[auto
ekmett@gmail.com**20090409090359
Ignore-this: 9d8c078002a0408bb3246f5cbc7aa6d0
] {
addfile ./doc/html/monoids/Data-Monoid-Sugar.html
addfile ./doc/html/monoids/src/Data-Monoid-Sugar.html
addfile ./monoids-0.1.35.tar.gz
hunk ./doc/html/monoids/Data-Generator-Combinators.html 22
->monoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkEq a => ModuleNatural (RLESeq a)
monoids-0.1.33: Monoids, specialized containers and a general map/reduce framework
monoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkModuleRightModuleRightModuleLeftModuleLeftModuleModulemonoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce framework IntSet
monoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce framework import Prelude hiding ((-), (+), negate, subtract)
+> import Prelude hiding ((-), (+), (*), (/), (^), (^^), negate, subtract, recip)
hunk ./doc/html/monoids/Data-Group-Sugar.html 112
->module Data.Monoid.Additive.Sugarmodule Data.Monoid.Sugar
monoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkmodule Data.Monoid.Additivemodule Data.Monoid.Multiplicative
monoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkmodule Data.Ring.Semi.Near
monoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce framework
Num and Bits instances for Bool as a Boolean &&/|| SemiRing
+
monoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce framework BoolRing
monoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce framework BoolBoolRing
hunk ./doc/html/monoids/Data-Monoid-Union.html 22
->monoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce framework r, r, r) => Module r) => RightModule r, r, r) => RightModule r) => LeftModule r, r, r) => LeftModule r) => Modulemonoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce framework
over Bool. Note well that the over any Bits instance. Note well that the of this ring is
- symmetric difference and not disjunction like you might expect. To get that
- you should use use of this ring is xor.
+ You should use use
-.
+
(BitSet a) a) => Module a) => Algebramonoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce framework.&./.|.. To get a
+ Boolean Ring, use Boolean (BitSet a).
hunk ./doc/html/monoids/Data-Ring-Semi-BitSet.html 174
->module Data.Ring.Semimodule Data.Ringcomplement :: (Enum a, Bounded a) => BitSet a -> BitSet a
monoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkmodule Data.Ring.Semi.Nearmodule Data.Ring
monoids-0.1.33: Monoids, specialized containers and a general map/reduce framework (Index)monoids-0.1.35: Monoids, specialized containers and a general map/reduce framework (Index)monoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkData.Monoid.Multiplicative.Sugar, Data.Ring.Sugar, Data.Group.Multiplicative.SugarData.Monoid.Sugar, Data.Group.Sugar, Data.Monoid.Applicative, Data.Ring.Algebra, Data.Ring.Module.AutomaticDifferentiation, Data.Field.VectorSpace, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Module.AutomaticDifferentiationData.Monoid.Additive.Sugar, Data.Monoid.Multiplicative.Sugar, Data.Ring.Sugar, Data.Group.Sugar, Data.Group.Multiplicative.SugarData.Monoid.Sugar, Data.Group.Sugar, Data.Group.Multiplicative.Sugar, Data.Monoid.Applicative, Data.Ring.Algebra, Data.Ring.Module.AutomaticDifferentiation, Data.Field.VectorSpace, Data.Monoid.Applicative, Data.Monoid.Monad, Data.Ring.Module.AutomaticDifferentiation
Data.Ring.Semi.BitSetData.Group.Sugarmonoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.33: Monoids, specialized containers and a general map/reduce frameworkmonoids-0.1.35: Monoids, specialized containers and a general map/reduce frameworkData.Field
{-# LANGUAGE UndecidableInstances, TypeOperators, FlexibleContexts, MultiParamTypeClasses, FlexibleInstances, TypeFamilies #-}
+
{-# LANGUAGE UndecidableInstances, TypeOperators, FlexibleContexts, MultiParamTypeClasses, FlexibleInstances, TypeFamilies, CPP #-}
hunk ./doc/html/monoids/src/Data-Generator.html 47
-importData.Array
-importData.Word(Word8)
-importData.Text(Text)
-importData.Foldable(fold,foldMap)
-importqualifiedData.TextasText
-importqualifiedData.ByteStringasStrict(ByteString,foldl')
-importqualifiedData.ByteString.Char8asStrict8(foldl')
-importqualifiedData.ByteString.LazyasLazy(ByteString,toChunks)
-importqualifiedData.ByteString.Lazy.Char8asLazy8(toChunks)
-importqualifiedData.SequenceasSeq
-importData.FingerTree(Measured,FingerTree)
-importData.Sequence(Seq)
-importqualifiedData.SetasSet
-importData.Set(Set)
-importqualifiedData.IntSetasIntSet
-importData.IntSet(IntSet)
-importqualifiedData.IntMapasIntMap
-importData.IntMap(IntMap)
-importqualifiedData.MapasMap
-importData.Map(Map)
-
-importControl.Parallel.Strategies
-importData.Monoid.Reducer
-
--- | minimal definition 'mapReduce' or 'mapTo'
-classGeneratorcwhere
-typeElemc::*
-mapReduce::(e`Reducer`m)=>(Elemc->e)->c->m
-mapTo::(e`Reducer`m)=>(Elemc->e)->m->c->m
-mapFrom::(e`Reducer`m)=>(Elemc->e)->c->m->m
-
-mapReducef=mapTofmempty
-mapTofm=mappendm.mapReducef
-mapFromf=mappend.mapReducef
-
-instanceGeneratorStrict.ByteStringwhere
-typeElemStrict.ByteString=Word8
-mapTof=Strict.foldl'(\a->snoca.f)
-
-instanceGeneratorLazy.ByteStringwhere
-typeElemLazy.ByteString=Word8
-mapReducef=fold.parMaprwhnf(mapReducef).Lazy.toChunks
+#ifdef M_ARRAY
+importData.Array
+#endif
+
+
+#ifdef M_TEXT
+importData.Text(Text)
+importqualifiedData.TextasText
+#endif
+
+
+#ifdef M_BYTESTRING
+importqualifiedData.ByteStringasStrict(ByteString,foldl')
+importqualifiedData.ByteString.Char8asStrict8(foldl')
+importqualifiedData.ByteString.LazyasLazy(ByteString,toChunks)
+importqualifiedData.ByteString.Lazy.Char8asLazy8(toChunks)
+importData.Word(Word8)
+#endif
+
+#ifdef M_FINGERTREE
+importData.FingerTree(Measured,FingerTree)
+#endif
+
+#ifdef M_CONTAINERS
+importqualifiedData.SequenceasSeq
+importData.Sequence(Seq)
+importqualifiedData.SetasSet
+importData.Set(Set)
+importqualifiedData.IntSetasIntSet
+importData.IntSet(IntSet)
+importqualifiedData.IntMapasIntMap
+importData.IntMap(IntMap)
+importqualifiedData.MapasMap
+importData.Map(Map)
+#endif
+
+#ifdef M_PARALLEL
+importControl.Parallel.Strategies
+#endif
+
+importData.Foldable(fold,foldMap)
+importData.Monoid.Reducer
hunk ./doc/html/monoids/src/Data-Generator.html 90
-instanceGeneratorTextwhere
-typeElemText=Char
-mapTof=Text.foldl'(\a->snoca.f)
-
-instanceGenerator[c]where
-typeElem[c]=c
-mapReducef=foldr(cons.f)mempty
-
-instanceMeasuredve=>Generator(FingerTreeve)where
-typeElem(FingerTreeve)=e
-mapReducef=foldMap(unit.f)
-
-instanceGenerator(Seqc)where
-typeElem(Seqc)=c
-mapReducef=foldMap(unit.f)
+-- | minimal definition 'mapReduce' or 'mapTo'
+classGeneratorcwhere
+typeElemc::*
+mapReduce::(e`Reducer`m)=>(Elemc->e)->c->m
+mapTo::(e`Reducer`m)=>(Elemc->e)->m->c->m
+mapFrom::(e`Reducer`m)=>(Elemc->e)->c->m->m
+
+mapReducef=mapTofmempty
+mapTofm=mappendm.mapReducef
+mapFromf=mappend.mapReducef
+
+#ifdef M_BYTESTRING
+instanceGeneratorStrict.ByteStringwhere
+typeElemStrict.ByteString=Word8
+mapTof=Strict.foldl'(\a->snoca.f)
hunk ./doc/html/monoids/src/Data-Generator.html 106
-instanceGeneratorIntSetwhere
-typeElemIntSet=Int
-mapReducef=mapReducef.IntSet.toList
-
-instanceGenerator(Seta)where
-typeElem(Seta)=a
-mapReducef=mapReducef.Set.toList
-
-instanceGenerator(IntMapv)where
-typeElem(IntMapv)=(Int,v)
-mapReducef=mapReducef.IntMap.toList
-
-instanceGenerator(Mapkv)where
-typeElem(Mapkv)=(k,v)
-mapReducef=mapReducef.Map.toList
-
-instanceIxi=>Generator(Arrayie)where
-typeElem(Arrayie)=(i,e)
-mapReducef=mapReducef.assocs
-
--- | a 'Generator' transformer that asks only for the keys of an indexed container
-newtypeKeysc=Keys{getKeys::c}
-
-instanceGenerator(Keys(IntMapv))where
-typeElem(Keys(IntMapv))=Int
-mapReducef=mapReducef.IntMap.keys.getKeys
-
-instanceGenerator(Keys(Mapkv))where
-typeElem(Keys(Mapkv))=k
-mapReducef=mapReducef.Map.keys.getKeys
-
-instanceIxi=>Generator(Keys(Arrayie))where
-typeElem(Keys(Arrayie))=i
-mapReducef=mapReducef.range.bounds.getKeys
-
--- | a 'Generator' transformer that asks only for the values contained in an indexed container
-newtypeValuesc=Values{getValues::c}
+instanceGeneratorLazy.ByteStringwhere
+typeElemLazy.ByteString=Word8
+mapReducef=fold.parMaprwhnf(mapReducef).Lazy.toChunks
+#endif
+
+#ifdef M_TEXT
+instanceGeneratorTextwhere
+typeElemText=Char
+mapTof=Text.foldl'(\a->snoca.f)
+#endif
+
+instanceGenerator[c]where
+typeElem[c]=c
+mapReducef=foldr(cons.f)mempty
+
+#ifdef M_FINGERTREE
+instanceMeasuredve=>Generator(FingerTreeve)where
+typeElem(FingerTreeve)=e
+mapReducef=foldMap(unit.f)
+#endif
+
+#ifdef M_CONTAINERS
+instanceGenerator(Seqc)where
+typeElem(Seqc)=c
+mapReducef=foldMap(unit.f)
+
+instanceGeneratorIntSetwhere
+typeElemIntSet=Int
+mapReducef=mapReducef.IntSet.toList
+
+instanceGenerator(Seta)where
+typeElem(Seta)=a
+mapReducef=mapReducef.Set.toList
+
+instanceGenerator(IntMapv)where
+typeElem(IntMapv)=(Int,v)
+mapReducef=mapReducef.IntMap.toList
hunk ./doc/html/monoids/src/Data-Generator.html 144
-instanceGenerator(Values(IntMapv))where
-typeElem(Values(IntMapv))=v
-mapReducef=mapReducef.IntMap.elems.getValues
-
-instanceGenerator(Values(Mapkv))where
-typeElem(Values(Mapkv))=v
-mapReducef=mapReducef.Map.elems.getValues
-
-instanceIxi=>Generator(Values(Arrayie))where
-typeElem(Values(Arrayie))=e
-mapReducef=mapReducef.elems.getValues
-
--- | a 'Generator' transformer that treats 'Word8' as 'Char'
--- This lets you use a 'ByteString' as a 'Char' source without going through a 'Monoid' transformer like 'UTF8'
-newtypeChar8c=Char8{getChar8::c}
-
-instanceGenerator(Char8Strict.ByteString)where
-typeElem(Char8Strict.ByteString)=Char
-mapTofm=Strict8.foldl'(\a->snoca.f)m.getChar8
-
-instanceGenerator(Char8Lazy.ByteString)where
-typeElem(Char8Lazy.ByteString)=Char
-mapReducef=fold.parMaprwhnf(mapReducef.Char8).Lazy8.toChunks.getChar8
+instanceGenerator(Mapkv)where
+typeElem(Mapkv)=(k,v)
+mapReducef=mapReducef.Map.toList
+#endif
+
+#ifdef M_ARRAY
+instanceIxi=>Generator(Arrayie)where
+typeElem(Arrayie)=(i,e)
+mapReducef=mapReducef.assocs
+#endif
+
+-- | a 'Generator' transformer that asks only for the keys of an indexed container
+newtypeKeysc=Keys{getKeys::c}
+
+#ifdef M_CONTAINERS
+instanceGenerator(Keys(IntMapv))where
+typeElem(Keys(IntMapv))=Int
+mapReducef=mapReducef.IntMap.keys.getKeys
+
+instanceGenerator(Keys(Mapkv))where
+typeElem(Keys(Mapkv))=k
+mapReducef=mapReducef.Map.keys.getKeys
+#endif
hunk ./doc/html/monoids/src/Data-Generator.html 168
--- | Apply a 'Reducer' directly to the elements of a 'Generator'
-reduce::(Generatorc,Elemc`Reducer`m)=>c->m
-reduce=mapReduceid
-{-# SPECIALIZE reduce :: (Word8 `Reducer` m) => Strict.ByteString -> m #-}
-{-# SPECIALIZE reduce :: (Word8 `Reducer` m) => Lazy.ByteString -> m #-}
-{-# SPECIALIZE reduce :: (Char `Reducer` m) => Char8 Strict.ByteString -> m #-}
-{-# SPECIALIZE reduce :: (Char `Reducer` m) => Char8 Lazy.ByteString -> m #-}
-{-# SPECIALIZE reduce :: (c `Reducer` m) => [c] -> m #-}
-{-# SPECIALIZE reduce :: (Generator (FingerTree v e), e `Reducer` m) => FingerTree v e -> m #-}
-{-# SPECIALIZE reduce :: (Char `Reducer` m) => Text -> m #-}
-{-# SPECIALIZE reduce :: (e `Reducer` m) => Seq e -> m #-}
-{-# SPECIALIZE reduce :: (Int `Reducer` m) => IntSet -> m #-}
-{-# SPECIALIZE reduce :: (a `Reducer` m) => Set a -> m #-}
-{-# SPECIALIZE reduce :: ((Int,v) `Reducer` m) => IntMap v -> m #-}
-{-# SPECIALIZE reduce :: ((k,v) `Reducer` m) => Map k v -> m #-}
-{-# SPECIALIZE reduce :: (Int `Reducer` m) => Keys (IntMap v) -> m #-}
-{-# SPECIALIZE reduce :: (k `Reducer` m) => Keys (Map k v) -> m #-}
-{-# SPECIALIZE reduce :: (v `Reducer` m) => Values (IntMap v) -> m #-}
-{-# SPECIALIZE reduce :: (v `Reducer` m) => Values (Map k v) -> m #-}
-
-mapReduceWith::(Generatorc,e`Reducer`m)=>(m->n)->(Elemc->e)->c->n
-mapReduceWithfg=f.mapReduceg
-{-# INLINE mapReduceWith #-}
-
-reduceWith::(Generatorc,Elemc`Reducer`m)=>(m->n)->c->n
-reduceWithf=f.reduce
-{-# INLINE reduceWith #-}
+#ifdef M_ARRAY
+instanceIxi=>Generator(Keys(Arrayie))where
+typeElem(Keys(Arrayie))=i
+mapReducef=mapReducef.range.bounds.getKeys
+#endif
+
+-- | a 'Generator' transformer that asks only for the values contained in an indexed container
+newtypeValuesc=Values{getValues::c}
+
+#ifdef M_CONTAINERS
+instanceGenerator(Values(IntMapv))where
+typeElem(Values(IntMapv))=v
+mapReducef=mapReducef.IntMap.elems.getValues
+
+instanceGenerator(Values(Mapkv))where
+typeElem(Values(Mapkv))=v
+mapReducef=mapReducef.Map.elems.getValues
+#endif
+
+#ifdef M_ARRAY
+instanceIxi=>Generator(Values(Arrayie))where
+typeElem(Values(Arrayie))=e
+mapReducef=mapReducef.elems.getValues
+#endif
+
+-- | a 'Generator' transformer that treats 'Word8' as 'Char'
+-- This lets you use a 'ByteString' as a 'Char' source without going through a 'Monoid' transformer like 'UTF8'
+newtypeChar8c=Char8{getChar8::c}
+
+#ifdef M_BYTESTRING
+instanceGenerator(Char8Strict.ByteString)where
+typeElem(Char8Strict.ByteString)=Char
+mapTofm=Strict8.foldl'(\a->snoca.f)m.getChar8
+
+instanceGenerator(Char8Lazy.ByteString)where
+typeElem(Char8Lazy.ByteString)=Char
+mapReducef=fold.parMaprwhnf(mapReducef.Char8).Lazy8.toChunks.getChar8
+#endif
+
+-- | Apply a 'Reducer' directly to the elements of a 'Generator'
+reduce::(Generatorc,Elemc`Reducer`m)=>c->m
+reduce=mapReduceid
+#ifdef M_BYTESTRING
+{-# SPECIALIZE reduce :: (Word8 `Reducer` m) => Strict.ByteString -> m #-}
+{-# SPECIALIZE reduce :: (Word8 `Reducer` m) => Lazy.ByteString -> m #-}
+{-# SPECIALIZE reduce :: (Char `Reducer` m) => Char8 Strict.ByteString -> m #-}
+{-# SPECIALIZE reduce :: (Char `Reducer` m) => Char8 Lazy.ByteString -> m #-}
+#endif
+{-# SPECIALIZE reduce :: (c `Reducer` m) => [c] -> m #-}
+#ifdef M_FINGERTREE
+{-# SPECIALIZE reduce :: (Generator (FingerTree v e), e `Reducer` m) => FingerTree v e -> m #-}
+#endif
+#ifdef M_TEXT
+{-# SPECIALIZE reduce :: (Char `Reducer` m) => Text -> m #-}
+#endif
+#ifdef M_CONTAINERS
+{-# SPECIALIZE reduce :: (e `Reducer` m) => Seq e -> m #-}
+{-# SPECIALIZE reduce :: (Int `Reducer` m) => IntSet -> m #-}
+{-# SPECIALIZE reduce :: (a `Reducer` m) => Set a -> m #-}
+{-# SPECIALIZE reduce :: ((Int,v) `Reducer` m) => IntMap v -> m #-}
+{-# SPECIALIZE reduce :: ((k,v) `Reducer` m) => Map k v -> m #-}
+{-# SPECIALIZE reduce :: (Int `Reducer` m) => Keys (IntMap v) -> m #-}
+{-# SPECIALIZE reduce :: (k `Reducer` m) => Keys (Map k v) -> m #-}
+{-# SPECIALIZE reduce :: (v `Reducer` m) => Values (IntMap v) -> m #-}
+{-# SPECIALIZE reduce :: (v `Reducer` m) => Values (Map k v) -> m #-}
+#endif
+
+mapReduceWith::(Generatorc,e`Reducer`m)=>(m->n)->(Elemc->e)->c->n
+mapReduceWithfg=f.mapReduceg
+{-# INLINE mapReduceWith #-}
+
+reduceWith::(Generatorc,Elemc`Reducer`m)=>(m->n)->c->n
+reduceWithf=f.reduce
+{-# INLINE reduceWith #-}
hunk ./doc/html/monoids/src/Data-Group-Sugar.html 20
--- > import Prelude hiding ((-), (+), negate, subtract)
+-- > import Prelude hiding ((-), (+), (*), (/), (^), (^^), negate, subtract, recip)
hunk ./doc/html/monoids/src/Data-Group-Sugar.html 26
-(moduleData.Monoid.Additive.Sugar
+(moduleData.Monoid.Sugar
hunk ./doc/html/monoids/src/Data-Group-Sugar.html 31
-)where
-
-importData.Monoid.Additive.Sugar
-importData.Group
-importPreludehiding((-),negate,subtract)
+,(/)
+,(.\.)
+,(^^)
+,recip
+)where
hunk ./doc/html/monoids/src/Data-Group-Sugar.html 37
-infixl7-
-
-(-)::Groupg=>g->g->g
-(-)=minus
+importData.Monoid.Sugar
+importData.Group.CombinatorsasGroup
+importData.Group
+importPreludehiding((-),(+),(*),(/),(^^),negate,subtract,recip)
hunk ./doc/html/monoids/src/Data-Group-Sugar.html 42
-negate::Groupg=>g->g
-negate=gnegate
-
-subtract::Groupg=>g->g->g
-subtract=gsubtract
+infixl8/
+infixr8.\.
