smallcheck-1.2.1: Test/SmallCheck/Series.hs
-- vim:fdm=marker:foldtext=foldtext()
--------------------------------------------------------------------
-- |
-- Module : Test.SmallCheck.Series
-- Copyright : (c) Colin Runciman et al.
-- License : BSD3
-- Maintainer: Roman Cheplyaka <roma@ro-che.info>
--
-- You need this module if you want to generate test values of your own
-- types.
--
-- You'll typically need the following extensions:
--
-- >{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-}
--
-- SmallCheck itself defines data generators for all the data types used
-- by the "Prelude".
--
-- In order to generate values and functions of your own types, you need
-- to make them instances of 'Serial' (for values) and 'CoSerial' (for
-- functions). There are two main ways to do so: using Generics or writing
-- the instances by hand.
--------------------------------------------------------------------
{-# LANGUAGE CPP #-}
#if __GLASGOW_HASKELL__ >= 702
{-# LANGUAGE DefaultSignatures #-}
#endif
{-# LANGUAGE DeriveFoldable #-}
{-# LANGUAGE DeriveFunctor #-}
{-# LANGUAGE DeriveTraversable #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeOperators #-}
#if MIN_VERSION_base(4,8,0)
{-# LANGUAGE Safe #-}
#else
{-# LANGUAGE OverlappingInstances #-}
#if __GLASGOW_HASKELL__ >= 704
{-# LANGUAGE Trustworthy #-}
#endif
#endif
#define HASCBOOL MIN_VERSION_base(4,10,0)
module Test.SmallCheck.Series (
-- {{{
-- * Generic instances
-- | The easiest way to create the necessary instances is to use GHC
-- generics (available starting with GHC 7.2.1).
--
-- Here's a complete example:
--
-- >{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses #-}
-- >{-# LANGUAGE DeriveGeneric #-}
-- >
-- >import Test.SmallCheck.Series
-- >import GHC.Generics
-- >
-- >data Tree a = Null | Fork (Tree a) a (Tree a)
-- > deriving Generic
-- >
-- >instance Serial m a => Serial m (Tree a)
--
-- Here we enable the @DeriveGeneric@ extension which allows to derive 'Generic'
-- instance for our data type. Then we declare that @Tree@ @a@ is an instance of
-- 'Serial', but do not provide any definitions. This causes GHC to use the
-- default definitions that use the 'Generic' instance.
--
-- One minor limitation of generic instances is that there's currently no
-- way to distinguish newtypes and datatypes. Thus, newtype constructors
-- will also count as one level of depth.
-- * Data Generators
-- | Writing 'Serial' instances for application-specific types is
-- straightforward. You need to define a 'series' generator, typically using
-- @consN@ family of generic combinators where N is constructor arity.
--
-- For example:
--
-- >data Tree a = Null | Fork (Tree a) a (Tree a)
-- >
-- >instance Serial m a => Serial m (Tree a) where
-- > series = cons0 Null \/ cons3 Fork
--
-- For newtypes use 'newtypeCons' instead of 'cons1'.
-- The difference is that 'cons1' is counts as one level of depth, while
-- 'newtypeCons' doesn't affect the depth.
--
-- >newtype Light a = Light a
-- >
-- >instance Serial m a => Serial m (Light a) where
-- > series = newtypeCons Light
--
-- For data types with more than 6 fields define @consN@ as
--
-- >consN f = decDepth $
-- > f <$> series
-- > <~> series
-- > <~> series
-- > <~> ... {- series repeated N times in total -}
-- ** What does @consN@ do, exactly?
-- | @consN@ has type
-- @(Serial t₁, ..., Serial tₙ) => (t₁ -> ... -> tₙ -> t) -> Series t@.
--
-- @consN@ @f@ is a series which, for a given depth \(d > 0\), produces values of the
-- form
--
-- >f x₁ ... xₙ
--
-- where @xₖ@ ranges over all values of type @tₖ@ of depth up to \(d-1\)
-- (as defined by the 'series' functions for @tₖ@).
--
-- @consN@ functions also ensure that xₖ are enumerated in the
-- breadth-first order. Thus, combinations of smaller depth come first
-- (assuming the same is true for @tₖ@).
--
-- If \(d \le 0\), no values are produced.
cons0, cons1, cons2, cons3, cons4, cons5, cons6, newtypeCons,
-- * Function Generators
-- | To generate functions of an application-specific argument type,
-- make the type an instance of 'CoSerial'.
--
-- Again there is a standard pattern, this time using the @altsN@
-- combinators where again N is constructor arity. Here are @Tree@ and
-- @Light@ instances:
--
--
-- >instance CoSerial m a => CoSerial m (Tree a) where
-- > coseries rs =
-- > alts0 rs >>- \z ->
-- > alts3 rs >>- \f ->
-- > return $ \t ->
-- > case t of
-- > Null -> z
-- > Fork t1 x t2 -> f t1 x t2
--
-- >instance CoSerial m a => CoSerial m (Light a) where
-- > coseries rs =
-- > newtypeAlts rs >>- \f ->
-- > return $ \l ->
-- > case l of
-- > Light x -> f x
--
-- For data types with more than 6 fields define @altsN@ as
--
-- >altsN rs = do
-- > rs <- fixDepth rs
-- > decDepthChecked
-- > (constM $ constM $ ... $ constM rs)
-- > (coseries $ coseries $ ... $ coseries rs)
-- > {- constM and coseries are repeated N times each -}
-- ** What does altsN do, exactly?
