   > check `for` 10080 $ \xs -> sort (sort xs) == sort (xs :: [Int])
--   +++ OK, passed 10080 tests.
--
-- -- Don't forget the dollar ($)! for :: Testable a => (WithOption a -> b) -> Int -> a -> b -- | Allows the user to customize instance information available when -- generalized. (For advanced users.) withInstances :: Testable a => (WithOption a -> b) -> Instances -> a -> b -- | Use withBackground to provide additional functions to -- appear in side-conditions. -- -- 
--   check `withBackground` [constant "isSpace" isSpace] $ \xs -> unwords (words xs) == xs
--   *** Failed! Falsifiable (after 4 tests):
--   " "
--   
--   Generalization:
--   ' ':_
--   
--   Conditional Generalization:
--   c:_  when  isSpace c
--
withBackground :: Testable a => (WithOption a -> b) -> [Expr] -> a -> b -- | Use withConditionSize to configure the maximum -- condition size allowed. withConditionSize :: Testable a => (WithOption a -> b) -> Int -> a -> b -- | Use minFailures to configure the minimum number of -- failures for a conditional generalization in function of the maximum -- number of tests. -- -- To set that conditional generalizations should fail for 10% of cases: -- > check minFailures (div 10) $ prop -- -- To set that conditional generalizations should fail for 5% of cases: -- > check minFailures (div 20) $ prop minFailures :: Testable a => (WithOption a -> b) -> Ratio Int -> a -> b maxSpeculateSize :: Testable a => (WithOption a -> b) -> Maybe Int -> a -> b conditionBound :: Testable a => (WithOption a -> b) -> Maybe Int -> a -> b -- | Configures a bound on the number of constants allowed in expressions -- that are considered when testing for equality in Speculate. -- -- Defaults to 2. constantBound :: Testable a => (WithOption a -> b) -> Maybe Int -> a -> b -- | Configures a bound on the depth of expressions that are considered -- when testing for equality in Speculate. -- -- Default to 3. depthBound :: Testable a => (WithOption a -> b) -> Maybe Int -> a -> b instance GHC.Show.Show Test.Extrapolate.IO.Result instance GHC.Classes.Eq Test.Extrapolate.IO.Result -- | This module is part of Extrapolate, a library for generalization of -- counter-examples. -- -- This is a module for deriving Generalizable instances. -- -- Needs GHC and Template Haskell (tested on GHC 8.0). -- -- If Extrapolate does not compile under later GHCs, this module is the -- probable culprit. module Test.Extrapolate.Derive -- | Derives a Generalizable instance for a given type Name. -- -- Consider the following Stack datatype: -- -- 
--   data Stack a = Stack a (Stack a) | Empty
--
-- -- Writing -- -- 
--   deriveGeneralizable ''Stack
--
-- -- will automatically derive the following Generalizable instance: -- -- 
--   instance Generalizable a => Generalizable (Stack a) where
--     expr s@(Stack x y) = constant "Stack" (Stack ->>: s) :$ expr x :$ expr y
--     expr s@Empty       = constant "Empty" (Empty   -: s)
--     instances s = this "s" s
--                 $ let Stack x y = Stack undefined undefined `asTypeOf` s
--                   in instances x
--                    . instances y
--