+infixl7-
+
+(-)::Groupg=>g->g->g
+(-)=minus
+
+negate::Groupg=>g->g
+negate=gnegate
+
+subtract::Groupg=>g->g->g
+subtract=gsubtract
+
+(/)::MultiplicativeGroupg=>g->g->g
+(/)=over
+
+(.\.)::MultiplicativeGroupg=>g->g->g
+(.\.)=under
+
+recip::MultiplicativeGroupg=>g->g
+recip=grecip
+
+(^^)::MultiplicativeGroupg=>g->Integer->g
+g^^n=getLog(Group.replicate(Logg)n)
hunk ./doc/html/monoids/src/Data-Group.html 23
-(moduleData.Monoid.Additive
+(moduleData.Monoid.Multiplicative
hunk ./doc/html/monoids/src/Data-Group.html 28
-)where
-
-importData.Monoid.Additive
-importData.Monoid.Self
-importData.Monoid.FromString
-importData.Monoid.Reducer
-
-infixl6`minus`
+,MultiplicativeGroup
+,over
+,under
+,grecip
+)where
+
+importData.Monoid.Multiplicative
+importData.Monoid.Self
hunk ./doc/html/monoids/src/Data-Group.html 37
--- | Minimal complete definition: 'gnegate' or 'minus'
-classMonoida=>Groupawhere
--- additive inverse
-gnegate::a->a
-minus::a->a->a
-gsubtract::a->a->a
-
-gnegate=minuszero
-a`minus`b=a`plus`gnegateb
-a`gsubtract`b=gnegatea`plus`b
-
-instanceNuma=>Group(Suma)where
-gnegate=Sum.negate.getSum
-Suma`minus`Sumb=Sum(a-b)
-
-instanceFractionala=>Group(Producta)where
-gnegate=Product.negate.getProduct
-Producta`minus`Productb=Product(a/b)
-
-instanceGroupa=>Group(Duala)where
-gnegate=Dual.gnegate.getDual
-
-instanceGroupa=>Group(Selfa)where
-gnegate=Self.gnegate.getSelf
-Selfa`minus`Selfb=Self(a`minus`b)
-
-instanceGroupa=>Group(FromStringa)where
-gnegate=FromString.gnegate.getFromString
-FromStringa`minus`FromStringb=FromString(a`minus`b)
-
-instanceGroupa=>Group(ReducedByas)where
-gnegate=Reduction.gnegate.getReduction
-Reductiona`minus`Reductionb=Reduction(a`minus`b)
-
+#ifdef X_OverloadedStrings
+importData.Monoid.FromString
+#endif
+
+infixl6`minus`
+
+-- | Minimal complete definition: 'gnegate' or 'minus'
+classMonoida=>Groupawhere
+-- additive inverse
+gnegate::a->a
+minus::a->a->a
+gsubtract::a->a->a
+
+gnegate=minuszero
+a`minus`b=a`plus`gnegateb
+a`gsubtract`b=gnegatea`plus`b
+
+instanceNuma=>Group(Suma)where
+gnegate=Sum.negate.getSum
+Suma`minus`Sumb=Sum(a-b)
+
+instanceFractionala=>Group(Producta)where
+gnegate=Product.negate.getProduct
+Producta`minus`Productb=Product(a/b)
+
+instanceGroupa=>Group(Duala)where
+gnegate=Dual.gnegate.getDual
+
+instanceGroupa=>Group(Selfa)where
+gnegate=Self.gnegate.getSelf
+Selfa`minus`Selfb=Self(a`minus`b)
+
+-- | Minimal definition over or grecip
+classMultiplicativeg=>MultiplicativeGroupgwhere
+-- | @x / y@
+over::g->g->g
+-- | @x \ y@
+under::g->g->g
+grecip::g->g
+
+x`under`y=grecipx`times`y
+x`over`y=x`times`grecipy
+grecipx=one`over`x
+
+instanceMultiplicativeGroupg=>Group(Logg)where
+Logx`minus`Logy=Log(x`over`y)
+Logx`gsubtract`Logy=Log(x`under`y)
+gnegate(Logx)=Log(grecipx)
+
+instanceGroupg=>MultiplicativeGroup(Expg)where
+Expx`over`Expy=Exp(x`minus`y)
+Expx`under`Expy=Exp(x`gsubtract`y)
+grecip(Expx)=Exp(gnegatex)
+
+instanceMultiplicativeGroupg=>MultiplicativeGroup(Selfg)where
+Selfx`over`Selfy=Self(x`over`y)
+Selfx`under`Selfy=Self(x`under`y)
+grecip(Selfx)=Self(grecipx)
+
+#ifdef M_REFLECTION
+instanceMultiplicativeGroupg=>MultiplicativeGroup(ReducedBygs)where
+Reductionx`over`Reductiony=Reduction(x`over`y)
+Reductionx`under`Reductiony=Reduction(x`under`y)
+grecip(Reductionx)=Reduction(grecipx)
+
+instanceGroupa=>Group(ReducedByas)where
+gnegate=Reduction.gnegate.getReduction
+Reductiona`minus`Reductionb=Reduction(a`minus`b)
+Reductiona`gsubtract`Reductionb=Reduction(a`gsubtract`b)
+#endif
+
+instanceMultiplicativeGroupa=>MultiplicativeGroup(Duala)where
+grecip=Dual.grecip.getDual
+
+#ifdef X_OverloadedStrings
+instanceMultiplicativeGroupg=>MultiplicativeGroup(FromStringg)where
+FromStringx`over`FromStringy=FromString(x`over`y)
+FromStringx`under`FromStringy=FromString(x`under`y)
+grecip(FromStringx)=FromString(grecipx)
+
+instanceGroupa=>Group(FromStringa)where
+gnegate=FromString.gnegate.getFromString
+FromStringa`minus`FromStringb=FromString(a`minus`b)
+FromStringa`gsubtract`FromStringb=FromString(a`gsubtract`b)
+#endif
+
hunk ./doc/html/monoids/src/Data-Monoid-Applicative.html 26
-,moduleData.Ring.Semi.Near
-,moduleData.Ring.Module
-,Traversal(Traversal,getTraversal)
-,Alt(Alt,getAlt)
-,App(App,getApp)
-,snocTraversal
-)where
-
-importControl.Applicative
-importData.Monoid.Reducer
-importData.Ring.Semi.Near
-importData.Ring.Module
-importControl.Functor.Pointed
-
--- | A 'Traversal' uses an glues together 'Applicative' actions with (*>)
--- in the manner of 'traverse_' from "Data.Foldable". Any values returned by
--- reduced actions are discarded.
-newtypeTraversalf=Traversal{getTraversal::f()}
-
-instanceApplicativef=>Monoid(Traversalf)where
-mempty=Traversal(pure())
-Traversala`mappend`Traversalb=Traversal(a*>b)
-
-instanceApplicativef=>Reducer(fa)(Traversalf)where
-unita=Traversal(a*>pure())
-a`cons`Traversalb=Traversal(a*>b)
-Traversala`snoc`b=Traversal(a*>b*>pure())
-
-
--- | Efficiently avoid needlessly rebinding when using 'snoc' on an action that already returns ()
--- A rewrite rule automatically applies this when possible
-snocTraversal::Reducer(f())(Traversalf)=>Traversalf->f()->Traversalf
-snocTraversala=mappenda.Traversal
-{-# RULES "unitTraversal" unit = Traversal #-}
-{-# RULES "snocTraversal" snoc = snocTraversal #-}
-
--- | A 'Alt' turns any 'Alternative' instance into a 'Monoid'.
--- It also provides a 'Multiplicative' instance for an 'Applicative' functor wrapped around a 'Monoid'
--- and asserts that any 'Alternative' applied to a 'Monoid' forms a 'RightSemiNearRing'
--- under these operations.
-
-newtypeAltfa=Alt{getAlt::fa}
-deriving(Eq,Ord,Show,Read,Functor,Applicative,Alternative,Copointed)
-
-instanceAlternativef=>Monoid(Altfa)where
-mempty=empty
-Alta`mappend`Altb=Alt(a<|>b)
-
-instance(Applicativef,Monoida)=>Multiplicative(Altfa)where
-one=puremempty
-times=liftA2mappend
-
-instanceApplicativef=>Pointed(Altf)where
-point=pure
-
-instanceAlternativef=>Reducer(fa)(Altfa)where
-unit=Alt
+,moduleData.Ring.Module
+,Traversal(Traversal,getTraversal)
+,Alt(Alt,getAlt)
+,App(App,getApp)
+,snocTraversal
+)where
+
+importControl.Applicative
+importData.Monoid.Reducer
+importData.Ring.Module
+importControl.Functor.Pointed
+
+-- | A 'Traversal' uses an glues together 'Applicative' actions with (*>)
+-- in the manner of 'traverse_' from "Data.Foldable". Any values returned by
+-- reduced actions are discarded.
+newtypeTraversalf=Traversal{getTraversal::f()}
+
+instanceApplicativef=>Monoid(Traversalf)where
+mempty=Traversal(pure())
+Traversala`mappend`Traversalb=Traversal(a*>b)
+
+instanceApplicativef=>Reducer(fa)(Traversalf)where
+unita=Traversal(a*>pure())
+a`cons`Traversalb=Traversal(a*>b)
+Traversala`snoc`b=Traversal(a*>b*>pure())
+
+
+-- | Efficiently avoid needlessly rebinding when using 'snoc' on an action that already returns ()
+-- A rewrite rule automatically applies this when possible
+snocTraversal::Reducer(f())(Traversalf)=>Traversalf->f()->Traversalf
+snocTraversala=mappenda.Traversal
+{-# RULES "unitTraversal" unit = Traversal #-}
+{-# RULES "snocTraversal" snoc = snocTraversal #-}
+
+-- | A 'Alt' turns any 'Alternative' instance into a 'Monoid'.
+-- It also provides a 'Multiplicative' instance for an 'Applicative' functor wrapped around a 'Monoid'
+-- and asserts that any 'Alternative' applied to a 'Monoid' forms a 'RightSemiNearRing'
+-- under these operations.
+
+newtypeAltfa=Alt{getAlt::fa}
+deriving(Eq,Ord,Show,Read,Functor,Applicative,Alternative,Copointed)
+
+instanceAlternativef=>Monoid(Altfa)where
+mempty=empty
+Alta`mappend`Altb=Alt(a<|>b)
+
+instance(Applicativef,Monoida)=>Multiplicative(Altfa)where
+one=puremempty
+times=liftA2mappend
+
+instanceApplicativef=>Pointed(Altf)where
+point=pure
+
+instanceAlternativef=>Reducer(fa)(Altfa)where
+unit=Alt
+
+instance(Alternativef,Monoida)=>Ringoid(Altfa)
hunk ./doc/html/monoids/src/Data-Monoid-Applicative.html 84
-instance(Alternativef,Monoida)=>Ringoid(Altfa)
+instance(Alternativef,Monoida)=>RightSemiNearRing(Altfa)
hunk ./doc/html/monoids/src/Data-Monoid-Applicative.html 86
-instance(Alternativef,Monoida)=>RightSemiNearRing(Altfa)
+-- | if @m@ is a 'Module' over @r@ and @f@ is a 'Applicative' then @f `App` m@ is a 'Module' over @r@ as well
hunk ./doc/html/monoids/src/Data-Monoid-Applicative.html 88
--- | if @m@ is a 'Module' over @r@ and @f@ is a 'Applicative' then @f `App` m@ is a 'Module' over @r@ as well
-
-newtypeAppfm=App{getApp::fm}
-deriving(Eq,Ord,Show,Read,Functor,Pointed,Applicative,Alternative,Copointed)
-
-instance(Monoidm,Applicativef)=>Monoid(f`App`m)where
-mempty=puremempty
-mappend=liftA2mappend
-
-instance(Groupm,Applicativef)=>Group(f`App`m)where
-gnegate=fmapgnegate
-minus=liftA2minus
-gsubtract=liftA2gsubtract
-
-instance(c`Reducer`m,Applicativef)=>Reducerc(f`App`m)where
-unit=pure.unit
-
-instance(LeftModulerm,Applicativef)=>LeftModuler(f`App`m)wherex*.m=(x*.)<$>m
-instance(RightModulerm,Applicativef)=>RightModuler(f`App`m)wherem.*y=(.*y)<$>m
-instance(Modulerm,Applicativef)=>Moduler(f`App`m)
+newtypeAppfm=App{getApp::fm}
+deriving(Eq,Ord,Show,Read,Functor,Applicative,Alternative,Pointed,Copointed)
+
+instance(Monoidm,Applicativef)=>Monoid(f`App`m)where
+mempty=puremempty
+mappend=liftA2mappend
+
+instance(Groupm,Applicativef)=>Group(f`App`m)where
+gnegate=fmapgnegate
+minus=liftA2minus
+gsubtract=liftA2gsubtract
+
+instance(c`Reducer`m,Applicativef)=>Reducerc(f`App`m)where
+unit=pure.unit
+
+instance(LeftModulerm,Applicativef)=>LeftModuler(f`App`m)wherex*.m=(x*.)<$>m
+instance(RightModulerm,Applicativef)=>RightModuler(f`App`m)wherem.*y=(.*y)<$>m
+instance(Modulerm,Applicativef)=>Moduler(f`App`m)
hunk ./doc/html/monoids/src/Data-Monoid-Combinators.html 9
-
{-# LANGUAGE UndecidableInstances, TypeOperators, FlexibleContexts, MultiParamTypeClasses, FlexibleInstances, TypeFamilies #-}
+
{-# LANGUAGE UndecidableInstances, TypeOperators, FlexibleContexts, MultiParamTypeClasses, FlexibleInstances, TypeFamilies, CPP #-}
hunk ./doc/html/monoids/src/Data-Monoid-Combinators.html 33
--- * QuickCheck Properties
-,prop_replicate_right_distributive
-)where
-
-importPreludehiding(replicate,cycle,repeat)
-importData.Monoid.Reducer
-importTest.QuickCheck
-
+#ifdef M_QUICKCHECK
+-- * QuickCheck Properties
+,prop_replicate_right_distributive
+#endif
+)where
+
+importPreludehiding(replicate,cycle,repeat)
+importData.Monoid.Reducer
hunk ./doc/html/monoids/src/Data-Monoid-Combinators.html 42
--- | A generalization of 'Data.List.cycle' to an arbitrary 'Monoid'. May fail to terminate for some values in some monoids.
-cycle::Monoidm=>m->m
-cyclexs=xs'wherexs'=xs`mappend`xs'
+#ifdef M_QUICKCHECK
+importTest.QuickCheck
+#endif
hunk ./doc/html/monoids/src/Data-Monoid-Combinators.html 46
--- | A generalization of 'Data.List.repeat' to an arbitrary 'Monoid'. May fail to terminate for some values in some monoids.
-repeat::(e`Reducer`m)=>e->m
-repeatx=xswherexs=consxxs
+-- | A generalization of 'Data.List.cycle' to an arbitrary 'Monoid'. May fail to terminate for some values in some monoids.
+cycle::Monoidm=>m->m
+cyclexs=xs'wherexs'=xs`mappend`xs'
hunk ./doc/html/monoids/src/Data-Monoid-Combinators.html 50
--- | A generalization of 'Data.List.replicate' to an arbitrary 'Monoid'. Adapted from
--- <http://augustss.blogspot.com/2008/07/lost-and-found-if-i-write-108-in.html>
-replicate::(Monoidm,Integraln)=>m->n->m
-replicatex0y0
-|y0<0=mempty-- error "negative length"
-|y0==0=mempty
-|otherwise=fx0y0
-where
-fxy
-|eveny=f(x`mappend`x)(y`quot`2)
-|y==1=x
-|otherwise=g(x`mappend`x)((y-1)`quot`2)x
-gxyz
-|eveny=g(x`mappend`x)(y`quot`2)z
-|y==1=x`mappend`z
-|otherwise=g(x`mappend`x)((y-1)`quot`2)(x`mappend`z)
-{-# INLINE replicate #-}
-
-prop_replicate_right_distributive::(Eqm,Monoidm,Arbitrarym,Integraln)=>m->n->n->Bool
-prop_replicate_right_distributivemxy
-=replicatem(x+y)==replicatemx`mappend`replicatemy
+-- | A generalization of 'Data.List.repeat' to an arbitrary 'Monoid'. May fail to terminate for some values in some monoids.
+repeat::(e`Reducer`m)=>e->m
+repeatx=xswherexs=consxxs
+
+-- | A generalization of 'Data.List.replicate' to an arbitrary 'Monoid'. Adapted from
+-- <http://augustss.blogspot.com/2008/07/lost-and-found-if-i-write-108-in.html>
+replicate::(Monoidm,Integraln)=>m->n->m
+replicatex0y0
+|y0<0=error"Data.Monoid.Combinators.replicate: negative length"
+|y0==0=mempty
+|otherwise=fx0y0
+where
+fxy
+|eveny=f(x`mappend`x)(y`quot`2)
+|y==1=x
+|otherwise=g(x`mappend`x)((y-1)`quot`2)x
+gxyz
+|eveny=g(x`mappend`x)(y`quot`2)z
+|y==1=x`mappend`z
+|otherwise=g(x`mappend`x)((y-1)`quot`2)(x`mappend`z)
+{-# INLINE replicate #-}
+
+#ifdef M_QUICKCHECK
+prop_replicate_right_distributive::(Eqm,Monoidm,Arbitrarym,Integraln)=>m->n->n->Bool
+prop_replicate_right_distributivemxy
+=replicatem(x+y)==replicatemx`mappend`replicatemy
+#endif
hunk ./doc/html/monoids/src/Data-Monoid-FromString.html 13
--- Module : Data.Monoid.Additive
+-- Module : Data.Monoid.FromString
hunk ./doc/html/monoids/src/Data-Monoid-FromString.html 34
-importGHC.Exts
+importData.String
hunk ./doc/html/monoids/src/Data-Monoid-Instances.html 9
-
{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, UndecidableInstances, OverloadedStrings #-}
+
{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, UndecidableInstances, OverloadedStrings, CPP #-}
hunk ./doc/html/monoids/src/Data-Monoid-Instances.html 38
--- This module is automatically included everywhere this functionality is required
--- within this package. You should only have to import this module yourself if you
--- want these instances for your own purposes.
------------------------------------------------------------------------------
-
-moduleData.Monoid.Instanceswhere
+-- * 'Num' and 'Bits' instances for 'Bool' as a 'Boolean' `&&`/`||` 'SemiRing'
+--
+-- This module is automatically included everywhere this functionality is required
+-- within this package. You should only have to import this module yourself if you
+-- want these instances for your own purposes.
+-----------------------------------------------------------------------------
hunk ./doc/html/monoids/src/Data-Monoid-Instances.html 45
-importControl.Monad.Reader
+moduleData.Monoid.Instances()where
hunk ./doc/html/monoids/src/Data-Monoid-Instances.html 47
-importqualifiedControl.Monad.RWS.LazyasLRWS
-importqualifiedControl.Monad.RWS.StrictasSRWS
-
-importqualifiedControl.Monad.State.LazyasLState
-importqualifiedControl.Monad.State.StrictasSState
-
+#ifdef M_MTL
+importControl.Monad.Reader
+importqualifiedControl.Monad.RWS.LazyasLRWS
+importqualifiedControl.Monad.RWS.StrictasSRWS
+importqualifiedControl.Monad.State.LazyasLState
+importqualifiedControl.Monad.State.StrictasSState
hunk ./doc/html/monoids/src/Data-Monoid-Instances.html 55
-
-importData.String
-
-importData.Ratio
-
-importData.FingerTree
-
-importText.Parsec.Prim
+#endif
+
+#ifdef X_OverloadedStrings
+importData.String
+#endif
+
+importData.Bits
+importData.Ratio
hunk ./doc/html/monoids/src/Data-Monoid-Instances.html 64
--- orphan Monoid instances for Monad Transformers
-instance(MonadPlusm,Monoidw)=>Monoid(SWriter.WriterTwmn)where
-mempty=mzero
-mappend=mplus
-
-instance(MonadPlusm,Monoidw)=>Monoid(WriterTwmn)where
-mempty=mzero
-mappend=mplus
-
-instance(MonadPlusm,Monoidw)=>Monoid(SRWS.RWSTrwsmn)where
+#ifdef M_FINGERTREE
+importData.FingerTree
+#endif
+
+#ifdef M_PARSEC
+importText.Parsec.Prim
+#endif
+
+#ifdef M_MTL
+instance(MonadPlusm,Monoidw)=>Monoid(SWriter.WriterTwmn)where
hunk ./doc/html/monoids/src/Data-Monoid-Instances.html 77
-instance(MonadPlusm,Monoidw)=>Monoid(LRWS.RWSTrwsmn)where
+instance(MonadPlusm,Monoidw)=>Monoid(WriterTwmn)where
hunk ./doc/html/monoids/src/Data-Monoid-Instances.html 81
-instanceMonadPlusm=>Monoid(ReaderTemn)where
+instance(MonadPlusm,Monoidw)=>Monoid(SRWS.RWSTrwsmn)where
hunk ./doc/html/monoids/src/Data-Monoid-Instances.html 85
-instanceMonadPlusm=>Monoid(SState.StateTsmn)where
+instance(MonadPlusm,Monoidw)=>Monoid(LRWS.RWSTrwsmn)where
hunk ./doc/html/monoids/src/Data-Monoid-Instances.html 89
-instanceMonadPlusm=>Monoid(LState.StateTsmn)where
+instanceMonadPlusm=>Monoid(ReaderTemn)where
hunk ./doc/html/monoids/src/Data-Monoid-Instances.html 93
--- orphan, which should be in Data.FingerTree
-instanceMeasuredva=>Monoid(FingerTreeva)where
-mempty=empty
-mappend=(><)
-
--- orphan, which should be in Parsec
-instanceStreamsmt=>Monoid(ParsecTsuma)where
-mempty=mzero
-a`mappend`b=trya<|>b
-
--- orphan, perhaps should be in Data.String
-instance(IsStringa,IsStringb)=>IsString(a,b)where
-fromStringa=(fromStringa,fromStringa)
-
-instance(IsStringa,IsStringb,IsStringc)=>IsString(a,b,c)where
-fromStringa=(fromStringa,fromStringa,fromStringa)
-
-instance(IsStringa,IsStringb,IsStringc,IsStringd)=>IsString(a,b,c,d)where
-fromStringa=(fromStringa,fromStringa,fromStringa,fromStringa)
-
-instance(IsStringa,IsStringb,IsStringc,IsStringd,IsStringe)=>IsString(a,b,c,d,e)where
-fromStringa=(fromStringa,fromStringa,fromStringa,fromStringa,fromStringa)
-
-instanceMonoidIntwhere
-mempty=0
-mappend=(+)
-
-instanceMonoidIntegerwhere
-mempty=0
-mappend=(+)
+instanceMonadPlusm=>Monoid(SState.StateTsmn)where
+mempty=mzero
+mappend=mplus
+
+instanceMonadPlusm=>Monoid(LState.StateTsmn)where
+mempty=mzero
+mappend=mplus
+#endif
+
+#ifdef M_FINGERTREE
+instanceMeasuredva=>Monoid(FingerTreeva)where
+mempty=empty
+mappend=(><)
+#endif
+
+#ifdef M_PARSEC
+instanceStreamsmt=>Monoid(ParsecTsuma)where
+mempty=mzero
+a`mappend`b=trya<|>b
+#endif
+
+#ifdef X_OverloadedStrings
+instance(IsStringa,IsStringb)=>IsString(a,b)where
+fromStringa=(fromStringa,fromStringa)
+
+instance(IsStringa,IsStringb,IsStringc)=>IsString(a,b,c)where
+fromStringa=(fromStringa,fromStringa,fromStringa)
+
+instance(IsStringa,IsStringb,IsStringc,IsStringd)=>IsString(a,b,c,d)where
+fromStringa=(fromStringa,fromStringa,fromStringa,fromStringa)
hunk ./doc/html/monoids/src/Data-Monoid-Instances.html 124
-instanceIntegralm=>Monoid(Ratiom)where
-mempty=0
-mappend=(+)
+instance(IsStringa,IsStringb,IsStringc,IsStringd,IsStringe)=>IsString(a,b,c,d,e)where
+fromStringa=(fromStringa,fromStringa,fromStringa,fromStringa,fromStringa)
+#endif
+
+instanceMonoidIntwhere
+mempty=0
+mappend=(+)
+
+instanceMonoidIntegerwhere
+mempty=0
+mappend=(+)
+
+instanceIntegralm=>Monoid(Ratiom)where
+mempty=0
+mappend=(+)
+
+instanceMonoidBoolwhere
+mempty=0
+mappend=(||)
+
+-- boolean semiring
+instanceNumBoolwhere
+(+)=(||)
+(*)=(&&)
+x-y=x&¬y
+negate=not
+abs=id
+signum=id
+fromInteger0=False
+fromInteger_=True
+
+instanceBitsBoolwhere
+(.&.)=(&&)
+(.|.)=(||)
+xorTrueTrue=False
+xorFalseFalse=False
+xor__=True
+complement=not
+shiftLab=a&&(b==0)
+shiftRab=a&&(b==0)
+shiftab=a&&(b==0)
+rotatea_=a
+bit=(==0)
+setBitab=a||(b==0)
+testBitab=a&&(b==0)
+bitSize_=1
+isSigned_=False
hunk ./doc/html/monoids/src/Data-Monoid-Monad.html 26
-,moduleData.Ring.Semi.Near
+,moduleData.Ring.Module
hunk ./doc/html/monoids/src/Data-Monoid-Monad.html 39
-importData.Ring.Semi.Near
-importData.Ring.Module
-importControl.Monad
-
--- | An 'Action' uses glues together 'Monad' actions with (>>)
--- in the manner of 'mapM_' from "Data.Foldable". Any values returned by
--- reduced actions are discarded.