-- | @altsN@ has type
-- @(Serial t₁, ..., Serial tₙ) => Series t -> Series (t₁ -> ... -> tₙ -> t)@.
--
-- @altsN@ @s@ is a series which, for a given depth \( d \), produces functions of
-- type
--
-- >t₁ -> ... -> tₙ -> t
--
-- If \( d \le 0 \), these are constant functions, one for each value produced
-- by @s@.
--
-- If \( d > 0 \), these functions inspect each of their arguments up to the depth
-- \( d-1 \) (as defined by the 'coseries' functions for the corresponding
-- types) and return values produced by @s@. The depth to which the
-- values are enumerated does not depend on the depth of inspection.
alts0, alts1, alts2, alts3, alts4, alts5, alts6, newtypeAlts,
-- * Basic definitions
Depth, Series, Serial(..), CoSerial(..),
#if __GLASGOW_HASKELL__ >= 702
-- * Generic implementations
genericSeries,
genericCoseries,
#endif
-- * Convenient wrappers
Positive(..), NonNegative(..), NonZero(..), NonEmpty(..),
-- * Other useful definitions
(\/), (><), (<~>), (>>-),
localDepth,
decDepth,
getDepth,
generate,
limit,
listSeries,
list,
listM,
fixDepth,
decDepthChecked,
constM
-- }}}
) where
import Control.Monad (liftM, guard, mzero, mplus, msum)
import Control.Monad.Logic (MonadLogic, (>>-), interleave, msplit, observeAllT)
import Control.Monad.Reader (ask, local)
import Control.Applicative (empty, pure, (<$>), (<|>))
import Data.Complex (Complex(..))
import Data.Foldable (Foldable)
import Data.Functor.Compose (Compose(..))
import Data.Void (Void, absurd)
import Control.Monad.Identity (Identity(..))
import Data.Int (Int, Int8, Int16, Int32, Int64)
import Data.List (intercalate)
import qualified Data.List.NonEmpty as NE
import Data.Ratio (Ratio, numerator, denominator, (%))
import Data.Traversable (Traversable)
import Data.Word (Word, Word8, Word16, Word32, Word64)
import Foreign.C.Types (CFloat(..), CDouble(..), CChar(..), CSChar(..), CUChar(..), CShort(..), CUShort(..), CInt(..), CUInt(..), CLong(..), CULong(..), CPtrdiff(..), CSize(..), CWchar(..), CSigAtomic(..), CLLong(..), CULLong(..), CIntPtr(..), CUIntPtr(..), CIntMax(..), CUIntMax(..), CClock(..), CTime(..))
#if __GLASGOW_HASKELL__ >= 702
import Foreign.C.Types (CUSeconds(..), CSUSeconds(..))
#endif
#if HASCBOOL
import Foreign.C.Types (CBool(..))
#endif
import Numeric.Natural (Natural)
import Test.SmallCheck.SeriesMonad
#if __GLASGOW_HASKELL__ >= 702
import GHC.Generics (Generic, (:+:)(..), (:*:)(..), C1, K1(..), M1(..), U1(..), V1(..), Rep, to, from)
#endif
------------------------------
-- Main types and classes
------------------------------
--{{{
class Monad m => Serial m a where
series :: Series m a
#if __GLASGOW_HASKELL__ >= 704
default series :: (Generic a, GSerial m (Rep a)) => Series m a
series = genericSeries
#endif
#if __GLASGOW_HASKELL__ >= 702
genericSeries
:: (Monad m, Generic a, GSerial m (Rep a))
=> Series m a
genericSeries = to <$> gSeries
#endif
class Monad m => CoSerial m a where
-- | A proper 'coseries' implementation should pass the depth unchanged to
-- its first argument. Doing otherwise will make enumeration of curried
-- functions non-uniform in their arguments.
coseries :: Series m b -> Series m (a->b)
#if __GLASGOW_HASKELL__ >= 704
default coseries :: (Generic a, GCoSerial m (Rep a)) => Series m b -> Series m (a->b)
coseries = genericCoseries
#endif
#if __GLASGOW_HASKELL__ >= 702
genericCoseries
:: (Monad m, Generic a, GCoSerial m (Rep a))
=> Series m b -> Series m (a->b)
genericCoseries rs = (. from) <$> gCoseries rs
#endif
-- }}}
------------------------------
-- Helper functions
------------------------------
-- {{{
-- | A simple series specified by a function from depth to the list of
-- values up to that depth.
generate :: (Depth -> [a]) -> Series m a
generate f = do
d <- getDepth
msum $ map return $ f d
-- | Limit a 'Series' to its first @n@ elements.
limit :: forall m a . Monad m => Int -> Series m a -> Series m a
limit n0 (Series s) = Series $ go n0 s
where
go 0 _ = empty
go n mb1 = do
cons :: Maybe (b, ml b) <- msplit mb1
case cons of
Nothing -> empty
Just (b, mb2) -> return b <|> go (n-1) mb2
suchThat :: Series m a -> (a -> Bool) -> Series m a
suchThat s p = s >>= \x -> if p x then pure x else empty
-- | Given a depth, return the list of values generated by a 'Serial' instance.