-- -- This function needs the TemplateHaskell extension. deriveGeneralizable :: Name -> DecsQ -- | Same as deriveGeneralizable but does not warn when instance -- already exists (deriveGeneralizable is preferable). deriveGeneralizableIfNeeded :: Name -> DecsQ -- | Derives a Generalizable instance for a given type Name -- cascading derivation of type arguments as well. deriveGeneralizableCascading :: Name -> DecsQ instance GHC.Show.Show Test.Extrapolate.Derive.Bla instance GHC.Classes.Ord Test.Extrapolate.Derive.Bla instance GHC.Classes.Eq Test.Extrapolate.Derive.Bla -- | This module is part of Extrapolate, a library for generalization of -- counter-examples. -- -- This provides the basic functionality of extrapolate. You will have -- better luck importing Test.Extrapolate directly. module Test.Extrapolate.Basic instance (GHC.Real.Integral a, Test.Extrapolate.Core.Generalizable a) => Test.Extrapolate.Core.Generalizable (GHC.Real.Ratio a) instance (Test.Extrapolate.Core.Generalizable a, Test.Extrapolate.Core.Generalizable b, Test.Extrapolate.Core.Generalizable c, Test.Extrapolate.Core.Generalizable d, Test.Extrapolate.Core.Generalizable e) => Test.Extrapolate.Core.Generalizable (a, b, c, d, e) instance (Test.Extrapolate.Core.Generalizable a, Test.Extrapolate.Core.Generalizable b, Test.Extrapolate.Core.Generalizable c, Test.Extrapolate.Core.Generalizable d, Test.Extrapolate.Core.Generalizable e, Test.Extrapolate.Core.Generalizable f) => Test.Extrapolate.Core.Generalizable (a, b, c, d, e, f) instance (Test.Extrapolate.Core.Generalizable a, Test.Extrapolate.Core.Generalizable b, Test.Extrapolate.Core.Generalizable c, Test.Extrapolate.Core.Generalizable d, Test.Extrapolate.Core.Generalizable e, Test.Extrapolate.Core.Generalizable f, Test.Extrapolate.Core.Generalizable g) => Test.Extrapolate.Core.Generalizable (a, b, c, d, e, f, g) instance (Test.Extrapolate.Core.Generalizable a, Test.Extrapolate.Core.Generalizable b, Test.Extrapolate.Core.Generalizable c, Test.Extrapolate.Core.Generalizable d, Test.Extrapolate.Core.Generalizable e, Test.Extrapolate.Core.Generalizable f, Test.Extrapolate.Core.Generalizable g, Test.Extrapolate.Core.Generalizable h) => Test.Extrapolate.Core.Generalizable (a, b, c, d, e, f, g, h) -- | Extrapolate is a property-based testing library capable of reporting -- generalized counter-examples. -- -- Consider the following faulty implementation of sort: -- -- 
--   sort :: Ord a => [a] -> [a]
--   sort []      =  []
--   sort (x:xs)  =  sort (filter (< x) xs)
--                ++ [x]
--                ++ sort (filter (> x) xs)
--
-- -- When tests pass, Extrapolate works like a regular property-based -- testing library. See: -- -- 
--   > check $ \xs -> sort (sort xs :: [Int]) == sort xs
--   +++ OK, passed 360 tests.
--
-- -- When tests fail, Extrapolate reports a fully defined counter-example -- and a generalization of failing inputs. See: -- -- 
--   > > check $ \xs -> length (sort xs :: [Int]) == length xs
--   *** Failed! Falsifiable (after 3 tests):
--   [0,0]
--   
--   Generalization:
--   x:x:_
--
-- -- The property fails for any integer x and for any list -- _ at the tail. module Test.Extrapolate -- | Checks a property printing results on stdout -- -- 
--   > check $ \xs -> sort (sort xs) == sort (xs::[Int])
--   +++ OK, passed 360 tests.
--   
--   > check $ \xs ys -> xs `union` ys == ys `union` (xs::[Int])
--   *** Failed! Falsifiable (after 4 tests):
--   [] [0,0]
--   
--   Generalization:
--   [] (x:x:_)
--
check :: Testable a => a -> IO () -- | Check a property printing results on stdout and returning -- True on success. -- -- There is no option to silence this function: for silence, you should -- use holds. checkResult :: Testable a => a -> IO Bool -- | Use for to configure the number of tests performed by -- check. -- -- 
--   > check `for` 10080 $ \xs -> sort (sort xs) == sort (xs :: [Int])
--   +++ OK, passed 10080 tests.