-newtypeActionm=Action{getAction::m()}
-
-instanceMonadm=>Monoid(Actionm)where
-mempty=Action(return())
-Actiona`mappend`Actionb=Action(a>>b)
-
-instanceMonadm=>Reducer(ma)(Actionm)where
-unita=Action(a>>return())
-a`cons`Actionb=Action(a>>b)
-Actiona`snoc`b=Action(a>>b>>return())
-
-{-# RULES "unitAction" unit = Action #-}
-{-# RULES "snocAction" snoc = snocAction #-}
-
--- | Efficiently avoid needlessly rebinding when using 'snoc' on an action that already returns ()
--- A rewrite rule automatically applies this when possible
-snocAction::Reducer(m())(Actionm)=>Actionm->m()->Actionm
-snocActiona=mappenda.Action
-
--- | A 'MonadSum' turns any 'MonadPlus' instance into a 'Monoid'.
--- It also provides a 'Multiplicative' instance for a 'Monad' wrapped around a 'Monoid'
--- and asserts that any 'MonadPlus' applied to a 'Monoid' forms a 'RightSemiNearRing'
--- under these operations.
-
-newtypeMonadSumma=MonadSum{getMonadSum::ma}
-deriving(Eq,Ord,Show,Read,Monad,MonadPlus)
-
-instanceMonadPlusm=>Monoid(MonadSumma)where
-mempty=mzero
-mappend=mplus
-
-instance(Monadm,Monoida)=>Multiplicative(MonadSumma)where
-one=returnmempty
-times=liftM2mappend
-
-instanceMonadm=>Functor(MonadSumm)where
-fmap=liftM
-
-instanceMonadm=>Applicative(MonadSumm)where
-pure=return
-(<*>)=ap
-
-instanceMonadm=>Pointed(MonadSumm)where
-point=return
-
-instanceMonadPlusm=>Reducer(ma)(MonadSumma)where
-unit=MonadSum
-
-instance(MonadPlusm,Monoida)=>Ringoid(MonadSumma)
-
-instance(MonadPlusm,Monoida)=>RightSemiNearRing(MonadSumma)
-
--- | if @m@ is a 'Module' over @r@ and @f@ is a 'Monad' then @f `Mon` m@ is a 'Module' as well
-
-newtypeMonfm=Mon{getMon::fm}
-deriving(Eq,Ord,Show,Read,Functor,Pointed,Monad,MonadPlus)
-
-instance(Monoidm,Monadf)=>Monoid(f`Mon`m)where
-mempty=returnmempty
-mappend=liftM2mappend
-
-instance(Groupm,Monadf)=>Group(f`Mon`m)where
-gnegate=liftMgnegate
-minus=liftM2minus
-gsubtract=liftM2gsubtract
-
-instance(c`Reducer`m,Monadf)=>Reducerc(f`Mon`m)where
-unit=return.unit
-
-instance(LeftModulerm,Monadf)=>LeftModuler(f`Mon`m)where
-x*.m=liftM(x*.)m
-
-instance(RightModulerm,Monadf)=>RightModuler(f`Mon`m)where
-m.*y=liftM(.*y)m
-
-instance(Modulerm,Monadf)=>Moduler(f`Mon`m)
+importData.Ring.Module
+importControl.Monad
+
+-- | An 'Action' uses glues together 'Monad' actions with (>>)
+-- in the manner of 'mapM_' from "Data.Foldable". Any values returned by
+-- reduced actions are discarded.
+newtypeActionm=Action{getAction::m()}
+
+instanceMonadm=>Monoid(Actionm)where
+mempty=Action(return())
+Actiona`mappend`Actionb=Action(a>>b)
+
+instanceMonadm=>Reducer(ma)(Actionm)where
+unita=Action(a>>return())
+a`cons`Actionb=Action(a>>b)
+Actiona`snoc`b=Action(a>>b>>return())
+
+{-# RULES "unitAction" unit = Action #-}
+{-# RULES "snocAction" snoc = snocAction #-}
+
+-- | Efficiently avoid needlessly rebinding when using 'snoc' on an action that already returns ()
+-- A rewrite rule automatically applies this when possible
+snocAction::Reducer(m())(Actionm)=>Actionm->m()->Actionm
+snocActiona=mappenda.Action
+
+-- | A 'MonadSum' turns any 'MonadPlus' instance into a 'Monoid'.
+-- It also provides a 'Multiplicative' instance for a 'Monad' wrapped around a 'Monoid'
+-- and asserts that any 'MonadPlus' applied to a 'Monoid' forms a 'RightSemiNearRing'
+-- under these operations.
+
+newtypeMonadSumma=MonadSum{getMonadSum::ma}
+deriving(Eq,Ord,Show,Read,Monad,MonadPlus)
+
+instanceMonadPlusm=>Monoid(MonadSumma)where
+mempty=mzero
+mappend=mplus
+
+instance(Monadm,Monoida)=>Multiplicative(MonadSumma)where
+one=returnmempty
+times=liftM2mappend
+
+instanceMonadm=>Functor(MonadSumm)where
+fmap=liftM
+
+instanceMonadm=>Applicative(MonadSumm)where
+pure=return
+(<*>)=ap
+
+instanceMonadm=>Pointed(MonadSumm)where
+point=return
+
+instanceMonadPlusm=>Reducer(ma)(MonadSumma)where
+unit=MonadSum
+
+instance(MonadPlusm,Monoida)=>Ringoid(MonadSumma)
+
+instance(MonadPlusm,Monoida)=>RightSemiNearRing(MonadSumma)
+
+-- | if @m@ is a 'Module' over @r@ and @f@ is a 'Monad' then @f `Mon` m@ is a 'Module' as well
+
+newtypeMonfm=Mon{getMon::fm}
+deriving(Eq,Ord,Show,Read,Functor,Pointed,Monad,MonadPlus)
+
+instance(Monoidm,Monadf)=>Monoid(f`Mon`m)where
+mempty=returnmempty
+mappend=liftM2mappend
+
+instance(Groupm,Monadf)=>Group(f`Mon`m)where
+gnegate=liftMgnegate
+minus=liftM2minus
+gsubtract=liftM2gsubtract
+
+instance(c`Reducer`m,Monadf)=>Reducerc(f`Mon`m)where
+unit=return.unit
+
+instance(LeftModulerm,Monadf)=>LeftModuler(f`Mon`m)where
+x*.m=liftM(x*.)m
+
+instance(RightModulerm,Monadf)=>RightModuler(f`Mon`m)where
+m.*y=liftM(.*y)m
+
+instance(Modulerm,Monadf)=>Moduler(f`Mon`m)
hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative-Sugar.html 20
--- > import Prelude hiding ((+),(*))
+-- > import Prelude hiding ((+),(*),(^))
hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative-Sugar.html 28
-,(*)
-)where
-
-importData.Monoid.Additive.Sugar
-importData.Monoid.Multiplicative
-importPreludehiding((*))
-
-infixl7*
-
-(*)::Multiplicativer=>r->r->r
-(*)=times
+,moduleData.Ring.Semi.Natural
+,(*)
+,(^)
+)where
+
+importData.Monoid.Additive.Sugar
+importData.Monoid.Multiplicative
+importData.Monoid.CombinatorsasMonoid
+importData.Ring.Semi.Natural
+importPreludehiding((*),(^))
+
+infixl7*
+
+(*)::Multiplicativer=>r->r->r
+(*)=times
+
+(^)::Multiplicativer=>r->Natural->r
+r^n=getLog(Monoid.replicate(Logr)n)
hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative.html 52
-
-importControl.Concurrent.STM
-
-importControl.Monad.Cont
-importControl.Monad.Identity
+importData.Monoid.Additive
+importData.Generator
+importData.Monoid.Instances()
+importData.Monoid.Self
+importData.Ratio
hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative.html 58
-importControl.Monad.Reader
-
-importqualifiedControl.Monad.RWS.LazyasLRWS
-importqualifiedControl.Monad.RWS.StrictasSRWS
-
-importqualifiedControl.Monad.State.LazyasLState
-importqualifiedControl.Monad.State.StrictasSState
-
-importqualifiedControl.Monad.Writer.LazyasLWriter
-importqualifiedControl.Monad.Writer.StrictasSWriter
-
-importqualifiedControl.Monad.ST.LazyasLST
-importqualifiedControl.Monad.ST.StrictasSST
-
-importData.FingerTree
-
-importData.Monoid.Additive
-importData.Monoid.FromString
-importData.Generator
-importData.Monoid.Instances()
-importData.Monoid.Self
+#ifdef M_STM
+importControl.Concurrent.STM
+#endif
+
+#ifdef M_MTL
+importControl.Monad.Cont
+importControl.Monad.Identity
+importControl.Monad.Reader
+importqualifiedControl.Monad.RWS.LazyasLRWS
+importqualifiedControl.Monad.RWS.StrictasSRWS
+importqualifiedControl.Monad.State.LazyasLState
+importqualifiedControl.Monad.State.StrictasSState
+importqualifiedControl.Monad.Writer.LazyasLWriter
+importqualifiedControl.Monad.Writer.StrictasSWriter
+importqualifiedControl.Monad.ST.LazyasLST
+importqualifiedControl.Monad.ST.StrictasSST
+#endif
+
+#ifdef M_FINGERTREE
+importData.FingerTree
+#endif
hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative.html 80
-importData.Ratio
-
-importqualifiedData.SequenceasSeq
-importData.Sequence(Seq)
+#ifdef M_CONTAINERS
+importqualifiedData.SequenceasSeq
+importData.Sequence(Seq)
+#endif
hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative.html 85
-importText.Parsec.Prim
-
-classMultiplicativemwhere
-one::m
-times::m->m->m
-
-instanceMultiplicativem=>Multiplicative(Dualm)where
-one=Dualone
-Dualx`times`Dualy=Dual(y`times`x)
-
-instanceMultiplicativem=>Multiplicative(m`ReducedBy`s)where
-one=Reductionone
-Reductionx`times`Reductiony=Reduction(x`times`y)
-
--- | Convert a 'Multiplicative' into a 'Monoid'. Mnemonic: @Log a + Log b = Log (a * b)@
-dataLogm=Log{getLog::m}
-
-instanceMultiplicativem=>Monoid(Logm)where
-mempty=Logone
-Loga`mappend`Logb=Log(a`times`b)
-
--- | Convert a 'Monoid' into a 'Multiplicative'. Mnemonic: @Exp a * Exp b = Exp (a + b)@
-dataExpm=Exp{getExp::m}
-
-instanceMonoidm=>Multiplicative(Expm)where
-one=Expmempty
-Expa`times`Expb=Exp(a`mappend`b)
-
--- simple monoid transformer instances
-instanceMultiplicativem=>Multiplicative(Selfm)where
-one=Selfone
-Selfa`times`Selfb=Self(a`times`b)
-
-instanceMultiplicativem=>Multiplicative(FromStringm)where
-one=FromStringone
-FromStringa`times`FromStringb=FromString(a`times`b)
-
--- the goal of this is that I can make left seminearrings out of any 'Alternative' wrapped around a monoid
--- in particular its useful for containers
-
-instanceMonoidm=>Multiplicative[m]where
-one=returnmempty
-times=liftM2mappend
-
-instanceMonoidm=>Multiplicative(Seqm)where
-one=returnmempty
-times=liftM2mappend
-
--- and things that can't quite be a Monad in Haskell
-instance(Measuredvm,Monoidm)=>Multiplicative(FingerTreevm)where
-one=singletonmempty
-xss`times`yss=getSelf$mapReduce(flipfmap'yss.mappend)xss
-
--- but it can at least serve as a canonical multiplication for any monad.
-instanceMonoidm=>Multiplicative(Maybem)where
-one=returnmempty
-times=liftM2mappend
-
-instanceMonoidm=>Multiplicative(Identitym)where
-one=returnmempty
-times=liftM2mappend
-
-instance(Monoidm)=>Multiplicative(Contrm)where
-one=returnmempty
-times=liftM2mappend
-
-instance(Monoidw,Monoidm)=>Multiplicative(SRWS.RWSrwsm)where
-one=returnmempty
-times=liftM2mappend
-
-instance(Monoidw,Monoidm)=>Multiplicative(LRWS.RWSrwsm)where
-one=returnmempty
-times=liftM2mappend
-
-instanceMonoidm=>Multiplicative(SState.Statesm)where
-one=returnmempty
-times=liftM2mappend
-
-instanceMonoidm=>Multiplicative(LState.Statesm)where
+#ifdef M_PARSEC
+importText.Parsec.Prim
+#endif
+
+#ifdef X_OverloadedStrings
+importData.Monoid.FromString
+#endif
+
+classMultiplicativemwhere
+one::m
+times::m->m->m
+
+instanceMultiplicativem=>Multiplicative(Dualm)where
+one=Dualone
+Dualx`times`Dualy=Dual(y`times`x)
+
+instanceMultiplicativem=>Multiplicative(m`ReducedBy`s)where
+one=Reductionone
+Reductionx`times`Reductiony=Reduction(x`times`y)
+
+-- | Convert a 'Multiplicative' into a 'Monoid'. Mnemonic: @Log a + Log b = Log (a * b)@
+dataLogm=Log{getLog::m}
+
+instanceMultiplicativem=>Monoid(Logm)where
+mempty=Logone
+Loga`mappend`Logb=Log(a`times`b)
+
+-- | Convert a 'Monoid' into a 'Multiplicative'. Mnemonic: @Exp a * Exp b = Exp (a + b)@
+dataExpm=Exp{getExp::m}
+
+instanceMonoidm=>Multiplicative(Expm)where
+one=Expmempty
+Expa`times`Expb=Exp(a`mappend`b)
+
+instanceMultiplicativem=>Multiplicative(Selfm)where
+one=Selfone
+Selfa`times`Selfb=Self(a`times`b)
+
+-- Monad instances
+instanceMonoidm=>Multiplicative[m]where
+one=returnmempty
+times=liftM2mappend
+instanceMonoidm=>Multiplicative(Maybem)where
+one=returnmempty
+times=liftM2mappend
+instanceMonoidn=>Multiplicative(IOn)where
+one=returnmempty
+times=liftM2mappend
+instanceMonoidn=>Multiplicative(SST.STsn)where
+one=returnmempty
+times=liftM2mappend
+instanceMonoidn=>Multiplicative(LST.STsn)where
+one=returnmempty
+times=liftM2mappend
+
+-- Applicative instances
+instanceMonoidn=>Multiplicative(ZipListn)where
+one=puremempty
+times=liftA2mappend
+
+instanceMonoidm=>Multiplicative(Constma)where
+one=pureundefined
+times=liftA2undefined
+
+-- Numeric instances
+instanceMultiplicativeIntwhere
+one=1
+times=(*)
+
+instanceMultiplicativeIntegerwhere
+one=1
+times=(*)
+
+instanceIntegralm=>Multiplicative(Ratiom)where
+one=1
+times=(*)
+
+#ifdef M_CONTAINERS
+instanceMonoidm=>Multiplicative(Seqm)where
hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative.html 166
-
-instanceMonoidm=>Multiplicative(Readerem)where
-one=returnmempty
-times=liftM2mappend
-
-instance(Monoidw,Monoidm)=>Multiplicative(SWriter.Writerwm)where
-one=returnmempty
-times=liftM2mappend
+#endif
+
+#ifdef M_FINGERTREE
+-- and things that can't quite be a Monad in Haskell
+instance(Measuredvm,Monoidm)=>Multiplicative(FingerTreevm)where
+one=singletonmempty
+xss`times`yss=getSelf$mapReduce(flipfmap'yss.mappend)xss
+#endif
hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative.html 175
-instance(Monoidw,Monoidm)=>Multiplicative(LWriter.Writerwm)where
-one=returnmempty
-times=liftM2mappend
-
-instance(Monadm,Monoidn)=>Multiplicative(ContTrmn)where
-one=returnmempty
+#ifdef M_MTL
+instanceMonoidm=>Multiplicative(Identitym)where
+one=returnmempty
+times=liftM2mappend
+instance(Monoidm)=>Multiplicative(Contrm)where
+one=returnmempty
hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative.html 182
-
-instance(Monadm,Monoidw,Monoidn)=>Multiplicative(SRWS.RWSTrwsmn)where
-one=returnmempty
-times=liftM2mappend
-
-instance(Monadm,Monoidw,Monoidn)=>Multiplicative(LRWS.RWSTrwsmn)where
-one=returnmempty
-times=liftM2mappend
-
-instance(Monadm,Monoidn)=>Multiplicative(SState.StateTsmn)where
+instance(Monoidw,Monoidm)=>Multiplicative(SRWS.RWSrwsm)where
+one=returnmempty
+times=liftM2mappend
+instance(Monoidw,Monoidm)=>Multiplicative(LRWS.RWSrwsm)where
+one=returnmempty
+times=liftM2mappend
+instanceMonoidm=>Multiplicative(SState.Statesm)where
+one=returnmempty
+times=liftM2mappend
+instanceMonoidm=>Multiplicative(LState.Statesm)where
hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative.html 194
-
-instance(Monadm,Monoidn)=>Multiplicative(LState.StateTsmn)where
-one=returnmempty
-times=liftM2mappend
-
-instance(Monadm,Monoidn)=>Multiplicative(ReaderTemn)where
-one=returnmempty
-times=liftM2mappend
-
-instance(Monadm,Monoidw,Monoidn)=>Multiplicative(SWriter.WriterTwmn)where
+instanceMonoidm=>Multiplicative(Readerem)where
+one=returnmempty
+times=liftM2mappend
+instance(Monoidw,Monoidm)=>Multiplicative(SWriter.Writerwm)where
+one=returnmempty
+times=liftM2mappend
+instance(Monoidw,Monoidm)=>Multiplicative(LWriter.Writerwm)where
+one=returnmempty
+times=liftM2mappend
+instance(Monadm,Monoidn)=>Multiplicative(ContTrmn)where
hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative.html 206
-
-instance(Monadm,Monoidw,Monoidn)=>Multiplicative(LWriter.WriterTwmn)where
-one=returnmempty
-times=liftM2mappend
-
-instanceMonoidn=>Multiplicative(IOn)where
-one=returnmempty
-times=liftM2mappend
-
-instanceMonoidn=>Multiplicative(SST.STsn)where
+instance(Monadm,Monoidw,Monoidn)=>Multiplicative(SRWS.RWSTrwsmn)where
+one=returnmempty
+times=liftM2mappend
+instance(Monadm,Monoidw,Monoidn)=>Multiplicative(LRWS.RWSTrwsmn)where
+one=returnmempty
+times=liftM2mappend
+instance(Monadm,Monoidn)=>Multiplicative(SState.StateTsmn)where
+one=returnmempty
+times=liftM2mappend
+instance(Monadm,Monoidn)=>Multiplicative(LState.StateTsmn)where
hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative.html 218
-
-instanceMonoidn=>Multiplicative(LST.STsn)where
-one=returnmempty
-times=liftM2mappend
-
-instanceMonoidn=>Multiplicative(STMn)where
-one=returnmempty
-times=liftM2mappend
-
-instance(Streamsmt,Monoidn)=>Multiplicative(ParsecTsumn)where
-one=returnmempty
-times=liftM2mappend
-
--- Applicative instances
-
-instanceMonoidn=>Multiplicative(ZipListn)where
-one=puremempty
-times=liftA2mappend
-
-instanceMonoidm=>Multiplicative(Constma)where
-one=pureundefined
-times=liftA2undefined
+instance(Monadm,Monoidn)=>Multiplicative(ReaderTemn)where
+one=returnmempty
+times=liftM2mappend
+instance(Monadm,Monoidw,Monoidn)=>Multiplicative(SWriter.WriterTwmn)where
+one=returnmempty
+times=liftM2mappend
+instance(Monadm,Monoidw,Monoidn)=>Multiplicative(LWriter.WriterTwmn)where
+one=returnmempty
+times=liftM2mappend
+#endif
+
+#ifdef M_STM
+instanceMonoidn=>Multiplicative(STMn)where
+one=returnmempty
+times=liftM2mappend
+#endif
+
+#ifdef M_PARSEC
+instance(Streamsmt,Monoidn)=>Multiplicative(ParsecTsumn)where
+one=returnmempty
+times=liftM2mappend
+#endif
hunk ./doc/html/monoids/src/Data-Monoid-Multiplicative.html 241
--- Numeric instances
-instanceMultiplicativeIntwhere
-one=1
-times=(*)
-
-instanceMultiplicativeIntegerwhere
-one=1
-times=(*)
-
-instanceIntegralm=>Multiplicative(Ratiom)where
-one=1
-times=(*)
-
+#ifdef X_OverloadedStrings
+instanceMultiplicativem=>Multiplicative(FromStringm)where
+one=FromStringone
+FromStringa`times`FromStringb=FromString(a`times`b)
+#endif
hunk ./doc/html/monoids/src/Data-Monoid-Ord.html 39
-importData.Ring.Semi
+importData.Ring
hunk ./doc/html/monoids/src/Data-Monoid-Reducer.html 9
-
{-# LANGUAGE UndecidableInstances , FlexibleContexts , MultiParamTypeClasses , FlexibleInstances , GeneralizedNewtypeDeriving, TypeOperators, ScopedTypeVariables, CPP #-}
hunk ./doc/html/monoids/src/Data-Monoid-Reducer.html 15
--- License : BSD-style
+-- License : BSD3
hunk ./doc/html/monoids/src/Data-Monoid-Reducer.html 44
-importData.FingerTree
-
-importqualifiedData.SequenceasSeq
-importData.Sequence(Seq)
+
+#ifdef M_FINGERTREE
+importData.FingerTree
+#endif
hunk ./doc/html/monoids/src/Data-Monoid-Reducer.html 49
-importqualifiedData.SetasSet
-importData.Set(Set)
-
-importqualifiedData.IntSetasIntSet
-importData.IntSet(IntSet)
-
-importqualifiedData.IntMapasIntMap
-importData.IntMap(IntMap)
-
-importData.Reflection
-
-importqualifiedData.MapasMap
+#ifdef M_CONTAINERS
+importqualifiedData.SequenceasSeq
+importData.Sequence(Seq)
+importqualifiedData.SetasSet
+importData.Set(Set)
+importqualifiedData.IntSetasIntSet
+importData.IntSet(IntSet)
+importqualifiedData.IntMapasIntMap
+importData.IntMap(IntMap)
+importqualifiedData.MapasMap
+importData.Map(Map)
+#endif
hunk ./doc/html/monoids/src/Data-Monoid-Reducer.html 62
-importData.Map(Map)
-
-importText.Parsec.Prim
+#ifdef M_REFLECTION
+importData.Reflection
+#endif
hunk ./doc/html/monoids/src/Data-Monoid-Reducer.html 66
---import qualified Data.BitSet as BitSet
---import Data.BitSet (BitSet)
-
--- | This type may be best read infix. A @c `Reducer` m@ is a 'Monoid' @m@ that maps
--- values of type @c@ through @unit@ to values of type @m@. A @c@-'Reducer' may also
--- supply operations which tack-on another @c@ to an existing 'Monoid' @m@ on the left
--- or right. These specialized reductions may be more efficient in some scenarios
--- and are used when appropriate by a 'Generator'. The names 'cons' and 'snoc' work
--- by analogy to the synonymous operations in the list monoid.