--
-- For example, list all integers up to depth 1:
--
-- * @listSeries 1 :: [Int] -- returns [0,1,-1]@
listSeries :: Serial Identity a => Depth -> [a]
listSeries d = list d series
-- | Return the list of values generated by a 'Series'. Useful for
-- debugging 'Serial' instances.
--
-- Examples:
--
-- * @'list' 3 'series' :: ['Int'] -- returns [0,1,-1,2,-2,3,-3]@
--
-- * @'list' 3 ('series' :: 'Series' 'Data.Functor.Identity' 'Int') -- returns [0,1,-1,2,-2,3,-3]@
--
-- * @'list' 2 'series' :: [['Bool']] -- returns [[],['True'],['False']]@
--
-- The first two are equivalent. The second has a more explicit type binding.
list :: Depth -> Series Identity a -> [a]
list d s = runIdentity $ observeAllT $ runSeries d s
-- | Monadic version of 'list'.
listM d s = observeAllT $ runSeries d s
-- | Sum (union) of series.
infixr 7 \/
(\/) :: Monad m => Series m a -> Series m a -> Series m a
(\/) = interleave
-- | Product of series
infixr 8 ><
(><) :: Monad m => Series m a -> Series m b -> Series m (a,b)
a >< b = (,) <$> a <~> b
-- | Fair version of 'Control.Applicative.ap' and '<*>'.
infixl 4 <~>
(<~>) :: Monad m => Series m (a -> b) -> Series m a -> Series m b
a <~> b = a >>- (<$> b)
uncurry3 :: (a->b->c->d) -> ((a,b,c)->d)
uncurry3 f (x,y,z) = f x y z
uncurry4 :: (a->b->c->d->e) -> ((a,b,c,d)->e)
uncurry4 f (w,x,y,z) = f w x y z
uncurry5 :: (a->b->c->d->e->f) -> ((a,b,c,d,e)->f)
uncurry5 f (v,w,x,y,z) = f v w x y z
uncurry6 :: (a->b->c->d->e->f->g) -> ((a,b,c,d,e,f)->g)
uncurry6 f (u,v,w,x,y,z) = f u v w x y z
-- | Query the current depth.
getDepth :: Series m Depth
getDepth = Series ask
-- | Run a series with a modified depth.
localDepth :: (Depth -> Depth) -> Series m a -> Series m a
localDepth f (Series a) = Series $ local f a
-- | Run a 'Series' with the depth decreased by 1.
--
-- If the current depth is less or equal to 0, the result is 'empty'.
decDepth :: Series m a -> Series m a
decDepth a = do
checkDepth
localDepth (subtract 1) a
checkDepth :: Series m ()
checkDepth = do
d <- getDepth
guard $ d > 0
-- | @'constM' = 'liftM' 'const'@
constM :: Monad m => m b -> m (a -> b)
constM = liftM const
-- | Fix the depth of a series at the current level. The resulting series
-- will no longer depend on the \"ambient\" depth.
fixDepth :: Series m a -> Series m (Series m a)
fixDepth s = getDepth >>= \d -> return $ localDepth (const d) s
-- | If the current depth is 0, evaluate the first argument. Otherwise,
-- evaluate the second argument with decremented depth.
decDepthChecked :: Series m a -> Series m a -> Series m a
decDepthChecked b r = do
d <- getDepth
if d <= 0
then b
else decDepth r
unwind :: MonadLogic m => m a -> m [a]
unwind a =
msplit a >>=
maybe (return []) (\(x,a') -> (x:) `liftM` unwind a')
-- }}}
------------------------------
-- cons* and alts* functions
------------------------------
-- {{{
cons0 :: a -> Series m a
cons0 x = decDepth $ pure x
cons1 :: Serial m a => (a->b) -> Series m b
cons1 f = decDepth $ f <$> series
-- | Same as 'cons1', but preserves the depth.