--
-- -- Don't forget the dollar ($)! for :: Testable a => (WithOption a -> b) -> Int -> a -> b -- | Use withBackground to provide additional functions to -- appear in side-conditions. -- -- 
--   check `withBackground` [constant "isSpace" isSpace] $ \xs -> unwords (words xs) == xs
--   *** Failed! Falsifiable (after 4 tests):
--   " "
--   
--   Generalization:
--   ' ':_
--   
--   Conditional Generalization:
--   c:_  when  isSpace c
--
withBackground :: Testable a => (WithOption a -> b) -> [Expr] -> a -> b -- | Use withConditionSize to configure the maximum -- condition size allowed. withConditionSize :: Testable a => (WithOption a -> b) -> Int -> a -> b -- | Use minFailures to configure the minimum number of -- failures for a conditional generalization in function of the maximum -- number of tests. -- -- To set that conditional generalizations should fail for 10% of cases: -- > check minFailures (div 10) $ prop -- -- To set that conditional generalizations should fail for 5% of cases: -- > check minFailures (div 20) $ prop minFailures :: Testable a => (WithOption a -> b) -> Ratio Int -> a -> b -- | Extrapolate can generalize counter-examples of any types that are -- Generalizable. -- -- The core (and only required functions) of the generalizable typeclass -- are the expr and instances functions. -- -- The following example shows a datatype and its instance: -- -- 
--   data Stack a = Stack a (Stack a) | Empty
--
-- -- 
--   instance Generalizable a => Generalizable (Stack a) where
--   name _ = "s"
--   expr s@(Stack x y) = constant "Stack" (Stack ->>: s) :$ expr x :$ expr y
--   expr s@Empty       = constant "Empty" (Empty   -: s)
--   instances s = this s $ instances (argTy1of1 s)
--
-- -- To declare instances and expr it may be useful to use: -- -- class (Listable a, Typeable a, Show a) => Generalizable a -- | Transforms a value into an manipulable expression tree. See -- constant and :$. expr :: Generalizable a => a -> Expr -- | Common name for a variable, defaults to "x". name :: Generalizable a => a -> String -- | List of symbols allowed to appear in side-conditions. Defaults to -- []. See constant. background :: Generalizable a => a -> [Expr] -- | Computes a list of reified instances. See this. instances :: Generalizable a => a -> Instances -> Instances this :: Generalizable a => a -> (Instances -> Instances) -> Instances -> Instances data Expr Constant :: String -> Dynamic -> Expr Var :: String -> TypeRep -> Expr (:$) :: Expr -> Expr -> Expr constant :: Typeable a => String -> a -> Expr showConstant :: (Typeable a, Show a) => a -> Expr bgEq :: (Eq a, Generalizable a) => a -> [Expr] bgOrd :: (Ord a, Generalizable a) => a -> [Expr] class Testable a -- | Derives a Generalizable instance for a given type Name. -- -- Consider the following Stack datatype: -- -- 
--   data Stack a = Stack a (Stack a) | Empty
--
-- -- Writing -- -- 
--   deriveGeneralizable ''Stack
--
-- -- will automatically derive the following Generalizable instance: -- -- 
--   instance Generalizable a => Generalizable (Stack a) where
--     expr s@(Stack x y) = constant "Stack" (Stack ->>: s) :$ expr x :$ expr y
--     expr s@Empty       = constant "Empty" (Empty   -: s)
--     instances s = this "s" s
--                 $ let Stack x y = Stack undefined undefined `asTypeOf` s
--                   in instances x
--                    . instances y
--
-- -- This function needs the TemplateHaskell extension. deriveGeneralizable :: Name -> DecsQ -- | Same as deriveGeneralizable but does not warn when instance -- already exists (deriveGeneralizable is preferable). deriveGeneralizableIfNeeded :: Name -> DecsQ -- | Derives a Generalizable instance for a given type Name -- cascading derivation of type arguments as well. deriveGeneralizableCascading :: Name -> DecsQ -- | Takes as argument an integer length and tiers of element values; -- returns tiers of lists of element values of the given length. -- -- 
--   listsOfLength 3 [[0],[1],[2],[3],[4]...] =
--     [ [[0,0,0]]
--     , [[0,0,1],[0,1,0],[1,0,0]]
--     , [[0,0,2],[0,1,1],[0,2,0],[1,0,1],[1,1,0],[2,0,0]]
--     , ...