---
--- This class deliberately avoids functional-dependencies, so that () can be a @c@-Reducer
--- for all @c@, and so many common reducers can work over multiple types, for instance,
--- First and Last may reduce both @a@ and 'Maybe' @a@. Since a 'Generator' has a fixed element
--- type, the input to the reducer is generally known and extracting from the monoid usually
--- is sufficient to fix the result type. Combinators are available for most scenarios where
--- this is not the case, and the few remaining cases can be handled by using an explicit
--- type annotation.
---
--- Minimal definition: 'unit' or 'snoc'
-classMonoidm=>Reducercmwhere
--- | Convert a value into a 'Monoid'
-unit::c->m
--- | Append a value to a 'Monoid' for use in left-to-right reduction
-snoc::m->c->m
--- | Prepend a value onto a 'Monoid' for use during right-to-left reduction
-cons::c->m->m
-
-unit=snocmempty
-snocm=mappendm.unit
-cons=mappend.unit
-
--- | Apply a 'Reducer' to a 'Foldable' container, after mapping the contents into a suitable form for reduction.
-foldMapReduce::(Foldablef,e`Reducer`m)=>(a->e)->fa->m
-foldMapReducef=foldMap(unit.f)
-
--- | Apply a 'Reducer' to a 'Foldable' mapping each element through 'unit'
-foldReduce::(Foldablef,e`Reducer`m)=>fe->m
-foldReduce=foldMapunit
-
-returnUnit::(Monadm,c`Reducer`n)=>c->mn
-returnUnit=return.unit
-
-pureUnit::(Applicativef,c`Reducer`n)=>c->fn
-pureUnit=pure.unit
-
-instance(Reducercm,Reducercn)=>Reducerc(m,n)where
-unitx=(unitx,unitx)
-(m,n)`snoc`x=(m`snoc`x,n`snoc`x)
-x`cons`(m,n)=(x`cons`m,x`cons`n)
-
-instance(Reducercm,Reducercn,Reducerco)=>Reducerc(m,n,o)where
-unitx=(unitx,unitx,unitx)
-(m,n,o)`snoc`x=(m`snoc`x,n`snoc`x,o`snoc`x)
-x`cons`(m,n,o)=(x`cons`m,x`cons`n,x`cons`o)
-
-instance(Reducercm,Reducercn,Reducerco,Reducercp)=>Reducerc(m,n,o,p)where
-unitx=(unitx,unitx,unitx,unitx)
-(m,n,o,p)`snoc`x=(m`snoc`x,n`snoc`x,o`snoc`x,p`snoc`x)
-x`cons`(m,n,o,p)=(x`cons`m,x`cons`n,x`cons`o,x`cons`p)
-
-instanceReducerc[c]where
-unit=return
-cons=(:)
-xs`snoc`x=xs++[x]
-
-instanceReducerc()where
-unit_=()
-_`snoc`_=()
-_`cons`_=()
-
-instanceReducerBoolAnywhere
-unit=Any
-
-instanceReducerBoolAllwhere
-unit=All
-
-instanceReducer(a->a)(Endoa)where
-unit=Endo
-
-instanceMonoida=>Reducera(Duala)where
-unit=Dual
-
-instanceNuma=>Reducera(Suma)where
-unit=Sum
-
-instanceNuma=>Reducera(Producta)where
-unit=Product
-
-instanceReducer(Maybea)(Firsta)where
-unit=First
-
-instanceReducera(Firsta)where
-unit=First.Just
-
-instanceReducer(Maybea)(Lasta)where
-unit=Last
-
-instanceReducera(Lasta)where
-unit=Last.Just
-
-instanceMeasuredva=>Reducera(FingerTreeva)where
-unit=singleton
-cons=(<|)
-snoc=(|>)
-
-instance(Streamsmt,c`Reducer`a)=>Reducerc(ParsecTsuma)where
-unit=return.unit
+#ifdef M_PARSEC
+importText.Parsec.Prim
+#endif
+
+-- | This type may be best read infix. A @c `Reducer` m@ is a 'Monoid' @m@ that maps
+-- values of type @c@ through @unit@ to values of type @m@. A @c@-'Reducer' may also
+-- supply operations which tack-on another @c@ to an existing 'Monoid' @m@ on the left
+-- or right. These specialized reductions may be more efficient in some scenarios
+-- and are used when appropriate by a 'Generator'. The names 'cons' and 'snoc' work
+-- by analogy to the synonymous operations in the list monoid.
+--
+-- This class deliberately avoids functional-dependencies, so that () can be a @c@-Reducer
+-- for all @c@, and so many common reducers can work over multiple types, for instance,
+-- First and Last may reduce both @a@ and 'Maybe' @a@. Since a 'Generator' has a fixed element
+-- type, the input to the reducer is generally known and extracting from the monoid usually
+-- is sufficient to fix the result type. Combinators are available for most scenarios where
+-- this is not the case, and the few remaining cases can be handled by using an explicit
+-- type annotation.
+--
+-- Minimal definition: 'unit' or 'snoc'
+classMonoidm=>Reducercmwhere
+-- | Convert a value into a 'Monoid'
+unit::c->m
+-- | Append a value to a 'Monoid' for use in left-to-right reduction
+snoc::m->c->m
+-- | Prepend a value onto a 'Monoid' for use during right-to-left reduction
+cons::c->m->m
+
+unit=snocmempty
+snocm=mappendm.unit
+cons=mappend.unit
+
+-- | Apply a 'Reducer' to a 'Foldable' container, after mapping the contents into a suitable form for reduction.
+foldMapReduce::(Foldablef,e`Reducer`m)=>(a->e)->fa->m
+foldMapReducef=foldMap(unit.f)
+
+-- | Apply a 'Reducer' to a 'Foldable' mapping each element through 'unit'
+foldReduce::(Foldablef,e`Reducer`m)=>fe->m
+foldReduce=foldMapunit
+
+returnUnit::(Monadm,c`Reducer`n)=>c->mn
+returnUnit=return.unit
+
+pureUnit::(Applicativef,c`Reducer`n)=>c->fn
+pureUnit=pure.unit
+
+instance(Reducercm,Reducercn)=>Reducerc(m,n)where
+unitx=(unitx,unitx)
+(m,n)`snoc`x=(m`snoc`x,n`snoc`x)
+x`cons`(m,n)=(x`cons`m,x`cons`n)
+
+instance(Reducercm,Reducercn,Reducerco)=>Reducerc(m,n,o)where
+unitx=(unitx,unitx,unitx)
+(m,n,o)`snoc`x=(m`snoc`x,n`snoc`x,o`snoc`x)
+x`cons`(m,n,o)=(x`cons`m,x`cons`n,x`cons`o)
+
+instance(Reducercm,Reducercn,Reducerco,Reducercp)=>Reducerc(m,n,o,p)where
+unitx=(unitx,unitx,unitx,unitx)
+(m,n,o,p)`snoc`x=(m`snoc`x,n`snoc`x,o`snoc`x,p`snoc`x)
+x`cons`(m,n,o,p)=(x`cons`m,x`cons`n,x`cons`o,x`cons`p)
+
+instanceReducerc[c]where
+unit=return
+cons=(:)
+xs`snoc`x=xs++[x]
+
+instanceReducerc()where
+unit_=()
+_`snoc`_=()
+_`cons`_=()
+
+instanceReducerBoolAnywhere
+unit=Any
+
+instanceReducerBoolAllwhere
+unit=All
+
+instanceReducer(a->a)(Endoa)where
+unit=Endo
+
+instanceMonoida=>Reducera(Duala)where
+unit=Dual
+
+instanceNuma=>Reducera(Suma)where
+unit=Sum
+
+instanceNuma=>Reducera(Producta)where
+unit=Product
+
+instanceReducer(Maybea)(Firsta)where
+unit=First
+
+instanceReducera(Firsta)where
+unit=First.Just
+
+instanceReducer(Maybea)(Lasta)where
+unit=Last
+
+instanceReducera(Lasta)where
+unit=Last.Just
+
+#ifdef M_FINGERTREE
+instanceMeasuredva=>Reducera(FingerTreeva)where
+unit=singleton
+cons=(<|)
+snoc=(|>)
+#endif
hunk ./doc/html/monoids/src/Data-Monoid-Reducer.html 174
-instanceReducera(Seqa)where
-unit=Seq.singleton
-cons=(Seq.<|)
-snoc=(Seq.|>)
+#ifdef M_PARSEC
+instance(Streamsmt,c`Reducer`a)=>Reducerc(ParsecTsuma)where
+unit=return.unit
+#endif
hunk ./doc/html/monoids/src/Data-Monoid-Reducer.html 179
-instanceReducerIntIntSetwhere
-unit=IntSet.singleton
-cons=IntSet.insert
-snoc=flipIntSet.insert-- left bias irrelevant
-
-instanceOrda=>Reducera(Seta)where
-unit=Set.singleton
-cons=Set.insert
--- pedantic about order in case 'Eq' doesn't implement structural equality
-snocsm|Set.memberms=s
-|otherwise=Set.insertms
-
-instanceReducer(Int,v)(IntMapv)where
-unit=uncurryIntMap.singleton
-cons=uncurryIntMap.insert
-snoc=flip.uncurry.IntMap.insertWith$constid
-
-instanceOrdk=>Reducer(k,v)(Mapkv)where
-unit=uncurryMap.singleton
-cons=uncurryMap.insert
-snoc=flip.uncurry.Map.insertWith$constid
-
-{-
-instance Enum a => Reducer a (BitSet a) where
- unit m = BitSet.insert m BitSet.empty
--}
-
-data(m`ReducedBy`s)=Reduction{getReduction::m}
+#ifdef M_CONTAINERS
+instanceReducera(Seqa)where
+unit=Seq.singleton
+cons=(Seq.<|)
+snoc=(Seq.|>)
+
+instanceReducerIntIntSetwhere
+unit=IntSet.singleton
+cons=IntSet.insert
+snoc=flipIntSet.insert-- left bias irrelevant
+
+instanceOrda=>Reducera(Seta)where
+unit=Set.singleton
+cons=Set.insert
+-- pedantic about order in case 'Eq' doesn't implement structural equality
+snocsm|Set.memberms=s
+|otherwise=Set.insertms
+
+instanceReducer(Int,v)(IntMapv)where
+unit=uncurryIntMap.singleton
+cons=uncurryIntMap.insert
+snoc=flip.uncurry.IntMap.insertWith$constid
+
+instanceOrdk=>Reducer(k,v)(Mapkv)where
+unit=uncurryMap.singleton
+cons=uncurryMap.insert
+snoc=flip.uncurry.Map.insertWith$constid
+#endif
hunk ./doc/html/monoids/src/Data-Monoid-Reducer.html 208
-instanceMonoidm=>Monoid(m`ReducedBy`s)where
-mempty=Reductionmempty
-Reductiona`mappend`Reductionb=Reduction(a`mappend`b)
-
-instance(s`Reflects`(a->m),Monoidm)=>Reducera(m`ReducedBy`s)where
-unit=Reduction.reflect(undefined::s)
+#ifdef M_REFLECTION
+data(m`ReducedBy`s)=Reduction{getReduction::m}
+
+instanceMonoidm=>Monoid(m`ReducedBy`s)where
+mempty=Reductionmempty
+Reductiona`mappend`Reductionb=Reduction(a`mappend`b)
+
+instance(s`Reflects`(a->m),Monoidm)=>Reducera(m`ReducedBy`s)where
+unit=Reduction.reflect(undefined::s)
+#endif
hunk ./doc/html/monoids/src/Data-Monoid-Sugar.html 1
+
+
+
+
+Data/Monoid/Sugar.hs
+
+
+
+
-----------------------------------------------------------------------------
+-- |
+-- Module : Data.Monoid.Additive.Sugar
+-- Copyright : (c) Edward Kmett 2009
+-- License : BSD-style
+-- Maintainer : ekmett@gmail.com
+-- Stability : experimental
+-- Portability : portable
+--
+-- Syntactic sugar for working with a 'Monoid' and 'Multiplicative' instances
+-- that conflicts with names from the "Prelude".
+--
+-- > import Prelude hiding ((+),(*),(^))
+-- > import Data.Monoid.Sugar
+--
+-----------------------------------------------------------------------------
+--
+moduleData.Monoid.Sugar
+(moduleData.Monoid.Multiplicative
+,moduleData.Ring.Semi.Natural
+,(+)
+,(*)
+,(^)
+)where
+
+importPreludehiding((*),(^),(+))
+importData.Monoid.Multiplicative
+importData.Ring.Semi.Natural
+importqualifiedData.Monoid.CombinatorsasMonoid
+
+infixl6+
+infixl7*
+
+(+)::Monoidm=>m->m->m
+(+)=mappend
+
+(*)::Multiplicativer=>r->r->r
+(*)=times
+
+(^)::Multiplicativer=>r->Natural->r
+r^n=getLog(Monoid.replicate(Logr)n)
+
+
hunk ./doc/html/monoids/src/Data-Ring-Boolean.html 20
--- A Boolean 'Ring' over 'Bool'. Note well that the 'mappend' of this ring is
--- symmetric difference and not disjunction like you might expect. To get that
--- you should use use 'Ord' from "Data.Ring.Semi.Ord.Order" on 'Bool' to get the '&&'/'||'-based
--- distributive-lattice 'SemiRing'
------------------------------------------------------------------------------
-
-moduleData.Ring.Boolean
-(moduleData.Ring
-,BoolRing(BoolRing,getBoolRing)
-)where
-
-importData.Ring
-importData.Monoid.Reducer
-importTest.QuickCheck
-
-newtypeBoolRing=BoolRing{getBoolRing::Bool}deriving(Eq,Ord,Show,Read,Arbitrary,CoArbitrary)
-
-instanceMonoidBoolRingwhere
-mempty=BoolRingFalse
-BoolRinga`mappend`BoolRingb=BoolRing((a||b)&¬(a&&b))
+-- A Boolean 'Ring' over any Bits instance. Note well that the 'mappend' of this ring is xor.
+-- You should use use 'Ord' from "Data.Ring.Semi.Ord.Order" on 'Bool' to get the '&&'/'||'-based
+-- distributive-lattice 'SemiRing'.
+--
+-- Also note that @gnegate = id@ in a Boolean Ring!
+-----------------------------------------------------------------------------
+
+moduleData.Ring.Boolean
+(moduleData.Ring
+,Boolean(Boolean,getBoolean)
+)where
+
+importData.Bits
+importData.Ring
+importData.Ring.Module
+importData.Ring.Semi.Natural
+importData.Monoid.Reducer
+importTest.QuickCheckhiding((.&.))