newtypeCons :: Serial m a => (a->b) -> Series m b
newtypeCons f = f <$> series
cons2 :: (Serial m a, Serial m b) => (a->b->c) -> Series m c
cons2 f = decDepth $ f <$> series <~> series
cons3 :: (Serial m a, Serial m b, Serial m c) =>
(a->b->c->d) -> Series m d
cons3 f = decDepth $
f <$> series
<~> series
<~> series
cons4 :: (Serial m a, Serial m b, Serial m c, Serial m d) =>
(a->b->c->d->e) -> Series m e
cons4 f = decDepth $
f <$> series
<~> series
<~> series
<~> series
cons5 :: (Serial m a, Serial m b, Serial m c, Serial m d, Serial m e) =>
(a->b->c->d->e->f) -> Series m f
cons5 f = decDepth $
f <$> series
<~> series
<~> series
<~> series
<~> series
cons6 :: (Serial m a, Serial m b, Serial m c, Serial m d, Serial m e, Serial m f) =>
(a->b->c->d->e->f->g) -> Series m g
cons6 f = decDepth $
f <$> series
<~> series
<~> series
<~> series
<~> series
<~> series
alts0 :: Series m a -> Series m a
alts0 s = s
alts1 :: CoSerial m a => Series m b -> Series m (a->b)
alts1 rs = do
rs <- fixDepth rs
decDepthChecked (constM rs) (coseries rs)
alts2
:: (CoSerial m a, CoSerial m b)
=> Series m c -> Series m (a->b->c)
alts2 rs = do
rs <- fixDepth rs
decDepthChecked
(constM $ constM rs)
(coseries $ coseries rs)
alts3 :: (CoSerial m a, CoSerial m b, CoSerial m c) =>
Series m d -> Series m (a->b->c->d)
alts3 rs = do
rs <- fixDepth rs
decDepthChecked
(constM $ constM $ constM rs)
(coseries $ coseries $ coseries rs)
alts4 :: (CoSerial m a, CoSerial m b, CoSerial m c, CoSerial m d) =>
Series m e -> Series m (a->b->c->d->e)
alts4 rs = do
rs <- fixDepth rs
decDepthChecked
(constM $ constM $ constM $ constM rs)
(coseries $ coseries $ coseries $ coseries rs)
alts5 :: (CoSerial m a, CoSerial m b, CoSerial m c, CoSerial m d, CoSerial m e) =>
Series m f -> Series m (a->b->c->d->e->f)
alts5 rs = do
rs <- fixDepth rs
decDepthChecked
(constM $ constM $ constM $ constM $ constM rs)
(coseries $ coseries $ coseries $ coseries $ coseries rs)
alts6 :: (CoSerial m a, CoSerial m b, CoSerial m c, CoSerial m d, CoSerial m e, CoSerial m f) =>
Series m g -> Series m (a->b->c->d->e->f->g)
alts6 rs = do
rs <- fixDepth rs
decDepthChecked
(constM $ constM $ constM $ constM $ constM $ constM rs)
(coseries $ coseries $ coseries $ coseries $ coseries $ coseries rs)
-- | Same as 'alts1', but preserves the depth.
newtypeAlts :: CoSerial m a => Series m b -> Series m (a->b)
newtypeAlts = coseries
-- }}}
------------------------------
-- Generic instances
------------------------------
-- {{{
class GSerial m f where
gSeries :: Series m (f a)
class GCoSerial m f where
gCoseries :: Series m b -> Series m (f a -> b)
#if __GLASGOW_HASKELL__ >= 702
instance {-# OVERLAPPABLE #-} GSerial m f => GSerial m (M1 i c f) where
gSeries = M1 <$> gSeries
{-# INLINE gSeries #-}
instance GCoSerial m f => GCoSerial m (M1 i c f) where
gCoseries rs = (. unM1) <$> gCoseries rs
{-# INLINE gCoseries #-}
instance Serial m c => GSerial m (K1 i c) where
gSeries = K1 <$> series
{-# INLINE gSeries #-}
instance CoSerial m c => GCoSerial m (K1 i c) where
gCoseries rs = (. unK1) <$> coseries rs
{-# INLINE gCoseries #-}
instance GSerial m U1 where
gSeries = pure U1
{-# INLINE gSeries #-}
instance GCoSerial m U1 where
gCoseries rs = constM rs
{-# INLINE gCoseries #-}
instance GSerial m V1 where
gSeries = mzero
{-# INLINE gSeries #-}
instance GCoSerial m V1 where
gCoseries = const $ return (\a -> a `seq` let x = x in x)
{-# INLINE gCoseries #-}
instance (Monad m, GSerial m a, GSerial m b) => GSerial m (a :*: b) where
gSeries = (:*:) <$> gSeries <~> gSeries
{-# INLINE gSeries #-}
instance (Monad m, GCoSerial m a, GCoSerial m b) => GCoSerial m (a :*: b) where
gCoseries rs = uncur <$> gCoseries (gCoseries rs)
where
uncur f (x :*: y) = f x y
{-# INLINE gCoseries #-}
instance (Monad m, GSerial m a, GSerial m b) => GSerial m (a :+: b) where
gSeries = (L1 <$> gSeries) `interleave` (R1 <$> gSeries)
{-# INLINE gSeries #-}
instance (Monad m, GCoSerial m a, GCoSerial m b) => GCoSerial m (a :+: b) where
gCoseries rs =
gCoseries rs >>- \f ->
gCoseries rs >>- \g ->
return $
\e -> case e of
L1 x -> f x
R1 y -> g y
{-# INLINE gCoseries #-}