--     ]
--
listsOfLength :: () => Int -> [[a]] -> [[[a]]] -- | Takes as argument tiers of element values; returns tiers of -- size-ordered lists of elements without repetition. -- -- 
--   setsOf [[0],[1],[2],...] =
--     [ [[]]
--     , [[0]]
--     , [[1]]
--     , [[0,1],[2]]
--     , [[0,2],[3]]
--     , [[0,3],[1,2],[4]]
--     , [[0,1,2],[0,4],[1,3],[5]]
--     , ...
--     ]
--
-- -- Can be used in the constructor of specialized Listable -- instances. For Set (from Data.Set), we would have: -- -- 
--   instance Listable a => Listable (Set a) where
--     tiers = mapT fromList $ setsOf tiers
--
setsOf :: () => [[a]] -> [[[a]]] -- | Takes as argument tiers of element values; returns tiers of -- size-ordered lists of elements possibly with repetition. -- -- 
--   bagsOf [[0],[1],[2],...] =
--     [ [[]]
--     , [[0]]
--     , [[0,0],[1]]
--     , [[0,0,0],[0,1],[2]]
--     , [[0,0,0,0],[0,0,1],[0,2],[1,1],[3]]
--     , [[0,0,0,0,0],[0,0,0,1],[0,0,2],[0,1,1],[0,3],[1,2],[4]]
--     , ...
--     ]
--
bagsOf :: () => [[a]] -> [[[a]]] -- | Takes as argument tiers of element values; returns tiers of lists with -- no repeated elements. -- -- 
--   noDupListsOf [[0],[1],[2],...] ==
--     [ [[]]
--     , [[0]]
--     , [[1]]
--     , [[0,1],[1,0],[2]]
--     , [[0,2],[2,0],[3]]
--     , ...
--     ]
--
noDupListsOf :: () => [[a]] -> [[[a]]] -- | Normalizes tiers by removing up to 12 empty tiers from the end of a -- list of tiers. -- -- 
--   normalizeT [xs0,xs1,...,xsN,[]]     =  [xs0,xs1,...,xsN]
--   normalizeT [xs0,xs1,...,xsN,[],[]]  =  [xs0,xs1,...,xsN]
--
-- -- The arbitrary limit of 12 tiers is necessary as this function would -- loop if there is an infinite trail of empty tiers. normalizeT :: () => [[a]] -> [[a]] -- | Delete the first occurence of an element in a tier. -- -- For normalized lists-of-tiers without repetitions, the following -- holds: -- -- 
--   deleteT x = normalizeT . (`suchThat` (/= x))
--
deleteT :: Eq a => a -> [[a]] -> [[a]] -- | Takes the product of N lists of tiers, producing lists of length N. -- -- Alternatively, takes as argument a list of lists of tiers of elements; -- returns lists combining elements of each list of tiers. -- -- 
--   products [xss] = mapT (:[]) xss
--   products [xss,yss] = mapT (\(x,y) -> [x,y]) (xss >< yss)
--   products [xss,yss,zss] = product3With (\x y z -> [x,y,z]) xss yss zss
--
products :: () => [[[a]]] -> [[[a]]] -- | Takes as argument tiers of element values; returns tiers of lists of -- elements. -- -- 
--   listsOf [[]] == [[[]]]
--
-- -- 
--   listsOf [[x]] == [ [[]]
--                    , [[x]]
--                    , [[x,x]]
--                    , [[x,x,x]]
--                    , ...