+
+newtypeBooleana=Boolean{getBoolean::a}deriving(Eq,Ord,Show,Read,Arbitrary,CoArbitrary)
hunk ./doc/html/monoids/src/Data-Ring-Boolean.html 41
-instanceGroupBoolRingwhere
-gnegate=BoolRing.not.getBoolRing
-
-instanceMultiplicativeBoolRingwhere
-one=BoolRingTrue
-BoolRinga`times`BoolRingb=BoolRing(a&&b)
-
-instanceRingoidBoolRing
-instanceLeftSemiNearRingBoolRing
-instanceRightSemiNearRingBoolRing
-instanceSemiRingBoolRing
-instanceRingBoolRing
-
-instanceReducerBoolBoolRingwhere
-unit=BoolRing
+-- | @xor@
+instanceBitsa=>Monoid(Booleana)where
+mempty=Boolean0
+Booleana`mappend`Booleanb=Boolean((a.|.b).&.complement(a.&.b))
+
+-- | @id@, since @x `xor` x = zero@
+instanceBitsa=>Group(Booleana)where
+gnegate=Boolean.id.getBoolean
+
+-- | @and@
+instanceBitsa=>Multiplicative(Booleana)where
+one=Boolean(complement0)
+Booleana`times`Booleanb=Boolean(a.&.b)
+
+-- | the boolean ring (using symmetric difference as addition) is a ring
+instanceBitsa=>Ringoid(Booleana)
+instanceBitsa=>LeftSemiNearRing(Booleana)
+instanceBitsa=>RightSemiNearRing(Booleana)
+instanceBitsa=>SemiRing(Booleana)
+instanceBitsa=>Ring(Booleana)
+
+-- | it reduces boolean values
+instanceBitsa=>Reducera(Booleana)where
+unit=Boolean
+
+-- | every monoid is a module over the naturals, boolring is idempotent
+instanceBitsa=>ModuleNatural(Booleana)
+instanceBitsa=>LeftModuleNatural(Booleana)where
+0*._=mempty
+_*.m=m
+instanceBitsa=>RightModuleNatural(Booleana)where
+_.*0=mempty
+m.*_=m
+instanceBitsa=>BimoduleNatural(Booleana)
+
+-- | every group is a module over the integers, boolring is idempotent
+instanceBitsa=>ModuleInteger(Booleana)
+instanceBitsa=>LeftModuleInteger(Booleana)where
+0*._=mempty
+_*.m=m
+instanceBitsa=>RightModuleInteger(Booleana)where
+_.*0=mempty
+m.*_=m
+instanceBitsa=>BimoduleInteger(Booleana)
+
+-- | every ring is a module over itself
+instanceBitsa=>Module(Booleana)(Booleana)
+instanceBitsa=>LeftModule(Booleana)(Booleana)where
+(*.)=times
+instanceBitsa=>RightModule(Booleana)(Booleana)where
+(.*)=times
+instanceBitsa=>Bimodule(Booleana)(Booleana)
+instanceBitsa=>Normed(Booleana)(Booleana)wheremabs=id
hunk ./doc/html/monoids/src/Data-Ring-Module-AutomaticDifferentiation.html 37
-lift::(r`Module`m)=>r->Dsrm
+lift::(r`Bimodule`m)=>r->Dsrm
hunk ./doc/html/monoids/src/Data-Ring-Module-AutomaticDifferentiation.html 40
-infinitesimal::(r`Module`m,Ringoidm)=>Dsrm
+infinitesimal::(r`Bimodule`m,Ringoidm)=>Dsrm
hunk ./doc/html/monoids/src/Data-Ring-Module-AutomaticDifferentiation.html 49
-instance(r`Module`m)=>Monoid(Dsrm)where
+instance(r`Bimodule`m)=>Monoid(Dsrm)where
hunk ./doc/html/monoids/src/Data-Ring-Module-AutomaticDifferentiation.html 53
-instance(r`Module`m)=>Multiplicative(Dsrm)where
+instance(r`Bimodule`m)=>Multiplicative(Dsrm)where
hunk ./doc/html/monoids/src/Data-Ring-Module-AutomaticDifferentiation.html 57
-instance(Groupr,r`Module`m,Groupm)=>Group(Dsrm)where
+instance(Groupr,r`Bimodule`m,Groupm)=>Group(Dsrm)where
hunk ./doc/html/monoids/src/Data-Ring-Module-AutomaticDifferentiation.html 75
-instance(Ringoidr,r`Module`m)=>Ringoid(Dsrm)
-instance(LeftSemiNearRingr,Modulerm)=>LeftSemiNearRing(Dsrm)
-instance(RightSemiNearRingr,Modulerm)=>RightSemiNearRing(Dsrm)
-instance(SemiRingr,r`Module`m)=>SemiRing(Dsrm)
-instance(Ringr,r`Module`m,Groupm)=>Ring(Dsrm)
+instance(Ringoidr,r`Bimodule`m)=>Ringoid(Dsrm)
+instance(LeftSemiNearRingr,Bimodulerm)=>LeftSemiNearRing(Dsrm)
+instance(RightSemiNearRingr,Bimodulerm)=>RightSemiNearRing(Dsrm)
+instance(SemiRingr,r`Bimodule`m)=>SemiRing(Dsrm)
+instance(Ringr,r`Bimodule`m,Groupm)=>Ring(Dsrm)
hunk ./doc/html/monoids/src/Data-Ring-Module-AutomaticDifferentiation.html 81
-instance(r`Module`m,c`Reducer`r,c`Reducer`m)=>Reducerc(Dsrm)where
+instance(r`Bimodule`m,c`Reducer`r,c`Reducer`m)=>Reducerc(Dsrm)where
hunk ./doc/html/monoids/src/Data-Ring-Module-AutomaticDifferentiation.html 93
-d::(r`Module`m,Ringoidm)=>(foralls.Dsrm->Dsrm)->(r,m)
+d::(r`Bimodule`m,Ringoidm)=>(foralls.Dsrm->Dsrm)->(r,m)
hunk ./doc/html/monoids/src/Data-Ring-Module.html 27
-,LeftModule
-,(*.)
-,RightModule
-,(.*)
-,Module
-)where
-
-importData.Ring
-importData.Monoid.Union
-
--- import qualified Data.Monoid.Combinators as Monoid
-
--- | @ (x * y) *. m = x * (y *. m) @
-class(Monoidr,Multiplicativer,Monoidm)=>LeftModulermwhere
-(*.)::r->m->m
-
--- | @ (m .* x) * y = m .* (x * y) @
-class(Monoidr,Multiplicativer,Monoidm)=>RightModulermwhere
-(.*)::m->r->m
-
--- | @ (x *. m) .* y = x *. (m .* y) @
-class(LeftModulerm,RightModulerm)=>Modulerm
-
-instance(LeftModulerm,LeftModulern)=>LeftModuler(m,n)where
-r*.(m,n)=(r*.m,r*.n)
-instance(LeftModulerm,LeftModulern,LeftModulero)=>LeftModuler(m,n,o)where
-r*.(m,n,o)=(r*.m,r*.n,r*.o)
-instance(LeftModulerm,LeftModulern,LeftModulero,LeftModulerp)=>LeftModuler(m,n,o,p)where
-r*.(m,n,o,p)=(r*.m,r*.n,r*.o,r*.p)
-instance(LeftModulerm,LeftModulern,LeftModulero,LeftModulerp,LeftModulerq)=>LeftModuler(m,n,o,p,q)where
-r*.(m,n,o,p,q)=(r*.m,r*.n,r*.o,r*.p,r*.q)
+-- * R-Modules
+,Module
+,LeftModule,(*.)
+,RightModule,(.*)
+,Bimodule
+-- * R-Normed Modules
+,Normed,mabs
+-- * Vector Spaces
+,VectorSpace
+-- * R-Algebras
+,Algebra
+)where
+
+importData.Ring
+importData.Monoid.Union
+
+-- import qualified Data.Monoid.Combinators as Monoid
+
+
+class(Ringoidr,Monoidm)=>Modulermwhere
+
+-- | @ (x * y) *. m = x * (y *. m) @
+class(Modulerm)=>LeftModulermwhere
+(*.)::r->m->m
+
+-- | @ (m .* x) * y = m .* (x * y) @
+class(Modulerm)=>RightModulermwhere
+(.*)::m->r->m
+
+-- | @ (x *. m) .* y = x *. (m .* y) @
+class(LeftModulerm,RightModulerm)=>Bimodulerm
hunk ./doc/html/monoids/src/Data-Ring-Module.html 59
-instance(RightModulerm,RightModulern)=>RightModuler(m,n)where
-(m,n).*r=(m.*r,n.*r)
-instance(RightModulerm,RightModulern,RightModulero)=>RightModuler(m,n,o)where
-(m,n,o).*r=(m.*r,n.*r,o.*r)
-instance(RightModulerm,RightModulern,RightModulero,RightModulerp)=>RightModuler(m,n,o,p)where
-(m,n,o,p).*r=(m.*r,n.*r,o.*r,p.*r)
-instance(RightModulerm,RightModulern,RightModulero,RightModulerp,RightModulerq)=>RightModuler(m,n,o,p,q)where
-(m,n,o,p,q).*r=(m.*r,n.*r,o.*r,p.*r,q.*r)
-
-instance(Modulerm,Modulern)=>Moduler(m,n)
-instance(Modulerm,Modulern,Modulero)=>Moduler(m,n,o)
-instance(Modulerm,Modulern,Modulero,Modulerp)=>Moduler(m,n,o,p)
-instance(Modulerm,Modulern,Modulero,Modulerp,Modulerq)=>Moduler(m,n,o,p,q)
-
-
--- we want an absorbing 0, for that we need a seminearring and a notion of equality
-instance(HasUnionWithf,Ordr,Eqr,RightSemiNearRingr)=>LeftModuler(UnionWithfr)where
-r*.m|r==zero=zero
-|otherwise=fmap(r`times`)m
-instance(HasUnionWithf,Ordr,Eqr,RightSemiNearRingr)=>RightModuler(UnionWithfr)where
-m.*r|r==zero=zero
-|otherwise=fmap(`times`r)m
-instance(HasUnionWithf,Ordr,Eqr,RightSemiNearRingr)=>Moduler(UnionWithfr)where
+class(Fieldf,Modulefg)=>VectorSpacefg
+
+-- | An r-normed module m satisfies:
+--
+-- (1) @mabs m >= 0@
+--
+-- 2 @mabs m == zero{-_r-} => m == zero{-_m-}@
+--
+-- 3 @mabs (m + n) <= mabs m + mabs n@
+--
+-- 4 @r * mabs m = mabs (r *. m) -- if m is an r-LeftModule@
+--
+-- 5 @mabs m * r = mabs (m .* r) -- if m is an r-RightModule@
+classModulerm=>Normedrmwhere
+mabs::m->r
+
+-- | Algebra over a (near) (semi) ring.
+-- @r *. (x * y) = (r *. x) * y = x * (r *. y)@
+-- @(x * y) .* r = y * (x .* r) = (y .* r) * x@
+class(r`Bimodule`m,Multiplicativem)=>Algebrarm
+
+instance(Modulerm,Modulern)=>Moduler(m,n)
+instance(Modulerm,Modulern,Modulero)=>Moduler(m,n,o)
+instance(Modulerm,Modulern,Modulero,Modulerp)=>Moduler(m,n,o,p)
+instance(Modulerm,Modulern,Modulero,Modulerp,Modulerq)=>Moduler(m,n,o,p,q)
+
+instance(LeftModulerm,LeftModulern)=>LeftModuler(m,n)where
+r*.(m,n)=(r*.m,r*.n)
+instance(LeftModulerm,LeftModulern,LeftModulero)=>LeftModuler(m,n,o)where
+r*.(m,n,o)=(r*.m,r*.n,r*.o)
+instance(LeftModulerm,LeftModulern,LeftModulero,LeftModulerp)=>LeftModuler(m,n,o,p)where
+r*.(m,n,o,p)=(r*.m,r*.n,r*.o,r*.p)
+instance(LeftModulerm,LeftModulern,LeftModulero,LeftModulerp,LeftModulerq)=>LeftModuler(m,n,o,p,q)where
+r*.(m,n,o,p,q)=(r*.m,r*.n,r*.o,r*.p,r*.q)
+
+instance(RightModulerm,RightModulern)=>RightModuler(m,n)where
+(m,n).*r=(m.*r,n.*r)
+instance(RightModulerm,RightModulern,RightModulero)=>RightModuler(m,n,o)where
+(m,n,o).*r=(m.*r,n.*r,o.*r)
+instance(RightModulerm,RightModulern,RightModulero,RightModulerp)=>RightModuler(m,n,o,p)where
+(m,n,o,p).*r=(m.*r,n.*r,o.*r,p.*r)
+instance(RightModulerm,RightModulern,RightModulero,RightModulerp,RightModulerq)=>RightModuler(m,n,o,p,q)where
+(m,n,o,p,q).*r=(m.*r,n.*r,o.*r,p.*r,q.*r)
+
+instance(Bimodulerm,Bimodulern)=>Bimoduler(m,n)
+instance(Bimodulerm,Bimodulern,Bimodulero)=>Bimoduler(m,n,o)
+instance(Bimodulerm,Bimodulern,Bimodulero,Bimodulerp)=>Bimoduler(m,n,o,p)
+instance(Bimodulerm,Bimodulern,Bimodulero,Bimodulerp,Bimodulerq)=>Bimoduler(m,n,o,p,q)
+
+-- we want an absorbing 0, for that we need a seminearring and a notion of equality
+instance(HasUnionWithf,Ordr,Eqr,RightSemiNearRingr)=>LeftModuler(UnionWithfr)where
+r*.m|r==zero=zero
+|otherwise=fmap(r`times`)m
+instance(HasUnionWithf,Ordr,Eqr,RightSemiNearRingr)=>RightModuler(UnionWithfr)where
+m.*r|r==zero=zero
+|otherwise=fmap(`times`r)m
+instance(HasUnionWithf,Ordr,Eqr,RightSemiNearRingr)=>Moduler(UnionWithfr)where
hunk ./doc/html/monoids/src/Data-Ring-Semi-BitSet.html 24
--- enumeration
---
--------------------------------------------------------------------------------
-
-moduleData.Ring.Semi.BitSet
-(moduleData.Monoid.Reducer
-,moduleData.Ring.Semi
--- * BitSet
-,BitSet
--- * Manipulation
-,empty
-,singleton
-,full
-,union
-,intersection
-,complement
-,insert
-,delete
-,(\\)
-,fromList
-,fromDistinctAscList
--- * Acessors
-,member
-,null
-,size
-,isComplemented
-,toInteger
-)where
-
-importPreludehiding(null,exponent,toInteger,foldl,foldr,foldl1,foldr1)
-importData.Bitshiding(complement)
-importqualifiedData.BitsasBits
+-- enumeration. Treated as a Boolean semiring over `.&.`/`.|.`. To get a
+-- 'Boolean' 'Ring', use @'Boolean' ('BitSet' a)@.
+--
+-------------------------------------------------------------------------------
+
+moduleData.Ring.Semi.BitSet
+(moduleData.Monoid.Reducer
+,moduleData.Ring
+-- * BitSet
+,BitSet
+-- * Manipulation
+,empty
+,singleton
+,full
+,union
+,intersection
+,complement
+,insert
+,delete
+,(\\)
+,fromList
+,fromDistinctAscList
+-- * Acessors
+,member
+,null
+,size
+,isComplemented
+,toInteger
+)where
+
+importPreludehiding(null,exponent,toInteger,foldl,foldr,foldl1,foldr1)
+importData.Bits
hunk ./doc/html/monoids/src/Data-Ring-Semi-BitSet.html 59
-importData.Ring.Semi
+importData.Ring
hunk ./doc/html/monoids/src/Data-Ring-Semi-BitSet.html 62
-importData.Ring.Algebra
+importData.Ring.Module
hunk ./doc/html/monoids/src/Data-Ring-Semi-BitSet.html 139
-full=complementempty
+full=complement'empty
hunk ./doc/html/monoids/src/Data-Ring-Semi-BitSet.html 142
--- | /O(d)/ Complements a 'BitSet' with respect to the bounds of @a@. Preserves order of 'null' and 'size'
-complement::(Enuma,Boundeda)=>BitSeta->BitSeta
-complementr@(BSabclhm_f)=BS(Bits.complementb)(Bits.complementa)(Bits.complementc)lh(Bits.complementm)ufwhere
-u=(fromEnum(minBound`asArgTypeOf`r),fromEnum(maxBound`asArgTypeOf`r))
-{-# INLINE complement #-}
+
+-- | /O(d)/ unsafe internal method: complement a set that has already been complemented at least once.
+recomplement::BitSeta->BitSeta
+recomplement(BSabclhmuf)=BS(complementb)(complementa)(complementc)lh(complementm)uf
+{-# INLINE recomplement #-}
hunk ./doc/html/monoids/src/Data-Ring-Semi-BitSet.html 148
--- | /O(d)/ unsafe internal method: complement a set that has already been complemented at least once.
-recomplement::BitSeta->BitSeta
-recomplement(BSabclhmuf)=BS(Bits.complementb)(Bits.complementa)(Bits.complementc)lh(Bits.complementm)uf
-{-# INLINE recomplement #-}
+-- | /O(d)/ unsafe internal method: complement a set that has already been complemented at least once.
+pseudoComplement::BitSeta->(Int,Int)->BitSeta
+pseudoComplement(BSabclhm_f)u=BS(complementb)(complementa)(complementc)lh(complementm)uf
+{-# INLINE pseudoComplement #-}
hunk ./doc/html/monoids/src/Data-Ring-Semi-BitSet.html 153
--- | /O(d)/ unsafe internal method: complement a set that has already been complemented at least once.
-pseudoComplement::BitSeta->(Int,Int)->BitSeta
-pseudoComplement(BSabclhm_f)u=BS(Bits.complementb)(Bits.complementa)(Bits.complementc)lh(Bits.complementm)uf
-{-# INLINE pseudoComplement #-}
+-- | /O(d * n)/ Make a 'BitSet' from a list of items.
+fromList::Enuma=>[a]->BitSeta
+fromList=foldrinsertempty
+{-# INLINE fromList #-}
hunk ./doc/html/monoids/src/Data-Ring-Semi-BitSet.html 158
--- | /O(d * n)/ Make a 'BitSet' from a list of items.
-fromList::Enuma=>[a]->BitSeta
-fromList=foldrinsertempty
-{-# INLINE fromList #-}
-
--- | /O(d * n)/ Make a 'BitSet' from a distinct ascending list of items
-fromDistinctAscList::Enuma=>[a]->BitSeta
-fromDistinctAscList[]=empty
-fromDistinctAscList(c:cs)=fromDistinctAscList'cs101
-where
-l=fromEnumc
-fromDistinctAscList'::Enuma=>[a]->Int->Int->Integer->BitSeta
-fromDistinctAscList'[]!n!h!m=BSnnnlhmundefinedtoEnum
-fromDistinctAscList'(c':cs')!n_!m=
-leth'=fromEnumc'in
-fromDistinctAscList'cs'(n+1)h'(setBitm(h'-l))
-{-# INLINE fromDistinctAscList #-}
-
--- | /O(d)/ Insert a single element of type @a@ into the 'BitSet'. Preserves order of 'null' and 'size'
-insert::Enuma=>a->BitSeta->BitSeta
-insertxr@(BSabclhmu_)
-|m<0,e<l=r
-|m<0,e>h=r
-|b==0=singletonx
-|a==-1=r
-|e<l=bs(a+1)(b+1)(c+1)eh(shiftLm(l-e).|.1)u
-|e>h=bs(a+1)(b+1)(c+1)lp(setBitmp)u
-|testBitmp=r
-|otherwise=bs(a+1)(b+1)(c+1)lh(setBitmp)u
-where
-e=fromEnumx
-p=e-l
-{-# INLINE insert #-}
-
--- | /O(d)/ Delete a single item from the 'BitSet'. Preserves order of 'null' and 'size'
-delete::Enuma=>a->BitSeta->BitSeta
-deletexr@(BSabclhmu_)
-|m<0,e<l=bs(a+1)(b+1)(c+1)eh(shiftLm(l-e).&.Bits.complement1)u
-|m<0,e>h=bs(a+1)(b+1)(c+1)lp(clearBitmp)u
-|b==0=r
-|a==-1=pseudoComplement(singletonx)u
-|e<l=r
-|e>h=r
-|testBitmp=bs(a-1)(b-1)(c-1)lh(clearBitmp)u
-|otherwise=r
-where
-e=fromEnumx
-p=e-l
-{-# INLINE delete #-}
-
--- | /O(1)/ Test for membership in a 'BitSet'
-member::Enuma=>a->BitSeta->Bool
-memberx(BS___lhm__)
-|e<l=m<0
-|e>h=m>0
-|otherwise=testBitm(e-l)
-where
-e=fromEnumx
-{-# INLINE member #-}
+-- | /O(d * n)/ Make a 'BitSet' from a distinct ascending list of items
+fromDistinctAscList::Enuma=>[a]->BitSeta
+fromDistinctAscList[]=empty
+fromDistinctAscList(c:cs)=fromDistinctAscList'cs101
+where
+l=fromEnumc
+fromDistinctAscList'::Enuma=>[a]->Int->Int->Integer->BitSeta
+fromDistinctAscList'[]!n!h!m=BSnnnlhmundefinedtoEnum
+fromDistinctAscList'(c':cs')!n_!m=
+leth'=fromEnumc'in
+fromDistinctAscList'cs'(n+1)h'(setBitm(h'-l))
+{-# INLINE fromDistinctAscList #-}
+
+-- | /O(d)/ Insert a single element of type @a@ into the 'BitSet'. Preserves order of 'null' and 'size'
+insert::Enuma=>a->BitSeta->BitSeta
+insertxr@(BSabclhmu_)
+|m<0,e<l=r
+|m<0,e>h=r
+|b==0=singletonx
+|a==-1=r
+|e<l=bs(a+1)(b+1)(c+1)eh(shiftLm(l-e).|.1)u
+|e>h=bs(a+1)(b+1)(c+1)lp(setBitmp)u
+|testBitmp=r
+|otherwise=bs(a+1)(b+1)(c+1)lh(setBitmp)u
+where
+e=fromEnumx
+p=e-l
+{-# INLINE insert #-}
+
+-- | /O(d)/ Delete a single item from the 'BitSet'. Preserves order of 'null' and 'size'
+delete::Enuma=>a->BitSeta->BitSeta
+deletexr@(BSabclhmu_)
+|m<0,e<l=bs(a+1)(b+1)(c+1)eh(shiftLm(l-e).&.complement1)u
+|m<0,e>h=bs(a+1)(b+1)(c+1)lp(clearBitmp)u
+|b==0=r
+|a==-1=pseudoComplement(singletonx)u
+|e<l=r
+|e>h=r
+|testBitmp=bs(a-1)(b-1)(c-1)lh(clearBitmp)u
+|otherwise=r
+where
+e=fromEnumx
+p=e-l
+{-# INLINE delete #-}
+
+-- | /O(1)/ Test for membership in a 'BitSet'
+member::Enuma=>a->BitSeta->Bool
+memberx(BS___lhm__)
+|e<l=m<0
+|e>h=m>0
+|otherwise=testBitm(e-l)
+where
+e=fromEnumx
+{-# INLINE member #-}
+
+-- | /O(d)/ convert to an Integer representation. Discards negative elements
+toInteger::BitSeta->Integer
+toIntegerx=mantissax`shift`exponentx
+{-# INLINE toInteger #-}
hunk ./doc/html/monoids/src/Data-Ring-Semi-BitSet.html 218
--- | /O(d)/ convert to an Integer representation. Discards negative elements
-toInteger::BitSeta->Integer
-toIntegerx=mantissax`shift`exponentx
-{-# INLINE toInteger #-}
-
--- | /O(d)/.