instance {-# OVERLAPPING #-} GSerial m f => GSerial m (C1 c f) where
gSeries = M1 <$> decDepth gSeries
{-# INLINE gSeries #-}
#endif
-- }}}
------------------------------
-- Instances for basic types
------------------------------
-- {{{
instance Monad m => Serial m () where
series = return ()
instance Monad m => CoSerial m () where
coseries rs = constM rs
instance Monad m => Serial m Integer where series = unM <$> series
instance Monad m => CoSerial m Integer where coseries = fmap (. M) . coseries
instance Monad m => Serial m Natural where series = unN <$> series
instance Monad m => CoSerial m Natural where coseries = fmap (. N) . coseries
instance Monad m => Serial m Int where series = unM <$> series
instance Monad m => CoSerial m Int where coseries = fmap (. M) . coseries
instance Monad m => Serial m Word where series = unN <$> series
instance Monad m => CoSerial m Word where coseries = fmap (. N) . coseries
instance Monad m => Serial m Int8 where series = unM <$> series
instance Monad m => CoSerial m Int8 where coseries = fmap (. M) . coseries
instance Monad m => Serial m Word8 where series = unN <$> series
instance Monad m => CoSerial m Word8 where coseries = fmap (. N) . coseries
instance Monad m => Serial m Int16 where series = unM <$> series
instance Monad m => CoSerial m Int16 where coseries = fmap (. M) . coseries
instance Monad m => Serial m Word16 where series = unN <$> series
instance Monad m => CoSerial m Word16 where coseries = fmap (. N) . coseries
instance Monad m => Serial m Int32 where series = unM <$> series
instance Monad m => CoSerial m Int32 where coseries = fmap (. M) . coseries
instance Monad m => Serial m Word32 where series = unN <$> series
instance Monad m => CoSerial m Word32 where coseries = fmap (. N) . coseries
instance Monad m => Serial m Int64 where series = unM <$> series
instance Monad m => CoSerial m Int64 where coseries = fmap (. M) . coseries
instance Monad m => Serial m Word64 where series = unN <$> series
instance Monad m => CoSerial m Word64 where coseries = fmap (. N) . coseries
-- | 'N' is a wrapper for 'Integral' types that causes only non-negative values
-- to be generated. Generated functions of type @N a -> b@ do not distinguish
-- different negative values of @a@.
newtype N a = N { unN :: a } deriving (Eq, Ord, Show)
instance Real a => Real (N a) where
toRational (N x) = toRational x
instance Enum a => Enum (N a) where
toEnum x = N (toEnum x)
fromEnum (N x) = fromEnum x
instance Num a => Num (N a) where
N x + N y = N (x + y)
N x * N y = N (x * y)
negate (N x) = N (negate x)
abs (N x) = N (abs x)
signum (N x) = N (signum x)
fromInteger x = N (fromInteger x)
instance Integral a => Integral (N a) where
quotRem (N x) (N y) = (N q, N r)
where
(q, r) = x `quotRem` y
toInteger (N x) = toInteger x
instance (Num a, Enum a, Serial m a) => Serial m (N a) where
series = generate $ \d -> take (d+1) [0..]
instance (Integral a, Monad m) => CoSerial m (N a) where
coseries rs =
-- This is a recursive function, because @alts1 rs@ typically calls
-- back to 'coseries' (but with lower depth).
--
-- The recursion stops when depth == 0. Then alts1 produces a constant
-- function, and doesn't call back to 'coseries'.
alts0 rs >>- \z ->
alts1 rs >>- \f ->
return $ \(N i) ->
if i > 0
then f (N $ i-1)
else z
-- | 'M' is a helper type to generate values of a signed type of increasing magnitude.
newtype M a = M { unM :: a } deriving (Eq, Ord, Show)
instance Real a => Real (M a) where
toRational (M x) = toRational x
instance Enum a => Enum (M a) where
toEnum x = M (toEnum x)
fromEnum (M x) = fromEnum x
instance Num a => Num (M a) where
M x + M y = M (x + y)
M x * M y = M (x * y)
negate (M x) = M (negate x)
abs (M x) = M (abs x)
signum (M x) = M (signum x)
fromInteger x = M (fromInteger x)
instance Integral a => Integral (M a) where
quotRem (M x) (M y) = (M q, M r)
where
(q, r) = x `quotRem` y
toInteger (M x) = toInteger x
instance (Num a, Enum a, Monad m) => Serial m (M a) where
series = others `interleave` positives
where positives = generate $ \d -> take d [1..]
others = generate $ \d -> take (d+1) [0,-1..]