--                    ]
--
-- -- 
--   listsOf [[x],[y]] == [ [[]]
--                        , [[x]]
--                        , [[x,x],[y]]
--                        , [[x,x,x],[x,y],[y,x]]
--                        , ...
--                        ]
--
listsOf :: () => [[a]] -> [[[a]]] -- | Take the product of lists of tiers by a function returning a -- Maybe value discarding Nothing values. productMaybeWith :: () => a -> b -> Maybe c -> [[a]] -> [[b]] -> [[c]] -- | Like productWith, but over 3 lists of tiers. product3With :: () => a -> b -> c -> d -> [[a]] -> [[b]] -> [[c]] -> [[d]] -- | Given a constructor that takes a list with no duplicate elements, -- return tiers of applications of this constructor. noDupListCons :: Listable a => [a] -> b -> [[b]] -- | Given a constructor that takes a map of elements (encoded as a list), -- lists tiers of applications of this constructor -- -- So long as the underlying Listable enumerations have no -- repetitions, this will generate no repetitions. -- -- This allows defining an efficient implementation of tiers that -- does not repeat maps given by: -- -- 
--   tiers = mapCons fromList
--
mapCons :: (Listable a, Listable b) => [(a, b)] -> c -> [[c]] -- | Given a constructor that takes a set of elements (as a list), lists -- tiers of applications of this constructor. -- -- A naive Listable instance for the Set (of -- Data.Set) would read: -- -- 
--   instance Listable a => Listable (Set a) where
--     tiers = cons0 empty \/ cons2 insert
--
-- -- The above instance has a problem: it generates repeated sets. A more -- efficient implementation that does not repeat sets is given by: -- -- 
--   tiers = setCons fromList
--
-- -- Alternatively, you can use setsOf direclty. setCons :: Listable a => [a] -> b -> [[b]] -- | Given a constructor that takes a bag of elements (as a list), lists -- tiers of applications of this constructor. -- -- For example, a Bag represented as a list. -- -- 
--   bagCons Bag
--
bagCons :: Listable a => [a] -> b -> [[b]] -- | Derives a Listable instance for a given type Name -- cascading derivation of type arguments as well. deriveListableCascading :: Name -> DecsQ -- | Derives a Listable instance for a given type Name. -- -- Consider the following Stack datatype: -- -- 
--   data Stack a = Stack a (Stack a) | Empty
--
-- -- Writing -- -- 
--   deriveListable ''Stack
--
-- -- will automatically derive the following Listable instance: -- -- 
--   instance Listable a => Listable (Stack a) where
--     tiers = cons2 Stack \/ cons0 Empty
--
-- -- Needs the TemplateHaskell extension. deriveListable :: Name -> DecsQ -- | Adds to the weight of tiers of a constructor -- -- addWeight is closely related to delay. addWeight :: () => [[a]] -> Int -> [[a]] -- | Resets the weight of a constructor (or tiers) Typically used as an -- infix constructor when defining Listable instances: -- -- 
--   cons<N> `ofWeight` <W>
--