-union::Enuma=>BitSeta->BitSeta->BitSeta
-unionx@(BSabclhmuf)y@(BSa'b'c'l'h'm'u'_)
-|l'<l=unionyx-- ensure left side has lower exponent
-|b==0=y-- fast empty union
-|b'==0=x-- fast empty union
-|a==-1=entireu-- fast full union, recomplement obligation met by negative size
-|a'==-1=entireu'-- fast full union, recomplement obligation met by negative size
-|m<0,m'<0=recomplement(intersection(recomplementx)(recomplementy))-- appeal to intersection, recomplement obligation met by 2s complement
-|m'<0=recomplement(diff(recomplementy)xu')-- union with complement, recomplement obligation met by 2s complement
-|m<0=recomplement(diff(recomplementx)yu)-- union with complement, recomplement obligation met by 2s complement
-|h<l'=bs(a+a')(b+b')(c+c')lh'm''u-- disjoint positive ranges
-|otherwise=bs(a`max`a')(b+b')(recountm'')l(h`max`h')m''u-- overlapped positives
-where
-m''=m.|.shiftLm'(l'-l)
-entireu''=BS(-1)(-1)(-1)00(-1)u''f
+-- | /O(d)/.
+union::Enuma=>BitSeta->BitSeta->BitSeta
+unionx@(BSabclhmuf)y@(BSa'b'c'l'h'm'u'_)
+|l'<l=unionyx-- ensure left side has lower exponent
+|b==0=y-- fast empty union
+|b'==0=x-- fast empty union
+|a==-1=entireu-- fast full union, recomplement obligation met by negative size
+|a'==-1=entireu'-- fast full union, recomplement obligation met by negative size
+|m<0,m'<0=recomplement(intersection(recomplementx)(recomplementy))-- appeal to intersection, recomplement obligation met by 2s complement
+|m'<0=recomplement(diff(recomplementy)xu')-- union with complement, recomplement obligation met by 2s complement
+|m<0=recomplement(diff(recomplementx)yu)-- union with complement, recomplement obligation met by 2s complement
+|h<l'=bs(a+a')(b+b')(c+c')lh'm''u-- disjoint positive ranges
+|otherwise=bs(a`max`a')(b+b')(recountm'')l(h`max`h')m''u-- overlapped positives
+where
+m''=m.|.shiftLm'(l'-l)
+entireu''=BS(-1)(-1)(-1)00(-1)u''f
+
+-- | /O(1)/ Check to see if we are represented as a complemented 'BitSet'.
+isComplemented::Enuma=>BitSeta->Bool
+isComplemented=(<0).mantissa
+{-# INLINE isComplemented #-}
hunk ./doc/html/monoids/src/Data-Ring-Semi-BitSet.html 240
--- | /O(1)/ Check to see if we are represented as a complemented 'BitSet'.
-isComplemented::Enuma=>BitSeta->Bool
-isComplemented=(<0).mantissa
-{-# INLINE isComplemented #-}
-
--- | /O(d)/
-intersection::Enuma=>BitSeta->BitSeta->BitSeta
-intersectionx@(BSab_lhmu_)y@(BSa'b'_l'h'm'u'_)
-|l'<l=intersectionyx
-|b==0=empty
-|b'==0=empty
-|a==-1=y
-|a'==-1=x
-|m<0,m'<0=recomplement(union(recomplementx)(recomplementy))
-|m'<0=diffx(recomplementy)u'
-|m<0=diffy(recomplementx)u
-|h<l'=empty
-|otherwise=bs0(b`min`b')(recountm'')l''(h`min`h')m''u
-where
-l''=maxll'
-m''=shiftm(l''-l).&.shiftm'(l''-l')
-
--- | Unsafe internal method for computing differences in a known universe of discourse.
---
--- Preconditions:
---
--- (1) @m >= 0@
--- 2 @m' >= 0@
--- 3 @a /= -1@
--- 4 @a' /= -1@
--- 5 @b /= 0@
--- 6 @b' /= 0@
--- 7 @u''@ is a previously obtained copy of @(fromEnum minBound, fromEnum maxBound)@
---
-diff::Enuma=>BitSeta->BitSeta->(Int,Int)->BitSeta
-diffx@(BSa__lhm__)(BS_b'_l'h'm'__)u''
-|h<l'=x
-|h'<l=x
-|otherwise=bs(max(a-b')0)a(recountm'')lhm''u''
-where
-m''=m.&.shift(Bits.complementm')(l'-l)
-{-# INLINE diff #-}
-
--- | /O(d)/ Remove all elements present in the second bitset from the first
-difference::Enuma=>BitSeta->BitSeta->BitSeta
-differencex@(BSab___mu_)y@(BSa'b'___m'__)
-|a==-1=pseudoComplementyu
-|a'==-1=empty
-|b==0=empty
-|b'==0=x
-|m<0,m'<0=diff(recomplementy)(recomplementx)u
-|m<0=pseudoComplement(recomplementx`union`y)u
-|m'<0=x`union`recomplementy
-|otherwise=diffxyu
-
--- | /O(d)/ Infix 'difference'
-(\\)::Enuma=>BitSeta->BitSeta->BitSeta
-(\\)=difference
-{-# INLINE (\\) #-}
-
-instanceEq(BitSeta)where
-x@(BS___l_mu_)==y@(BS___l'_m'__)
-|signumm==signumm'=shiftm(l-l'')==shiftm'(l'-l'')
-|m'<0=y==x
-|otherwise=mask.&.shiftm(l-ul)==shiftm'(l-ul)
-where
-l''=minll'
-mask=setBit0(uh-ul+1)-1
-ul=fstu
-uh=sndu
-
-instance(Enuma,Boundeda)=>Bounded(BitSeta)where
-minBound=empty
-maxBound=resultwhere
-result=BSnnnlhm(l,h)toEnum
-n=h-l+1
-l=fromEnum(minBound`asArgTypeOf`result)
-h=fromEnum(maxBound`asArgTypeOf`result)
-m=setBit0n-1
+-- | /O(d)/
+intersection::Enuma=>BitSeta->BitSeta->BitSeta
+intersectionx@(BSab_lhmu_)y@(BSa'b'_l'h'm'u'_)
+|l'<l=intersectionyx
+|b==0=empty
+|b'==0=empty
+|a==-1=y
+|a'==-1=x
+|m<0,m'<0=recomplement(union(recomplementx)(recomplementy))
+|m'<0=diffx(recomplementy)u'
+|m<0=diffy(recomplementx)u
+|h<l'=empty
+|otherwise=bs0(b`min`b')(recountm'')l''(h`min`h')m''u
+where
+l''=maxll'
+m''=shiftm(l''-l).&.shiftm'(l''-l')
+
+-- | Unsafe internal method for computing differences in a known universe of discourse.
+--
+-- Preconditions:
+--
+-- (1) @m >= 0@
+-- 2 @m' >= 0@
+-- 3 @a /= -1@
+-- 4 @a' /= -1@
+-- 5 @b /= 0@
+-- 6 @b' /= 0@
+-- 7 @u''@ is a previously obtained copy of @(fromEnum minBound, fromEnum maxBound)@
+--
+diff::Enuma=>BitSeta->BitSeta->(Int,Int)->BitSeta
+diffx@(BSa__lhm__)(BS_b'_l'h'm'__)u''
+|h<l'=x
+|h'<l=x
+|otherwise=bs(max(a-b')0)a(recountm'')lhm''u''
+where
+m''=m.&.shift(complementm')(l'-l)
+{-# INLINE diff #-}
+
+-- | /O(d)/ Remove all elements present in the second bitset from the first
+difference::Enuma=>BitSeta->BitSeta->BitSeta
+differencex@(BSab___mu_)y@(BSa'b'___m'__)
+|a==-1=pseudoComplementyu
+|a'==-1=empty
+|b==0=empty
+|b'==0=x
+|m<0,m'<0=diff(recomplementy)(recomplementx)u
+|m<0=pseudoComplement(recomplementx`union`y)u
+|m'<0=x`union`recomplementy
+|otherwise=diffxyu
+
+-- | /O(d)/ Infix 'difference'
+(\\)::Enuma=>BitSeta->BitSeta->BitSeta
+(\\)=difference
+{-# INLINE (\\) #-}
+
+instanceEq(BitSeta)where
+x@(BS___l_mu_)==y@(BS___l'_m'__)
+|signumm==signumm'=shiftm(l-l'')==shiftm'(l'-l'')
+|m'<0=y==x
+|otherwise=mask.&.shiftm(l-ul)==shiftm'(l-ul)
+where
+l''=minll'
+mask=setBit0(uh-ul+1)-1
+ul=fstu
+uh=sndu
+
+instance(Enuma,Boundeda)=>Bounded(BitSeta)where
+minBound=empty
+maxBound=resultwhere
+result=BSnnnlhm(l,h)toEnum
+n=h-l+1
+l=fromEnum(minBound`asArgTypeOf`result)
+h=fromEnum(maxBound`asArgTypeOf`result)
+m=setBit0n-1
+
+-- | Utility function to avoid requiring ScopedTypeVariables
+asArgTypeOf::a->fa->a
+asArgTypeOf=const
+{-# INLINE asArgTypeOf #-}
hunk ./doc/html/monoids/src/Data-Ring-Semi-BitSet.html 320
--- | Utility function to avoid requiring ScopedTypeVariables
-asArgTypeOf::a->fa->a
-asArgTypeOf=const
-{-# INLINE asArgTypeOf #-}
-
--- | /O(d)/
-recount::Integer->Int
-recount!n
-|n<0=Bits.complement(recount(Bits.complementn))
-|otherwise=recount'00
-where
-h=hwmn
-recount'!i!c
-|i>h=c
-|otherwise=recount'(i+1)(iftestBitnithenc+1elsec)
-
--- | /O(d)/. Computes the equivalent of (truncate . logBase 2 . abs) extended with 0 at 0
-hwm::Integer->Int
-hwm!n
-|n<0=hwm(-n)
-|n>1=scanp(2*p)
-|otherwise=0
-where
-p=probe1
--- incrementally compute 2^(2^(i+1)) until it exceeds n
-probe::Int->Int
-probe!i
-|bit(2*i)>n=i
-|otherwise=probe(2*i)
-
--- then scan the powers for the highest set bit
-scan::Int->Int->Int
-scan!l!h
-|l==h=l
-|bit(m+1)>n=scanlm
-|otherwise=scan(m+1)h
-where
-m=l+(h-l)`div`2
-
-instanceShowa=>Show(BitSeta)where
-showsPrecdx@(BS_____mu_)
-|m<0=showParen(d>10)$showString"pseudoComplement ".showsPrec11(recomplementx).showString" ".showsPrec11u
-|otherwise=showParen(d>10)$showString"fromDistinctAscList ".showsPrec11(toListx)
-
-instance(Enuma,Reada)=>Read(BitSeta)where
-readPrec=parens$complemented+++normalwhere
-complemented=prec10$do
-Ident"pseudoComplement"<-lexP
-x<-stepreadPrec
-pseudoComplementx`fmap`stepreadPrec
-normal=prec10$do
-Ident"fromDistinctAscList"<-lexP
-fromDistinctAscList`fmap`stepreadPrec
-
--- note that operations on values generated by toEnum are pretty slow because the bounds are suboptimal
-instance(Enuma,Boundeda)=>Enum(BitSeta)where
-fromEnumb@(BS___l_m__)=fromInteger(shiftLm(l-l'))
-where
-l'=fromEnum(minBound`asArgTypeOf`b)
-toEnumi=result
-where
-result=BSai(recountm)lhmundefinedtoEnum-- n <= 2^n, so i serves as a valid upper bound
-l=fromEnum(minBound`asArgTypeOf`result)
-h=fromEnum(maxBound`asArgTypeOf`result)
-m=fromIntegrali
-a|m/=0=1-- allow a fast null check, but not much else
-|otherwise=0
-
-instanceFoldableBitSetwhere
-fold=fold.toList
-foldMapf=foldMapf.toList
-foldrfz=foldrfz.toList
-foldlfz=foldlfz.toList
-foldr1f=foldr1f.toList
-foldl1f=foldl1f.toList
-
-instanceEnuma=>Monoid(BitSeta)where
-mempty=empty
-mappend=union
+-- | /O(d)/
+recount::Integer->Int
+recount!n
+|n<0=complement(recount(complementn))
+|otherwise=recount'00
+where
+h=hwmn
+recount'!i!c
+|i>h=c
+|otherwise=recount'(i+1)(iftestBitnithenc+1elsec)
+
+-- | /O(d)/. Computes the equivalent of (truncate . logBase 2 . abs) extended with 0 at 0
+hwm::Integer->Int
+hwm!n
+|n<0=hwm(-n)
+|n>1=scanp(2*p)
+|otherwise=0
+where
+p=probe1
+-- incrementally compute 2^(2^(i+1)) until it exceeds n
+probe::Int->Int
+probe!i
+|bit(2*i)>n=i
+|otherwise=probe(2*i)
+
+-- then scan the powers for the highest set bit
+scan::Int->Int->Int
+scan!l!h
+|l==h=l
+|bit(m+1)>n=scanlm
+|otherwise=scan(m+1)h
+where
+m=l+(h-l)`div`2
+
+instanceShowa=>Show(BitSeta)where
+showsPrecdx@(BS_____mu_)
+|m<0=showParen(d>10)$showString"pseudoComplement ".showsPrec11(recomplementx).showString" ".showsPrec11u
+|otherwise=showParen(d>10)$showString"fromDistinctAscList ".showsPrec11(toListx)
+
+instance(Enuma,Reada)=>Read(BitSeta)where
+readPrec=parens$complemented+++normalwhere
+complemented=prec10$do
+Ident"pseudoComplement"<-lexP
+x<-stepreadPrec
+pseudoComplementx`fmap`stepreadPrec
+normal=prec10$do
+Ident"fromDistinctAscList"<-lexP
+fromDistinctAscList`fmap`stepreadPrec
+
+-- note that operations on values generated by toEnum are pretty slow because the bounds are suboptimal
+instance(Enuma,Boundeda)=>Enum(BitSeta)where
+fromEnumb@(BS___l_m__)=fromInteger(shiftLm(l-l'))
+where
+l'=fromEnum(minBound`asArgTypeOf`b)
+toEnumi=result
+where
+result=BSai(recountm)lhmundefinedtoEnum-- n <= 2^n, so i serves as a valid upper bound
+l=fromEnum(minBound`asArgTypeOf`result)
+h=fromEnum(maxBound`asArgTypeOf`result)
+m=fromIntegrali
+a|m/=0=1-- allow a fast null check, but not much else
+|otherwise=0
+
+instanceFoldableBitSetwhere
+fold=fold.toList
+foldMapf=foldMapf.toList
+foldrfz=foldrfz.toList
+foldlfz=foldlfz.toList
+foldr1f=foldr1f.toList
+foldl1f=foldl1f.toList
+
+instanceEnuma=>Monoid(BitSeta)where
+mempty=empty
+mappend=union
+
+instanceEnuma=>Reducera(BitSeta)where
+unit=singleton
+snoc=flipinsert
+cons=insert
hunk ./doc/html/monoids/src/Data-Ring-Semi-BitSet.html 400
-instanceEnuma=>Reducera(BitSeta)where
-unit=singleton
-snoc=flipinsert
-cons=insert
-
-instance(Boundeda,Enuma)=>Multiplicative(BitSeta)where
-one=full
-times=intersection
+instance(Boundeda,Enuma)=>Multiplicative(BitSeta)where
+one=full
+times=intersection
+
+instance(Boundeda,Enuma)=>Ringoid(BitSeta)
+instance(Boundeda,Enuma)=>LeftSemiNearRing(BitSeta)
+instance(Boundeda,Enuma)=>RightSemiNearRing(BitSeta)
+instance(Boundeda,Enuma)=>SemiRing(BitSeta)
hunk ./doc/html/monoids/src/Data-Ring-Semi-BitSet.html 409
-instance(Boundeda,Enuma)=>Ringoid(BitSeta)
-instance(Boundeda,Enuma)=>LeftSemiNearRing(BitSeta)
-instance(Boundeda,Enuma)=>RightSemiNearRing(BitSeta)
-instance(Boundeda,Enuma)=>SemiRing(BitSeta)
-
--- idempotent monoid
-instanceEnuma=>LeftModuleNatural(BitSeta)where
-0*._=empty
-_*.m=m
-instanceEnuma=>RightModuleNatural(BitSeta)where
-_.*0=empty
-m.*_=m
-instanceEnuma=>ModuleNatural(BitSeta)
-
-instance(Boundeda,Enuma)=>LeftModule(BitSeta)(BitSeta)where(*.)=times
-instance(Boundeda,Enuma)=>RightModule(BitSeta)(BitSeta)where(.*)=times
-instance(Boundeda,Enuma)=>Module(BitSeta)(BitSeta)
-
-instance(Boundeda,Enuma)=>RAlgebraNatural(BitSeta)
-
-instanceGenerator(BitSeta)where
-typeElem(BitSeta)=a
-mapReducef=mapReducef.toList
+-- idempotent monoid
+instanceEnuma=>ModuleNatural(BitSeta)
+instanceEnuma=>LeftModuleNatural(BitSeta)where
+0*._=empty
+_*.m=m
+instanceEnuma=>RightModuleNatural(BitSeta)where
+_.*0=empty
+m.*_=m
+instanceEnuma=>BimoduleNatural(BitSeta)
+instance(Boundeda,Enuma)=>AlgebraNatural(BitSeta)
+
+instance(Boundeda,Enuma)=>Module(BitSeta)(BitSeta)
+instance(Boundeda,Enuma)=>LeftModule(BitSeta)(BitSeta)where(*.)=times
+instance(Boundeda,Enuma)=>RightModule(BitSeta)(BitSeta)where(.*)=times
+instance(Boundeda,Enuma)=>Bimodule(BitSeta)(BitSeta)
+instance(Boundeda,Enuma)=>Algebra(BitSeta)(BitSeta)
+
+instanceGenerator(BitSeta)where
+typeElem(BitSeta)=a
+mapReducef=mapReducef.toList
+
+instance(Showa,Boundeda,Enuma)=>Num(BitSeta)where
+(+)=union
+(-)=difference
+(*)=intersection
+fromIntegerm=rwhere
+r=BSccc0(hwmm)mutoEnumwhere
+c=recountm
+u=(fromEnum(minBound`asArgTypeOf`r),fromEnum(maxBound`asArgTypeOf`r))
+absb|mantissab<0=recomplementb
+|otherwise=b
+signum=error"BitSet.signum undefined"
+
+instance(Showa,Boundeda,Enuma)=>Bits(BitSeta)where
+(.&.)=intersection
+(.|.)=union
+a`xor`b=(a.|.b).&.complement(a.&.b)
+
+-- | /O(d)/ Complements a 'BitSet' with respect to the bounds of @a@. Preserves order of 'null' and 'size'
+complementr@(BSabclhm__)=BS(complementb)(complementa)(complementc)lh(complementm)utoEnumwhere
+u=(fromEnum(minBound`asArgTypeOf`r),fromEnum(maxBound`asArgTypeOf`r))
+{-# INLINE complement #-}
+{-
+ shift (BS a b c l h m _ f) n = BS a b c ((l + r) `max` uh) ((h + r) `max` uh) m (ul,uh) toEnum) where
+ ul = fromEnum (minBound `asArgTypeOf` r)
+ uh = fromEnum (maxBound `asArgTypeOf` r)
+ -}
+shift=error"BitSet.shift undefined"
+rotate=error"BitSet.rotate undefined"
+bit=singleton.toEnum
+setBitsb=s`union`singleton(toEnumb)
+clearBitsb=s`difference`singleton(toEnumb)
+complementBitsb=s`xor`singleton(toEnumb)
+testBitsb=member(toEnumb)s
+bitSizer=fromEnum(maxBound`asArgTypeOf`r)-fromEnum(minBound`asArgTypeOf`r)
+isSigned_=True
+
+complement'::(Boundeda,Enuma)=>BitSeta->BitSeta
+complement'r@(BSabclhm__)=BS(complementb)(complementa)(complementc)lh(complementm)utoEnumwhere
+u=(fromEnum(minBound`asArgTypeOf`r),fromEnum(maxBound`asArgTypeOf`r))
hunk ./doc/html/monoids/src/Data-Ring-Semi-Kleene.html 10
-(moduleData.Ring.Semi
+(moduleData.Ring
hunk ./doc/html/monoids/src/Data-Ring-Semi-Kleene.html 15
-importData.Ring.Semi
+importData.Ring
hunk ./doc/html/monoids/src/Data-Ring-Semi-Natural.html 26
-(moduleData.Ring.Semi
+(moduleData.Ring
hunk ./doc/html/monoids/src/Data-Ring-Semi-Natural.html 28
-,natural
-)where
-
-importPreludehiding(id,(.))