instance (Ord a, Num a, Monad m) => CoSerial m (M a) where
coseries rs =
alts0 rs >>- \z ->
alts1 rs >>- \f ->
alts1 rs >>- \g ->
pure $ \ i -> case compare i 0 of
GT -> f (M (i - 1))
LT -> g (M (abs i - 1))
EQ -> z
instance Monad m => Serial m Float where
series =
series >>- \(sig, exp) ->
guard (odd sig || sig==0 && exp==0) >>
return (encodeFloat sig exp)
instance Monad m => CoSerial m Float where
coseries rs =
coseries rs >>- \f ->
return $ f . decodeFloat
instance Monad m => Serial m Double where
series = (realToFrac :: Float -> Double) <$> series
instance Monad m => CoSerial m Double where
coseries rs =
(. (realToFrac :: Double -> Float)) <$> coseries rs
instance (Integral i, Serial m i) => Serial m (Ratio i) where
series = pairToRatio <$> series
where
pairToRatio (n, Positive d) = n % d
instance (Integral i, CoSerial m i) => CoSerial m (Ratio i) where
coseries rs = (. ratioToPair) <$> coseries rs
where
ratioToPair r = (numerator r, denominator r)
instance Monad m => Serial m Char where
series = generate $ \d -> take (d+1) ['a'..'z']
instance Monad m => CoSerial m Char where
coseries rs =
coseries rs >>- \f ->
return $ \c -> f (N (fromEnum c - fromEnum 'a'))
instance (Serial m a, Serial m b) => Serial m (a,b) where
series = cons2 (,)
instance (CoSerial m a, CoSerial m b) => CoSerial m (a,b) where
coseries rs = uncurry <$> alts2 rs
instance (Serial m a, Serial m b, Serial m c) => Serial m (a,b,c) where
series = cons3 (,,)
instance (CoSerial m a, CoSerial m b, CoSerial m c) => CoSerial m (a,b,c) where
coseries rs = uncurry3 <$> alts3 rs
instance (Serial m a, Serial m b, Serial m c, Serial m d) => Serial m (a,b,c,d) where
series = cons4 (,,,)
instance (CoSerial m a, CoSerial m b, CoSerial m c, CoSerial m d) => CoSerial m (a,b,c,d) where
coseries rs = uncurry4 <$> alts4 rs
instance (Serial m a, Serial m b, Serial m c, Serial m d, Serial m e) => Serial m (a,b,c,d,e) where
series = cons5 (,,,,)
instance (CoSerial m a, CoSerial m b, CoSerial m c, CoSerial m d, CoSerial m e) => CoSerial m (a,b,c,d,e) where
coseries rs = uncurry5 <$> alts5 rs
instance (Serial m a, Serial m b, Serial m c, Serial m d, Serial m e, Serial m f) => Serial m (a,b,c,d,e,f) where
series = cons6 (,,,,,)
instance (CoSerial m a, CoSerial m b, CoSerial m c, CoSerial m d, CoSerial m e, CoSerial m f) => CoSerial m (a,b,c,d,e,f) where
coseries rs = uncurry6 <$> alts6 rs
instance Monad m => Serial m Bool where
series = cons0 True \/ cons0 False
instance Monad m => CoSerial m Bool where
coseries rs =
rs >>- \r1 ->
rs >>- \r2 ->
return $ \x -> if x then r1 else r2
instance Monad m => Serial m Ordering where
series = cons0 LT \/ cons0 EQ \/ cons0 GT
instance Monad m => CoSerial m Ordering where
coseries rs =
rs >>- \r1 ->
rs >>- \r2 ->
rs >>- \r3 ->
pure $ \x -> case x of
LT -> r1
EQ -> r2
GT -> r3
instance (Serial m a) => Serial m (Maybe a) where
series = cons0 Nothing \/ cons1 Just
instance (CoSerial m a) => CoSerial m (Maybe a) where
coseries rs =
maybe <$> alts0 rs <~> alts1 rs
instance (Serial m a, Serial m b) => Serial m (Either a b) where
series = cons1 Left \/ cons1 Right
instance (CoSerial m a, CoSerial m b) => CoSerial m (Either a b) where
coseries rs =
either <$> alts1 rs <~> alts1 rs
instance Serial m a => Serial m [a] where
series = cons0 [] \/ cons2 (:)
instance CoSerial m a => CoSerial m [a] where
coseries rs =
alts0 rs >>- \y ->
alts2 rs >>- \f ->
return $ \xs -> case xs of [] -> y; x:xs' -> f x xs'
instance Serial m a => Serial m (NE.NonEmpty a) where
series = cons2 (NE.:|)
instance CoSerial m a => CoSerial m (NE.NonEmpty a) where
coseries rs =
alts2 rs >>- \f ->
return $ \(x NE.:| xs') -> f x xs'
#if MIN_VERSION_base(4,4,0)
instance Serial m a => Serial m (Complex a) where
#else
instance (RealFloat a, Serial m a) => Serial m (Complex a) where
#endif
series = cons2 (:+)
#if MIN_VERSION_base(4,4,0)
instance CoSerial m a => CoSerial m (Complex a) where
#else
instance (RealFloat a, CoSerial m a) => CoSerial m (Complex a) where
#endif
coseries rs =
alts2 rs >>- \f ->
return $ \(x :+ xs') -> f x xs'
instance Monad m => Serial m Void where
series = mzero
instance Monad m => CoSerial m Void where
coseries = const $ return absurd
instance (CoSerial m a, Serial m b) => Serial m (a->b) where
series = coseries series
-- Thanks to Ralf Hinze for the definition of coseries
-- using the nest auxiliary.