-- -- Be careful: do not apply ofWeight 0 to recursive data -- structure constructors. In general this will make the list of size 0 -- infinite, breaking the tier invariant (each tier must be finite). -- -- ofWeight is closely related to reset. ofWeight :: () => [[a]] -> Int -> [[a]] cons12 :: (Listable a, Listable b, Listable c, Listable d, Listable e, Listable f, Listable g, Listable h, Listable i, Listable j, Listable k, Listable l) => a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> k -> l -> m -> [[m]] cons11 :: (Listable a, Listable b, Listable c, Listable d, Listable e, Listable f, Listable g, Listable h, Listable i, Listable j, Listable k) => a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> k -> l -> [[l]] cons10 :: (Listable a, Listable b, Listable c, Listable d, Listable e, Listable f, Listable g, Listable h, Listable i, Listable j) => a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> k -> [[k]] cons9 :: (Listable a, Listable b, Listable c, Listable d, Listable e, Listable f, Listable g, Listable h, Listable i) => a -> b -> c -> d -> e -> f -> g -> h -> i -> j -> [[j]] cons8 :: (Listable a, Listable b, Listable c, Listable d, Listable e, Listable f, Listable g, Listable h) => a -> b -> c -> d -> e -> f -> g -> h -> i -> [[i]] cons7 :: (Listable a, Listable b, Listable c, Listable d, Listable e, Listable f, Listable g) => a -> b -> c -> d -> e -> f -> g -> h -> [[h]] cons6 :: (Listable a, Listable b, Listable c, Listable d, Listable e, Listable f) => a -> b -> c -> d -> e -> f -> g -> [[g]] -- | Boolean implication operator. Useful for defining conditional -- properties: -- -- 
--   prop_something x y = condition x y ==> something x y
--
(==>) :: Bool -> Bool -> Bool infixr 0 ==> -- | There exists an assignment of values that satisfies a property -- up to a number of test values? -- -- 
--   exists 1000 $ \x -> x > 10
--
exists :: Testable a => Int -> a -> Bool -- | Does a property fail for a number of test values? -- -- 
--   fails 1000 $ \xs -> xs ++ ys == ys ++ xs
--
fails :: Testable a => Int -> a -> Bool -- | Does a property hold up to a number of test values? -- -- 
--   holds 1000 $ \xs -> length (sort xs) == length xs
--
holds :: Testable a => Int -> a -> Bool -- | Up to a number of tests to a property, returns Just the first -- witness or Nothing if there is none. witness :: Testable a => Int -> a -> Maybe [String] -- | Lists all witnesses up to a number of tests to a property, witnesses :: Testable a => Int -> a -> [[String]] -- | Take a tiered product of lists of tiers. -- -- 
--   [t0,t1,t2,...] >< [u0,u1,u2,...] =
--   [ t0**u0
--   , t0**u1 ++ t1**u0
--   , t0**u2 ++ t1**u1 ++ t2**u0
--   , ...       ...       ...       ...
--   ]
--   where xs ** ys = [(x,y) | x <- xs, y <- ys]
--
-- -- Example: -- -- 
--   [[0],[1],[2],...] >< [[0],[1],[2],...]
--   == [  [(0,0)]
--      ,  [(1,0),(0,1)]
--      ,  [(2,0),(1,1),(0,2)]
--      ,  [(3,0),(2,1),(1,2),(0,3)]
--      ...
--      ]
--
(><) :: () => [[a]] -> [[b]] -> [[(a, b)]] infixr 8 >< -- | Interleave tiers --- sum of two tiers enumerations. When in doubt, use -- \/ instead. -- -- 
--   [xs,ys,zs,...] \/ [as,bs,cs,...] = [xs+|as,ys+|bs,zs+|cs,...]
--
(\\//) :: () => [[a]] -> [[a]] -> [[a]] infixr 7 \\// -- | Append tiers --- sum of two tiers enumerations. -- -- 
--   [xs,ys,zs,...] \/ [as,bs,cs,...] = [xs++as,ys++bs,zs++cs,...]