-importNumeric(readDec,showInt)
-importControl.Applicative
-importControl.Monad
-importData.Ring.Semi
-importqualifiedData.Monoid.CombinatorsasMonoid
--- import Data.Word
-importData.Monoid.Monad
-importData.Monoid.Applicative
-importData.Monoid.Multiplicative
-importData.Monoid.Categorical
-importData.Monoid.Self
-importData.Monoid.FromString
+,toNatural
+,fromNatural
+)where
+
+importPreludehiding(id,(.))
+importNumeric(readDec,showInt)
+importControl.Applicative
+importControl.Monad
+importData.Ring
+importqualifiedData.Monoid.CombinatorsasMonoid
+-- import Data.Word
+importData.Monoid.Monad
+importData.Monoid.Applicative
+importData.Monoid.Multiplicative
+importData.Monoid.Categorical
+importData.Monoid.Self
hunk ./doc/html/monoids/src/Data-Ring-Semi-Natural.html 47
-importData.Generator.Compressive.RLE
-importData.Sequence(Seq)
-
-natural::Integer->Natural
-natural=fromInteger
-
-newtypeNatural=Natural{getNatural::Integer}
-deriving(Eq,Ord)
-
-instanceReadNaturalwhere
-readsPrec=constreadDec
-
-instanceShowNaturalwhere
-showsPrec=constshowInt
-
-instanceNumNaturalwhere
-Naturala+Naturalb=Natural(a+b)
-Naturala-Naturalb=fromInteger(a-b)
-Naturala*Naturalb=Natural(a*b)
-abs=id
-signum=Natural.signum.getNatural
-fromIntegerx|x<0=error"Natural < 0"
-|otherwise=Naturalx
-negate0=0
-negate_=error"Natural < 0"
+
+#ifdef M_CONTAINERS
+-- used with Seq
+importData.Generator.Compressive.RLE
+importData.Sequence(Seq)
+#endif
+
+#ifdef X_OverloadedStrings
+importData.Monoid.FromString
+#endif
+
+toNatural::Integer->Natural
+toNatural=fromInteger
+
+fromNatural::Ringoidr=>Natural->r
+fromNatural=Monoid.replicateone.getNatural
+
+newtypeNatural=Natural{getNatural::Integer}
+deriving(Eq,Ord)
+
+instanceReadNaturalwhere
+readsPrec=constreadDec
+
+instanceShowNaturalwhere
+showsPrec=constshowInt
hunk ./doc/html/monoids/src/Data-Ring-Semi-Natural.html 73
-instanceEnumNaturalwhere
-succ(Naturaln)=Natural(n+1)
-pred(Natural0)=error"Natural < 0"
-pred(Naturaln)=Natural(n-1)
-toEnumn|n<0=error"Natural < 0"
-toEnumn=Natural(fromIntegraln)
-fromEnum=fromIntegral
-enumFrom(Naturaln)=Natural`map`enumFromn
-enumFromThen(Naturaln)(Naturalnp)
-|np<n=Natural`map`enumFromThenTonnp0
-|otherwise=Natural`map`enumFromThennnp
-enumFromTo(Naturaln)(Naturalm)=Natural`map`enumFromTonm
-enumFromThenTo(Naturaln)(Naturalm)(Naturalo)=Natural`map`enumFromThenTonmo
-
-instanceRealNaturalwhere
-toRational=toRational.getNatural
-
-instanceIntegralNaturalwhere
-toInteger=getNatural
-Naturala`quot`Naturalb=Natural(a`quot`b)
-Naturala`rem`Naturalb=Natural(a`rem`b)
-Naturala`div`Naturalb=Natural(a`div`b)
-Naturala`mod`Naturalb=Natural(a`mod`b)
-Naturala`quotRem`Naturalb=(Naturalq,Naturalr)where~(q,r)=a`quotRem`b
-Naturala`divMod`Naturalb=(Naturalq,Naturalr)where~(q,r)=a`divMod`b
-
-instanceMonoidNaturalwhere
-mempty=0
-mappend=(+)
-
-instanceMultiplicativeNaturalwhere
-one=1
-times=(*)
-
-instanceRingoidNatural
-instanceLeftSemiNearRingNatural
-instanceRightSemiNearRingNatural
-instanceSemiRingNatural
-
-instanceLeftModuleNatural()where_*._=()
-instanceRightModuleNatural()where_.*_=()
-instanceModuleNatural()
-
--- idempotent monoids
-instanceLeftModuleNaturalAnywhere
-0*._=mempty
-_*.m=m
-instanceRightModuleNaturalAnywhere
-_.*0=mempty
-m.*_=m
-instanceModuleNaturalAny
-
-instanceLeftModuleNaturalAllwhere
-0*._=mempty
-_*.m=m
-instanceRightModuleNaturalAllwhere
-_.*0=mempty
-m.*_=m
-instanceModuleNaturalAll
-
-instanceLeftModuleNatural(Firsta)where
-0*._=mempty
-_*.m=m
-instanceRightModuleNatural(Firsta)where
-_.*0=mempty
-m.*_=m
-instanceModuleNatural(Firsta)
-
-instanceLeftModuleNatural(Lasta)where
-0*._=mempty
-_*.m=m
-instanceRightModuleNatural(Lasta)where
-_.*0=mempty
-m.*_=m
-instanceModuleNatural(Lasta)
-
-instanceLeftModuleNaturalOrderingwhere
-0*._=mempty
-_*.m=m
-instanceRightModuleNaturalOrderingwhere
-_.*0=mempty
-m.*_=m
-instanceModuleNaturalOrdering
-
--- other monoids
-
-instanceLeftModuleNatural[a]where(*.)=flipMonoid.replicate
-instanceRightModuleNatural[a]where(.*)=Monoid.replicate
-instanceModuleNatural[a]
-
-instanceMonoidm=>LeftModuleNatural(a->m)where(*.)=flipMonoid.replicate
-instanceMonoidm=>RightModuleNatural(a->m)where(.*)=Monoid.replicate
-instanceMonoidm=>ModuleNatural(a->m)
-
-instanceNuma=>LeftModuleNatural(Suma)where(*.)=flipMonoid.replicate
-instanceNuma=>RightModuleNatural(Suma)where(.*)=Monoid.replicate
-instanceNuma=>ModuleNatural(Suma)
-
-instanceNuma=>LeftModuleNatural(Producta)where(*.)=flip(.*)
-instanceNuma=>RightModuleNatural(Producta)whereProductm.*Naturaln=Product(m^n)
-instanceNuma=>ModuleNatural(Producta)
-
-instanceLeftModuleNatural(Endoa)where(*.)=flipMonoid.replicate
-instanceRightModuleNatural(Endoa)where(.*)=Monoid.replicate
-instanceModuleNatural(Endoa)
-
-instanceMonoidm=>LeftModuleNatural(Dualm)where(*.)=flipMonoid.replicate
-instanceMonoidm=>RightModuleNatural(Dualm)where(.*)=Monoid.replicate
-instanceMonoidm=>ModuleNatural(Dualm)
-
--- FromString
-instanceMonoidm=>LeftModuleNatural(FromStringm)where(*.)=flipMonoid.replicate
-instanceMonoidm=>RightModuleNatural(FromStringm)where(.*)=Monoid.replicate
-instanceMonoidm=>ModuleNatural(FromStringm)
-
--- Self
-instanceMonoidm=>LeftModuleNatural(Selfm)where(*.)=flipMonoid.replicate
-instanceMonoidm=>RightModuleNatural(Selfm)where(.*)=Monoid.replicate
-instanceMonoidm=>ModuleNatural(Selfm)
-
--- Free Generator
-instanceLeftModuleNatural(Freea)where(*.)=flipMonoid.replicate
-instanceRightModuleNatural(Freea)where(.*)=Monoid.replicate
-instanceModuleNatural(Freea)
-
--- RLE Seq
-instanceEqa=>LeftModuleNatural(RLESeqa)where(*.)=flipMonoid.replicate
-instanceEqa=>RightModuleNatural(RLESeqa)where(.*)=Monoid.replicate
-instanceEqa=>ModuleNatural(RLESeqa)
-
--- Categorical
-instanceCategoryk=>LeftModuleNatural(GEndoka)where(*.)=flipMonoid.replicate
-instanceCategoryk=>RightModuleNatural(GEndoka)where(.*)=Monoid.replicate
-instanceCategoryk=>ModuleNatural(GEndoka)
-
-instanceMonoidm=>LeftModuleNatural(CMonoidmmm)where(*.)=flipMonoid.replicate
-instanceMonoidm=>RightModuleNatural(CMonoidmmm)where(.*)=Monoid.replicate
-instanceMonoidm=>ModuleNatural(CMonoidmmm)
-
--- Alternative
-instanceApplicativef=>LeftModuleNatural(Traversalf)where(*.)=flipMonoid.replicate
-instanceApplicativef=>RightModuleNatural(Traversalf)where(.*)=Monoid.replicate
-instanceApplicativef=>ModuleNatural(Traversalf)
-
-instanceAlternativef=>LeftModuleNatural(Altfa)where(*.)=flipMonoid.replicate
-instanceAlternativef=>RightModuleNatural(Altfa)where(.*)=Monoid.replicate
-instanceAlternativef=>ModuleNatural(Altfa)
-
---instance (Alternative f, Monoid m) => LeftModule Natural (App f m) where (*.) = flip Monoid.replicate
---instance (Alternative f, Monoid m) => RightModule Natural (App f m) where (.*) = Monoid.replicate
---instance (Alternative f, Monoid m) => Module Natural (App f m)
-
--- Monad
-instanceMonadf=>LeftModuleNatural(Actionf)where(*.)=flipMonoid.replicate
-instanceMonadf=>RightModuleNatural(Actionf)where(.*)=Monoid.replicate
-instanceMonadf=>ModuleNatural(Actionf)
-
-instanceMonadPlusf=>LeftModuleNatural(MonadSumfa)where(*.)=flipMonoid.replicate
-instanceMonadPlusf=>RightModuleNatural(MonadSumfa)where(.*)=Monoid.replicate
-instanceMonadPlusf=>ModuleNatural(MonadSumfa)
-
---instance (MonadPlus f, Monoid m) => LeftModule Natural (Mon f m) where (*.) = flip Monoid.replicate
---instance (MonadPlus f, Monoid m) => RightModule Natural (Mon f m) where (.*) = Monoid.replicate
---instance (MonadPlus f, Monoid m) => Module Natural (Mon f m)
-
--- Lexical
-instanceLeftModuleNatural(SourcePositionf)where
-0*._=mempty
-n*.Columnsx=Columns(fromIntegraln*x)
-n*.Lineslc=Lines(fromIntegraln*l)c
-_*.Posflc=Posflc
-n*.t=Monoid.replicatetn
-
-instanceRightModuleNatural(SourcePositionf)where(.*)=flip(*.)
-instanceModuleNatural(SourcePositionf)
-
-instanceCharReducerm=>LeftModuleNatural(UTF8m)where(*.)=flipMonoid.replicate
-instanceCharReducerm=>RightModuleNatural(UTF8m)where(.*)=Monoid.replicate
-instanceCharReducerm=>ModuleNatural(UTF8m)
-
-instanceMultiplicativem=>LeftModuleNatural(Logm)where(*.)=flipMonoid.replicate
-instanceMultiplicativem=>RightModuleNatural(Logm)where(.*)=Monoid.replicate
-instanceMultiplicativem=>ModuleNatural(Logm)
-
+instanceNumNaturalwhere
+Naturala+Naturalb=Natural(a+b)
+Naturala-Naturalb=fromInteger(a-b)
+Naturala*Naturalb=Natural(a*b)
+abs=id
+signum=Natural.signum.getNatural
+fromIntegerx|x<0=error"Natural < 0"
+|otherwise=Naturalx
+negate0=0
+negate_=error"Natural < 0"
+
+instanceEnumNaturalwhere
+succ(Naturaln)=Natural(n+1)
+pred(Natural0)=error"Natural < 0"
+pred(Naturaln)=Natural(n-1)
+toEnumn|n<0=error"Natural < 0"
+toEnumn=Natural(fromIntegraln)
+fromEnum=fromIntegral
+enumFrom(Naturaln)=Natural`map`enumFromn
+enumFromThen(Naturaln)(Naturalnp)
+|np<n=Natural`map`enumFromThenTonnp0
+|otherwise=Natural`map`enumFromThennnp
+enumFromTo(Naturaln)(Naturalm)=Natural`map`enumFromTonm
+enumFromThenTo(Naturaln)(Naturalm)(Naturalo)=Natural`map`enumFromThenTonmo
+
+instanceRealNaturalwhere
+toRational=toRational.getNatural
+
+instanceIntegralNaturalwhere
+toInteger=getNatural
+Naturala`quot`Naturalb=Natural(a`quot`b)
+Naturala`rem`Naturalb=Natural(a`rem`b)
+Naturala`div`Naturalb=Natural(a`div`b)
+Naturala`mod`Naturalb=Natural(a`mod`b)
+Naturala`quotRem`Naturalb=(Naturalq,Naturalr)where~(q,r)=a`quotRem`b
+Naturala`divMod`Naturalb=(Naturalq,Naturalr)where~(q,r)=a`divMod`b
+
+instanceMonoidNaturalwhere
+mempty=0
+mappend=(+)
+
+instanceMultiplicativeNaturalwhere
+one=1
+times=(*)
+
+instanceRingoidNatural
+instanceLeftSemiNearRingNatural
+instanceRightSemiNearRingNatural
+instanceSemiRingNatural
+
+instanceLeftModuleNatural()where_*._=()
+instanceRightModuleNatural()where_.*_=()
+instanceModuleNatural()
+
+-- idempotent monoids
+instanceLeftModuleNaturalAnywhere
+0*._=mempty
+_*.m=m
+instanceRightModuleNaturalAnywhere
+_.*0=mempty
+m.*_=m
+instanceModuleNaturalAny
+
+instanceLeftModuleNaturalAllwhere
+0*._=mempty
+_*.m=m
+instanceRightModuleNaturalAllwhere
+_.*0=mempty
+m.*_=m
+instanceModuleNaturalAll
+
+instanceLeftModuleNatural(Firsta)where
+0*._=mempty
+_*.m=m
+instanceRightModuleNatural(Firsta)where
+_.*0=mempty
+m.*_=m
+instanceModuleNatural(Firsta)
+
+instanceLeftModuleNatural(Lasta)where
+0*._=mempty
+_*.m=m
+instanceRightModuleNatural(Lasta)where
+_.*0=mempty
+m.*_=m
+instanceModuleNatural(Lasta)
+
+instanceLeftModuleNaturalOrderingwhere
+0*._=mempty
+_*.m=m
+instanceRightModuleNaturalOrderingwhere
+_.*0=mempty
+m.*_=m
+instanceModuleNaturalOrdering
+
+-- other monoids
+
+instanceLeftModuleNatural[a]where(*.)=flipMonoid.replicate
+instanceRightModuleNatural[a]where(.*)=Monoid.replicate
+instanceModuleNatural[a]
+
+instanceMonoidm=>LeftModuleNatural(a->m)where(*.)=flipMonoid.replicate
+instanceMonoidm=>RightModuleNatural(a->m)where(.*)=Monoid.replicate
+instanceMonoidm=>ModuleNatural(a->m)
+
+instanceNuma=>LeftModuleNatural(Suma)where(*.)=flipMonoid.replicate
+instanceNuma=>RightModuleNatural(Suma)where(.*)=Monoid.replicate
+instanceNuma=>ModuleNatural(Suma)
+
+instanceNuma=>LeftModuleNatural(Producta)where(*.)=flip(.*)
+instanceNuma=>RightModuleNatural(Producta)whereProductm.*Naturaln=Product(m^n)
+instanceNuma=>ModuleNatural(Producta)
+
+instanceLeftModuleNatural(Endoa)where(*.)=flipMonoid.replicate
+instanceRightModuleNatural(Endoa)where(.*)=Monoid.replicate
+instanceModuleNatural(Endoa)
+
+instanceMonoidm=>LeftModuleNatural(Dualm)where(*.)=flipMonoid.replicate
+instanceMonoidm=>RightModuleNatural(Dualm)where(.*)=Monoid.replicate
+instanceMonoidm=>ModuleNatural(Dualm)
+
+-- Self
+instanceMonoidm=>LeftModuleNatural(Selfm)where(*.)=flipMonoid.replicate
+instanceMonoidm=>RightModuleNatural(Selfm)where(.*)=Monoid.replicate
+instanceMonoidm=>ModuleNatural(Selfm)
+
+-- Free Generator
+instanceLeftModuleNatural(Freea)where(*.)=flipMonoid.replicate
+instanceRightModuleNatural(Freea)where(.*)=Monoid.replicate
+instanceModuleNatural(Freea)
+
+-- Categorical
+instanceCategoryk=>LeftModuleNatural(GEndoka)where(*.)=flipMonoid.replicate
+instanceCategoryk=>RightModuleNatural(GEndoka)where(.*)=Monoid.replicate
+instanceCategoryk=>ModuleNatural(GEndoka)
+
+instanceMonoidm=>LeftModuleNatural(CMonoidmmm)where(*.)=flipMonoid.replicate
+instanceMonoidm=>RightModuleNatural(CMonoidmmm)where(.*)=Monoid.replicate
+instanceMonoidm=>ModuleNatural(CMonoidmmm)
+
+-- Alternative
+instanceApplicativef=>LeftModuleNatural(Traversalf)where(*.)=flipMonoid.replicate
+instanceApplicativef=>RightModuleNatural(Traversalf)where(.*)=Monoid.replicate
+instanceApplicativef=>ModuleNatural(Traversalf)
+
+instanceAlternativef=>LeftModuleNatural(Altfa)where(*.)=flipMonoid.replicate
+instanceAlternativef=>RightModuleNatural(Altfa)where(.*)=Monoid.replicate
+instanceAlternativef=>ModuleNatural(Altfa)
+
+--instance (Alternative f, Monoid m) => LeftModule Natural (App f m) where (*.) = flip Monoid.replicate
+--instance (Alternative f, Monoid m) => RightModule Natural (App f m) where (.*) = Monoid.replicate
+--instance (Alternative f, Monoid m) => Module Natural (App f m)
+
+-- Monad
+instanceMonadf=>LeftModuleNatural(Actionf)where(*.)=flipMonoid.replicate
+instanceMonadf=>RightModuleNatural(Actionf)where(.*)=Monoid.replicate
+instanceMonadf=>ModuleNatural(Actionf)
+
+instanceMonadPlusf=>LeftModuleNatural(MonadSumfa)where(*.)=flipMonoid.replicate
+instanceMonadPlusf=>RightModuleNatural(MonadSumfa)where(.*)=Monoid.replicate
+instanceMonadPlusf=>ModuleNatural(MonadSumfa)
+
+--instance (MonadPlus f, Monoid m) => LeftModule Natural (Mon f m) where (*.) = flip Monoid.replicate
+--instance (MonadPlus f, Monoid m) => RightModule Natural (Mon f m) where (.*) = Monoid.replicate
+--instance (MonadPlus f, Monoid m) => Module Natural (Mon f m)
+
+-- Lexical
+instanceLeftModuleNatural(SourcePositionf)where
+0*._=mempty
+n*.Columnsx=Columns(fromIntegraln*x)
+n*.Lineslc=Lines(fromIntegraln*l)c
+_*.Posflc=Posflc
+n*.t=Monoid.replicatetn
+
+instanceRightModuleNatural(SourcePositionf)where(.*)=flip(*.)
+instanceModuleNatural(SourcePositionf)
+
+instanceCharReducerm=>LeftModuleNatural(UTF8m)where(*.)=flipMonoid.replicate
+instanceCharReducerm=>RightModuleNatural(UTF8m)where(.*)=Monoid.replicate
+instanceCharReducerm=>ModuleNatural(UTF8m)
+
+instanceMultiplicativem=>LeftModuleNatural(Logm)where(*.)=flipMonoid.replicate
+instanceMultiplicativem=>RightModuleNatural(Logm)where(.*)=Monoid.replicate
+instanceMultiplicativem=>ModuleNatural(Logm)
hunk ./doc/html/monoids/src/Data-Ring-Semi-Natural.html 258
--- TODO
---
--- Control.Monad.*
--- ParsecT
--- FingerTree
--- Int, Integer, Ratio
--- SourcePosition
--- Replace Natural here with some other notion of NonNegative a
--- Words, Lines, Unspaced, Unlined
--- Union/UnionWith, Map, Set, etc.
--- Max, Min, MaxPriority, MinPriority idempotent
--- BoolRing
--- Seq
+#ifdef M_CONTAINERS
+-- RLE Seq
+instanceEqa=>LeftModuleNatural(RLESeqa)where(*.)=flipMonoid.replicate
+instanceEqa=>RightModuleNatural(RLESeqa)where(.*)=Monoid.replicate
+instanceEqa=>ModuleNatural(RLESeqa)
+#endif
+
+#ifdef X_OverloadedStrings
+-- FromString
+instanceMonoidm=>LeftModuleNatural(FromStringm)where(*.)=flipMonoid.replicate
+instanceMonoidm=>RightModuleNatural(FromStringm)where(.*)=Monoid.replicate
+instanceMonoidm=>ModuleNatural(FromStringm)
+#endif
+
+-- TODO
+--
+-- Control.Monad.*
+-- ParsecT
+-- FingerTree
+-- Int, Integer, Ratio
+-- SourcePosition
+-- Replace Natural here with some other notion of NonNegative a
+-- Words, Lines, Unspaced, Unlined
+-- Union/UnionWith, Map, Set, etc.