instance (Serial m a, CoSerial m a, Serial m b, CoSerial m b) => CoSerial m (a->b) where
coseries r = do
args <- unwind series
g <- nest r args
return $ \f -> g $ map f args
where
nest :: forall a b m c . (Serial m b, CoSerial m b) => Series m c -> [a] -> Series m ([b] -> c)
nest rs args = do
case args of
[] -> const `liftM` rs
_:rest -> do
let sf = coseries $ nest rs rest
f <- sf
return $ \(b:bs) -> f b bs
-- show the extension of a function (in part, bounded both by
-- the number and depth of arguments)
instance (Serial Identity a, Show a, Show b) => Show (a -> b) where
show f =
if maxarheight == 1
&& sumarwidth + length ars * length "->;" < widthLimit then
"{"++
intercalate ";" [a++"->"++r | (a,r) <- ars]
++"}"
else
concat $ [a++"->\n"++indent r | (a,r) <- ars]
where
ars = take lengthLimit [ (show x, show (f x))
| x <- list depthLimit series ]
maxarheight = maximum [ max (height a) (height r)
| (a,r) <- ars ]
sumarwidth = sum [ length a + length r
| (a,r) <- ars]
indent = unlines . map (" "++) . lines
height = length . lines
(widthLimit,lengthLimit,depthLimit) = (80,20,3)::(Int,Int,Depth)
instance (Monad m, Serial m (f (g a))) => Serial m (Compose f g a) where
series = Compose <$> series
instance (Monad m, CoSerial m (f (g a))) => CoSerial m (Compose f g a) where
coseries = fmap (. getCompose) . coseries
-- }}}
------------------------------
-- Convenient wrappers
------------------------------
-- {{{
--------------------------------------------------------------------------
-- | 'Positive' @x@ guarantees that \( x > 0 \).
newtype Positive a = Positive { getPositive :: a }
deriving (Eq, Ord, Functor, Foldable, Traversable)
instance Real a => Real (Positive a) where
toRational (Positive x) = toRational x
instance (Num a, Bounded a) => Bounded (Positive a) where
minBound = Positive 1
maxBound = Positive (maxBound :: a)
instance Enum a => Enum (Positive a) where
toEnum x = Positive (toEnum x)
fromEnum (Positive x) = fromEnum x
instance Num a => Num (Positive a) where
Positive x + Positive y = Positive (x + y)
Positive x * Positive y = Positive (x * y)
negate (Positive x) = Positive (negate x)
abs (Positive x) = Positive (abs x)
signum (Positive x) = Positive (signum x)
fromInteger x = Positive (fromInteger x)
instance Integral a => Integral (Positive a) where
quotRem (Positive x) (Positive y) = (Positive q, Positive r)
where
(q, r) = x `quotRem` y
toInteger (Positive x) = toInteger x
instance (Num a, Ord a, Serial m a) => Serial m (Positive a) where
series = Positive <$> series `suchThat` (> 0)
instance Show a => Show (Positive a) where
showsPrec n (Positive x) = showsPrec n x
-- | 'NonNegative' @x@ guarantees that \( x \ge 0 \).
newtype NonNegative a = NonNegative { getNonNegative :: a }
deriving (Eq, Ord, Functor, Foldable, Traversable)
instance Real a => Real (NonNegative a) where
toRational (NonNegative x) = toRational x
instance (Num a, Bounded a) => Bounded (NonNegative a) where
minBound = NonNegative 0
maxBound = NonNegative (maxBound :: a)
instance Enum a => Enum (NonNegative a) where
toEnum x = NonNegative (toEnum x)
fromEnum (NonNegative x) = fromEnum x
instance Num a => Num (NonNegative a) where
NonNegative x + NonNegative y = NonNegative (x + y)
NonNegative x * NonNegative y = NonNegative (x * y)
negate (NonNegative x) = NonNegative (negate x)
abs (NonNegative x) = NonNegative (abs x)
signum (NonNegative x) = NonNegative (signum x)
fromInteger x = NonNegative (fromInteger x)
instance Integral a => Integral (NonNegative a) where
quotRem (NonNegative x) (NonNegative y) = (NonNegative q, NonNegative r)
where
(q, r) = x `quotRem` y
toInteger (NonNegative x) = toInteger x
instance (Num a, Ord a, Serial m a) => Serial m (NonNegative a) where
series = NonNegative <$> series `suchThat` (>= 0)
instance Show a => Show (NonNegative a) where
showsPrec n (NonNegative x) = showsPrec n x
-- | 'NonZero' @x@ guarantees that \( x \ne 0 \).
newtype NonZero a = NonZero { getNonZero :: a }
deriving (Eq, Ord, Functor, Foldable, Traversable)
instance Real a => Real (NonZero a) where
toRational (NonZero x) = toRational x
instance (Eq a, Num a, Bounded a) => Bounded (NonZero a) where
minBound = let x = minBound in NonZero (if x == 0 then 1 else x)
maxBound = let x = maxBound in NonZero (if x == 0 then -1 else x)
instance Enum a => Enum (NonZero a) where
toEnum x = NonZero (toEnum x)
fromEnum (NonZero x) = fromEnum x
instance Num a => Num (NonZero a) where
NonZero x + NonZero y = NonZero (x + y)
NonZero x * NonZero y = NonZero (x * y)
negate (NonZero x) = NonZero (negate x)
abs (NonZero x) = NonZero (abs x)
signum (NonZero x) = NonZero (signum x)
fromInteger x = NonZero (fromInteger x)
instance Integral a => Integral (NonZero a) where
quotRem (NonZero x) (NonZero y) = (NonZero q, NonZero r)
where
(q, r) = x `quotRem` y
toInteger (NonZero x) = toInteger x
instance (Num a, Ord a, Serial m a) => Serial m (NonZero a) where
series = NonZero <$> series `suchThat` (/= 0)
instance Show a => Show (NonZero a) where
showsPrec n (NonZero x) = showsPrec n x
-- | 'NonEmpty' @xs@ guarantees that @xs@ is not null.