--
(\/) :: () => [[a]] -> [[a]] -> [[a]] infixr 7 \/ -- | Lazily interleaves two lists, switching between elements of the two. -- Union/sum of the elements in the lists. -- -- 
--   [x,y,z] +| [a,b,c] == [x,a,y,b,z,c]
--
(+|) :: () => [a] -> [a] -> [a] infixr 5 +| -- | Tiers of values that follow a property -- -- 
--   cons<N> `suchThat` condition
--
suchThat :: () => [[a]] -> a -> Bool -> [[a]] -- | Resets any delays in a list-of tiers. Conceptually this -- function makes a constructor "weightless", assuring the first tier is -- non-empty. Typically used when defining Listable instances: -- -- 
--   reset (cons<N> <Constr>)
--
-- -- Be careful: do not apply reset to recursive data structure -- constructors. In general this will make the list of size 0 infinite, -- breaking the tiers invariant (each tier must be finite). reset :: () => [[a]] -> [[a]] -- | Delays the enumeration of tiers. Conceptually this function -- adds to the weight of a constructor. Typically used when defining -- Listable instances: -- -- 
--   delay (cons<N> <Constr>)
--
delay :: () => [[a]] -> [[a]] -- | Returns tiers of applications of a 5-argument constructor. -- -- Test.LeanCheck.Basic defines cons6 up to cons12. -- Those are exported by default from Test.LeanCheck, but are -- hidden from the Haddock documentation. cons5 :: (Listable a, Listable b, Listable c, Listable d, Listable e) => a -> b -> c -> d -> e -> f -> [[f]] -- | Returns tiers of applications of a 4-argument constructor. cons4 :: (Listable a, Listable b, Listable c, Listable d) => a -> b -> c -> d -> e -> [[e]] -- | Returns tiers of applications of a 3-argument constructor. cons3 :: (Listable a, Listable b, Listable c) => a -> b -> c -> d -> [[d]] -- | Given a constructor with two Listable arguments, return -- tiers of applications of this constructor. By default, returned -- values will have size/weight of 1. cons2 :: (Listable a, Listable b) => a -> b -> c -> [[c]] -- | Given a constructor with one Listable argument, return -- tiers of applications of this constructor. By default, returned -- values will have size/weight of 1. cons1 :: Listable a => a -> b -> [[b]] -- | Given a constructor with no arguments, returns tiers of all -- possible applications of this constructor. Since in this case there is -- only one possible application (to no arguments), only a single value, -- of size/weight 0, will be present in the resulting list of tiers. cons0 :: () => a -> [[a]] -- | concatMap over tiers concatMapT :: () => a -> [[b]] -> [[a]] -> [[b]] -- | concat tiers of tiers concatT :: () => [[[[a]]]] -> [[a]] -- | filter tiers filterT :: () => a -> Bool -> [[a]] -> [[a]] -- | map over tiers mapT :: () => a -> b -> [[a]] -> [[b]] -- | Tiers of Fractional values. This can be used as the -- implementation of tiers for Fractional types. tiersFractional :: Fractional a => [[a]] -- | Tiers of Integral values. Can be used as a default -- implementation of list for Integral types. listIntegral :: (Enum a, Num a) => [a] -- | Takes a list of values xs and transform it into tiers on -- which each tier is occupied by a single element from xs. -- -- To convert back to a list, just concat. toTiers :: () => [a] -> [[a]] -- | A type is Listable when there exists a function that is able to -- list (ideally all of) its values. -- -- Ideally, instances should be defined by a tiers function that -- returns a (potentially infinite) list of finite sub-lists (tiers): the -- first sub-list contains elements of size 0, the second sub-list -- contains elements of size 1 and so on. Size here is defined by the -- implementor of the type-class instance. -- -- For algebraic data types, the general form for tiers is -- -- 
--   tiers = cons<N> ConstructorA
--        \/ cons<N> ConstructorB
--        \/ ...
--        \/ cons<N> ConstructorZ
--
-- -- where N is the number of arguments of each constructor -- A...Z. -- -- Instances can be alternatively defined by list. In this case, -- each sub-list in tiers is a singleton list (each succeeding -- element of list has +1 size). -- -- The function deriveListable from Test.LeanCheck.Derive -- can automatically derive instances of this typeclass. -- -- A Listable instance for functions is also available but is not -- exported by default. Import Test.LeanCheck.Function if you need -- to test higher-order properties. class Listable a tiers :: Listable a => [[a]] list :: Listable a => [a]