newtype NonEmpty a = NonEmpty { getNonEmpty :: [a] }
instance (Serial m a) => Serial m (NonEmpty a) where
series = NonEmpty <$> cons2 (:)
instance Show a => Show (NonEmpty a) where
showsPrec n (NonEmpty x) = showsPrec n x
-- }}}
------------------------------
-- Foreign.C.Types
------------------------------
-- {{{
#if MIN_VERSION_base(4,5,0)
instance Monad m => Serial m CFloat where
series = newtypeCons CFloat
instance Monad m => CoSerial m CFloat where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CFloat x -> f x
instance Monad m => Serial m CDouble where
series = newtypeCons CDouble
instance Monad m => CoSerial m CDouble where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CDouble x -> f x
#if HASCBOOL
instance Monad m => Serial m CBool where
series = newtypeCons CBool
instance Monad m => CoSerial m CBool where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CBool x -> f x
#endif
instance Monad m => Serial m CChar where
series = newtypeCons CChar
instance Monad m => CoSerial m CChar where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CChar x -> f x
instance Monad m => Serial m CSChar where
series = newtypeCons CSChar
instance Monad m => CoSerial m CSChar where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CSChar x -> f x
instance Monad m => Serial m CUChar where
series = newtypeCons CUChar
instance Monad m => CoSerial m CUChar where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CUChar x -> f x
instance Monad m => Serial m CShort where
series = newtypeCons CShort
instance Monad m => CoSerial m CShort where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CShort x -> f x
instance Monad m => Serial m CUShort where
series = newtypeCons CUShort
instance Monad m => CoSerial m CUShort where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CUShort x -> f x
instance Monad m => Serial m CInt where
series = newtypeCons CInt
instance Monad m => CoSerial m CInt where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CInt x -> f x
instance Monad m => Serial m CUInt where
series = newtypeCons CUInt
instance Monad m => CoSerial m CUInt where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CUInt x -> f x
instance Monad m => Serial m CLong where
series = newtypeCons CLong
instance Monad m => CoSerial m CLong where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CLong x -> f x
instance Monad m => Serial m CULong where
series = newtypeCons CULong
instance Monad m => CoSerial m CULong where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CULong x -> f x
instance Monad m => Serial m CPtrdiff where
series = newtypeCons CPtrdiff
instance Monad m => CoSerial m CPtrdiff where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CPtrdiff x -> f x
instance Monad m => Serial m CSize where
series = newtypeCons CSize
instance Monad m => CoSerial m CSize where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CSize x -> f x
instance Monad m => Serial m CWchar where
series = newtypeCons CWchar
instance Monad m => CoSerial m CWchar where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CWchar x -> f x
instance Monad m => Serial m CSigAtomic where
series = newtypeCons CSigAtomic
instance Monad m => CoSerial m CSigAtomic where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CSigAtomic x -> f x
instance Monad m => Serial m CLLong where
series = newtypeCons CLLong
instance Monad m => CoSerial m CLLong where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CLLong x -> f x
instance Monad m => Serial m CULLong where
series = newtypeCons CULLong
instance Monad m => CoSerial m CULLong where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CULLong x -> f x
instance Monad m => Serial m CIntPtr where
series = newtypeCons CIntPtr
instance Monad m => CoSerial m CIntPtr where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CIntPtr x -> f x
instance Monad m => Serial m CUIntPtr where
series = newtypeCons CUIntPtr
instance Monad m => CoSerial m CUIntPtr where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CUIntPtr x -> f x
instance Monad m => Serial m CIntMax where
series = newtypeCons CIntMax
instance Monad m => CoSerial m CIntMax where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CIntMax x -> f x
instance Monad m => Serial m CUIntMax where
series = newtypeCons CUIntMax
instance Monad m => CoSerial m CUIntMax where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CUIntMax x -> f x
instance Monad m => Serial m CClock where
series = newtypeCons CClock
instance Monad m => CoSerial m CClock where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CClock x -> f x
instance Monad m => Serial m CTime where
series = newtypeCons CTime
instance Monad m => CoSerial m CTime where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CTime x -> f x
instance Monad m => Serial m CUSeconds where
series = newtypeCons CUSeconds
instance Monad m => CoSerial m CUSeconds where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CUSeconds x -> f x
instance Monad m => Serial m CSUSeconds where
series = newtypeCons CSUSeconds
instance Monad m => CoSerial m CSUSeconds where
coseries rs = newtypeAlts rs >>- \f -> return $ \l -> case l of CSUSeconds x -> f x
#endif
-- }}}