+-- Max, Min, MaxPriority, MinPriority idempotent
+-- BoolRing
+-- Seq
hunk ./doc/html/monoids/src/Data-Ring-Semi-Near-Trie.html 11
-(moduleData.Ring.Semi.Near
+(moduleData.Ring
hunk ./doc/html/monoids/src/Data-Ring-Semi-Near-Trie.html 18
-
-importData.Map(Map)
-importqualifiedData.MapasMap
---import Data.Monoid.Multiplicative
---import Data.Monoid.Reducer
-importData.Monoid.Unionhiding(empty)
---import Data.Ring.Module
-importData.Ring.Semi.Near
-importPreludehiding(null)
-
-singleton::(Ordc,c`Reducer`m)=>c->Triecm
-singleton=unit
-
-empty::(Ordc,Monoidm)=>Triecm
-empty=zero
-
-null::Ordc=>Triecm->Bool
-null=Map.null.getUnionWith.children
-
-dataTriecm=Trie{total::m,label::m,children::UnionWith(Mapc)(Triecm)}
-deriving(Eq,Show)
-
-instanceFunctor(Triec)where
-fmapf(Trieter)=Trie(ft)(fe)(fmap(fmapf)r)
+importData.Map(Map)
+importqualifiedData.MapasMap
+importData.Monoid.Unionhiding(empty)
+importData.Ring
+importPreludehiding(null)
+
+singleton::(Ordc,c`Reducer`m)=>c->Triecm
+singleton=unit
+
+empty::(Ordc,Monoidm)=>Triecm
+empty=zero
+
+null::Ordc=>Triecm->Bool
+null=Map.null.getUnionWith.children
+
+dataTriecm=Trie{total::m,label::m,children::UnionWith(Mapc)(Triecm)}
+deriving(Eq,Show)
+
+instanceFunctor(Triec)where
+fmapf(Trieter)=Trie(ft)(fe)(fmap(fmapf)r)
+
+instance(Ordc,Monoidm)=>Monoid(Triecm)where
+mempty=Triememptymemptymempty
+Triexyz`mappend`Triex'y'z'=Trie(x`mappend`x')(y`mappend`y')(z`mappend`z')
hunk ./doc/html/monoids/src/Data-Ring-Semi-Near-Trie.html 43
-instance(Ordc,Monoidm)=>Monoid(Triecm)where
-mempty=Triememptymemptymempty
-Triexyz`mappend`Triex'y'z'=Trie(x`mappend`x')(y`mappend`y')(z`mappend`z')
-
-instance(Ordc,c`Reducer`m)=>Reducerc(Triecm)where
-unitc=Trierzero.UnionWith$flipMap.singleton(Trierrzero)cwherer=unitc
-
-{-
-instance (Ord c, Eq r, RightSemiNearRing r) => Multiplicative (Trie c r) where
- one = Trie one one zero
- Trie t e r `times` rhs@(Trie t' e' r') =
- Trie (t `times` t') (e `times` e') (r .* rhs `plus` lhs *. r') where
- lhs = Trie e e zero `asTypeOf` rhs
-
-instance (Ord c, Eq r, RightSemiNearRing r) => RightSemiNearRing (Trie c r)
-
-toList :: (Ord c, c `Reducer` [c]) => Trie c m -> [[c]]
-toList = fmap merge . Map.assocs . getUnionWith . children where
- merge (k,t) = k `times` toList t
--}
+instance(Ordc,c`Reducer`m)=>Reducerc(Triecm)where
+unitc=Trierzero.UnionWith$flipMap.singleton(Trierrzero)cwherer=unitc
+
+{-
+instance (Ord c, Eq r, RightSemiNearRing r) => Multiplicative (Trie c r) where
+ one = Trie one one zero
+ Trie t e r `times` rhs@(Trie t' e' r') =
+ Trie (t `times` t') (e `times` e') (r .* rhs `plus` lhs *. r') where
+ lhs = Trie e e zero `asTypeOf` rhs
+
+instance (Ord c, Eq r, RightSemiNearRing r) => RightSemiNearRing (Trie c r)
+
+toList :: (Ord c, c `Reducer` [c]) => Trie c m -> [[c]]
+toList = fmap merge . Map.assocs . getUnionWith . children where
+ merge (k,t) = k `times` toList t
+-}
hunk ./doc/html/monoids/src/Data-Ring-Semi-Ord.html 23
-(moduleData.Ring.Semi
+(moduleData.Ring
hunk ./doc/html/monoids/src/Data-Ring-Semi-Ord.html 28
-importTest.QuickCheck
--- import Control.Applicative
-importControl.Functor.Pointed
-importData.Ring.Semi
-importData.Monoid.Ord
-importData.Monoid.Reducer
-
--- | A 'SemiRing' using a type's built-in Bounded instance.
-newtypeOrdera=Order{getOrder::a}deriving(Eq,Ord,Read,Show,Bounded,Arbitrary,CoArbitrary)
+-- import Control.Applicative
+importControl.Functor.Pointed
+importData.Ring
+importData.Monoid.Ord
+importData.Monoid.Reducer
+
+#ifdef M_QUICKCHECK
+importTest.QuickCheck
+#endif
hunk ./doc/html/monoids/src/Data-Ring-Semi-Ord.html 38
-instance(Boundeda,Orda)=>Monoid(Ordera)where
-mappend=max
-mempty=minBound
-
-instance(Boundeda,Orda)=>Multiplicative(Ordera)where
-times=min
-one=maxBound
-
-instance(Boundeda,Orda)=>Ringoid(Ordera)
-instance(Boundeda,Orda)=>RightSemiNearRing(Ordera)
-instance(Boundeda,Orda)=>LeftSemiNearRing(Ordera)
-instance(Boundeda,Orda)=>SemiRing(Ordera)
-instance(Boundeda,Orda)=>Reducera(Ordera)where
-unit=Order
-
-instanceFunctorOrderwhere
-fmapf(Ordera)=Order(fa)
-
-instancePointedOrderwhere
-point=Order
-
-instanceCopointedOrderwhere
-extract=getOrder
-
--- | A 'SemiRing' which adds 'minBound' and 'maxBound' to a pre-existing type.
-dataPrioritya=MinBound|Prioritya|MaxBoundderiving(Eq,Read,Show)
-
-instanceBounded(Prioritya)where
-minBound=MinBound
-maxBound=MaxBound
+-- | A 'SemiRing' using a type's built-in Bounded instance.
+newtypeOrdera=Order{getOrder::a}deriving
+(Eq
+,Ord
+,Read
+,Show
+,Bounded
+#ifdef M_QUICKCHECK
+,Arbitrary
+,CoArbitrary
+#endif
+)
+
+instance(Boundeda,Orda)=>Monoid(Ordera)where
+mappend=max
+mempty=minBound
+
+instance(Boundeda,Orda)=>Multiplicative(Ordera)where
+times=min
+one=maxBound
+
+instance(Boundeda,Orda)=>Ringoid(Ordera)
+instance(Boundeda,Orda)=>RightSemiNearRing(Ordera)
+instance(Boundeda,Orda)=>LeftSemiNearRing(Ordera)
+instance(Boundeda,Orda)=>SemiRing(Ordera)
+instance(Boundeda,Orda)=>Reducera(Ordera)where
+unit=Order
+
+instanceFunctorOrderwhere
+fmapf(Ordera)=Order(fa)
hunk ./doc/html/monoids/src/Data-Ring-Semi-Ord.html 69
-instanceOrda=>Ord(Prioritya)where
-MinBound<=_=True
-Priority_<=MinBound=False
-Prioritya<=Priorityb=a<=b
-Priority_<=MaxBound=True
-MaxBound<=MaxBound=True
-MaxBound<=_=False
-
-MinBound`min`_=MinBound
-_`min`MinBound=MinBound
-Prioritya`min`Priorityb=Priority(a`min`b)
-u`min`MaxBound=u
-MaxBound`min`v=v
-
-MinBound`max`v=v
-u`max`MinBound=u
-Prioritya`max`Priorityb=Priority(a`max`b)
-_`max`MaxBound=MaxBound
-MaxBound`max`_=MaxBound
-
-instanceArbitrarya=>Arbitrary(Prioritya)where
-arbitrary=frequency[(1,returnMinBound)
-,(10,fmapPriorityarbitrary)
-,(1,returnMaxBound)]
-shrink(Priorityx)=MinBound:MaxBound:fmapPriority(shrinkx)
-shrinkMinBound=[]
-shrinkMaxBound=[]
-
-instanceCoArbitrarya=>CoArbitrary(Prioritya)where
-coarbitraryMinBound=variant(0::Int)
-coarbitrary(Prioritya)=variant(1::Int).coarbitrarya
-coarbitraryMaxBound=variant(2::Int)
+instancePointedOrderwhere
+point=Order
+
+instanceCopointedOrderwhere
+extract=getOrder
+
+-- | A 'SemiRing' which adds 'minBound' and 'maxBound' to a pre-existing type.
+dataPrioritya=MinBound|Prioritya|MaxBoundderiving(Eq,Read,Show)
+
+instanceBounded(Prioritya)where
+minBound=MinBound
+maxBound=MaxBound
+
+instanceOrda=>Ord(Prioritya)where
+MinBound<=_=True
+Priority_<=MinBound=False
+Prioritya<=Priorityb=a<=b
+Priority_<=MaxBound=True
+MaxBound<=MaxBound=True
+MaxBound<=_=False
+
+MinBound`min`_=MinBound
+_`min`MinBound=MinBound
+Prioritya`min`Priorityb=Priority(a`min`b)
+u`min`MaxBound=u
+MaxBound`min`v=v
+
+MinBound`max`v=v
+u`max`MinBound=u
+Prioritya`max`Priorityb=Priority(a`max`b)
+_`max`MaxBound=MaxBound
+MaxBound`max`_=MaxBound
hunk ./doc/html/monoids/src/Data-Ring-Semi-Ord.html 102
-instanceOrda=>Monoid(Prioritya)where
-mappend=max
-mempty=minBound
-
-instanceOrda=>Multiplicative(Prioritya)where
-times=min
-one=maxBound
-
-instanceOrda=>Ringoid(Prioritya)
-instanceOrda=>LeftSemiNearRing(Prioritya)
-instanceOrda=>RightSemiNearRing(Prioritya)
-instanceOrda=>SemiRing(Prioritya)
-
-instanceOrda=>Reducera(Prioritya)where
-unit=Priority
-
-instanceOrda=>Reducer(MinPrioritya)(Prioritya)where
-unit(MinPriorityNothing)=MaxBound
-unit(MinPriority(Justx))=Priorityx
-
-instanceOrda=>Reducer(MaxPrioritya)(Prioritya)where
-unit(MaxPriorityNothing)=MinBound
-unit(MaxPriority(Justx))=Priorityx
-
-instanceFunctorPrioritywhere
-fmap_MaxBound=MaxBound
-fmapf(Prioritya)=Priority(fa)
-fmap_MinBound=MinBound
-
-instancePointedPrioritywhere
-point=Priority
+#ifdef M_QUICKCHECK
+instanceArbitrarya=>Arbitrary(Prioritya)where
+arbitrary=frequency[(1,returnMinBound)
+,(10,fmapPriorityarbitrary)
+,(1,returnMaxBound)]
+shrink(Priorityx)=MinBound:MaxBound:fmapPriority(shrinkx)
+shrinkMinBound=[]
+shrinkMaxBound=[]
+
+instanceCoArbitrarya=>CoArbitrary(Prioritya)where
+coarbitraryMinBound=variant(0::Int)
+coarbitrary(Prioritya)=variant(1::Int).coarbitrarya
+coarbitraryMaxBound=variant(2::Int)
+#endif
+
+instanceOrda=>Monoid(Prioritya)where
+mappend=max
+mempty=minBound
+
+instanceOrda=>Multiplicative(Prioritya)where
+times=min
+one=maxBound
+
+instanceOrda=>Ringoid(Prioritya)
+instanceOrda=>LeftSemiNearRing(Prioritya)
+instanceOrda=>RightSemiNearRing(Prioritya)
+instanceOrda=>SemiRing(Prioritya)
+
+instanceOrda=>Reducera(Prioritya)where
+unit=Priority
+
+instanceOrda=>Reducer(MinPrioritya)(Prioritya)where
+unit(MinPriorityNothing)=MaxBound
+unit(MinPriority(Justx))=Priorityx
+
+instanceOrda=>Reducer(MaxPrioritya)(Prioritya)where
+unit(MaxPriorityNothing)=MinBound
+unit(MaxPriority(Justx))=Priorityx
+
+instanceFunctorPrioritywhere
+fmap_MaxBound=MaxBound
+fmapf(Prioritya)=Priority(fa)
+fmap_MinBound=MinBound
+
+instancePointedPrioritywhere
+point=Priority
hunk ./doc/html/monoids/src/Data-Ring-Semi-Tropical.html 23
-,moduleData.Ring.Semi
+,moduleData.Ring
hunk ./doc/html/monoids/src/Data-Ring-Semi-Tropical.html 29
-importTest.QuickCheck
-importControl.Functor.Pointed
-importData.Monoid.Reducer(Reducer,unit,Monoid,mappend,mempty)
-importData.Ring.Semi
-importData.Monoid.Ordhiding(infinity)
-
-infinity::Tropicala
-infinity=TropicalNothing
-
--- | The 'SemiRing' @('min','+')@ over @'a' extended with 'infinity'@.
--- When @a@ has a Num instance with an addition that respects order, then this is
--- transformed into a tropical semiring. It is assumed that 0 is the least element
--- of a.
---
--- <http://hal.archives-ouvertes.fr/docs/00/11/37/79/PDF/Tropical.pdf>
-
-newtypeTropicala=Tropical{getTropical::Maybea}
-deriving(Eq,Show,Read,Arbitrary,CoArbitrary)
-
-instanceOrda=>Ord(Tropicala)where
-TropicalNothing`compare`TropicalNothing=EQ
-TropicalNothing`compare`_=GT
-_`compare`TropicalNothing=LT
-Tropical(Justa)`compare`Tropical(Justb)=a`compare`b
-
-instanceOrda=>Monoid(Tropicala)where
-mempty=infinity
-mappend=min
-
-instanceOrda=>Reducera(Tropicala)where
-unit=Tropical.Just
+importControl.Functor.Pointed
+importData.Monoid.Reducer
+importData.Monoid.CombinatorsasMonoid
+importData.Ring.Semi.Natural
+importData.Ring
+importData.Ring.Module
+importData.Monoid.Ordhiding(infinity)
+
+#ifdef M_QUICKCHECK
+importTest.QuickCheck
+#endif
+
+infinity::Tropicala
+infinity=TropicalNothing
+
+-- | The 'SemiRing' @('min','+')@ over @'a' extended with 'infinity'@.
+-- When @a@ has a Num instance with an addition that respects order, then this is
+-- transformed into a tropical semiring. It is assumed that 0 is the least element
+-- of a.
+--
+-- <http://hal.archives-ouvertes.fr/docs/00/11/37/79/PDF/Tropical.pdf>
+
+newtypeTropicala=Tropical{getTropical::Maybea}deriving
+(Eq
+,Show
+,Read
+#ifdef M_QUICKCHECK
+,Arbitrary
+,CoArbitrary
+#endif
+)
hunk ./doc/html/monoids/src/Data-Ring-Semi-Tropical.html 61
-instanceOrda=>Reducer(Maybea)(Tropicala)where
-unit=Tropical
-
-instanceOrda=>Reducer(MinPrioritya)(Tropicala)where
-unit=Tropical.getMinPriority
+instanceOrda=>Ord(Tropicala)where
+TropicalNothing`compare`TropicalNothing=EQ
+TropicalNothing`compare`_=GT
+_`compare`TropicalNothing=LT
+Tropical(Justa)`compare`Tropical(Justb)=a`compare`b
hunk ./doc/html/monoids/src/Data-Ring-Semi-Tropical.html 67
-instanceFunctorTropicalwhere
-fmapf(Tropicala)=Tropical(fmapfa)
-
-instancePointedTropicalwhere
-point=Tropical.Just
-
-instanceNuma=>Multiplicative(Tropicala)where
-one=point$fromInteger0
-TropicalNothing`times`_=infinity
-Tropical(Justa)`times`Tropical(Justb)=point(a+b)
-_`times`TropicalNothing=infinity
-
-instance(Orda,Numa)=>Ringoid(Tropicala)
-instance(Orda,Numa)=>LeftSemiNearRing(Tropicala)
-instance(Orda,Numa)=>RightSemiNearRing(Tropicala)
-instance(Orda,Numa)=>SemiRing(Tropicala)
+instanceOrda=>Monoid(Tropicala)where
+mempty=infinity
+mappend=min
+
+instanceOrda=>Reducera(Tropicala)where
+unit=Tropical.Just
+
+instanceOrda=>Reducer(Maybea)(Tropicala)where
+unit=Tropical
+
+instanceOrda=>Reducer(MinPrioritya)(Tropicala)where
+unit=Tropical.getMinPriority
+
+instanceFunctorTropicalwhere
+fmapf(Tropicala)=Tropical(fmapfa)
+
+instancePointedTropicalwhere
+point=Tropical.Just
+
+instanceNuma=>Multiplicative(Tropicala)where
+one=point$fromInteger0
+TropicalNothing`times`_=infinity
+Tropical(Justa)`times`Tropical(Justb)=point(a+b)
+_`times`TropicalNothing=infinity
+
+instance(Orda,Numa)=>Ringoid(Tropicala)
+instance(Orda,Numa)=>LeftSemiNearRing(Tropicala)
+instance(Orda,Numa)=>RightSemiNearRing(Tropicala)
+instance(Orda,Numa)=>SemiRing(Tropicala)
+
+instance(Orda,Numa)=>Module(Tropicala)(Tropicala)
+instance(Orda,Numa)=>LeftModule(Tropicala)(Tropicala)where(*.)=times
+instance(Orda,Numa)=>RightModule(Tropicala)(Tropicala)where(.*)=times
+instance(Orda,Numa)=>Bimodule(Tropicala)(Tropicala)
+
+instance(Orda,Numa)=>ModuleNatural(Tropicala)
+instance(Orda,Numa)=>LeftModuleNatural(Tropicala)where(*.)=flipMonoid.replicate
+instance(Orda,Numa)=>RightModuleNatural(Tropicala)where(.*)=Monoid.replicate
+instance(Orda,Numa)=>BimoduleNatural(Tropicala)
hunk ./doc/html/monoids/src/Data-Ring-Sugar.html 27
-,moduleData.Ring.Semi.Near
-)where
-
-importData.Monoid.Multiplicative.Sugar
-importData.Ring.Semi.Near
+,moduleData.Ring
+,moduleData.Ring.Semi.Natural
+,(^^)
+)where
+
+importPreludehiding((^^))
+importData.Monoid.Multiplicative.Sugar
+importData.Group.CombinatorsasGroup
+importData.Ring
+importData.Ring.Semi.Natural
+
+(^^)::MultiplicativeGroupr=>r->Integer->r
+r^^n=getLog(Group.replicate(Logr)n)
+
hunk ./doc/html/monoids/src/Data-Ring.html 9
-
{-# OPTIONS_GHC -fno-warn-orphans #-}
+{-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, UndecidableInstances #-}
+-----------------------------------------------------------------------------
+-- |
+-- Module : Data.Ring
+-- Copyright : (c) Edward Kmett 2009
+-- License : BSD-style
+-- Maintainer : ekmett@gmail.com
+-- Stability : experimental
+-- Portability : portable (instances use MPTCs)
+--
+--
+-- Defines left- and right- seminearrings. Every 'MonadPlus' wrapped around
+-- a 'Monoid' qualifies due to the distributivity of (>>=) over 'mplus'.
+--
+-- See <http://conway.rutgers.edu/~ccshan/wiki/blog/posts/WordNumbers1/>
+--
+-----------------------------------------------------------------------------
+
+moduleData.Ring
+(moduleData.Group
+,Ringoid
+,LeftSemiNearRing
+,RightSemiNearRing
+,SemiRing
+,Ring
+,DivisionRing
+,Field
+)where
+
+importData.Group
+importData.Monoid.Self
+
+#ifdef X_OverloadedStrings
+importData.Monoid.FromString
+#endif
+
+#ifdef M_MTL
+importControl.Monad.Reader
+importqualifiedControl.Monad.RWS.LazyasLRWS
+importqualifiedControl.Monad.RWS.StrictasSRWS
+importqualifiedControl.Monad.State.LazyasLState
+importqualifiedControl.Monad.State.StrictasSState
+importqualifiedControl.Monad.Writer.LazyasLWriter
+importqualifiedControl.Monad.Writer.StrictasSWriter
+#endif
+
+#ifdef M_FINGERTREE
+importData.FingerTree
+#endif
+
+#ifdef M_CONTAINERS
+importqualifiedData.SequenceasSeq
+importData.Sequence(Seq)
+#endif
+
+#ifdef M_PARSEC
+importText.Parsec.Prim
+#endif
+
+#ifdef X_OverloadedStrings
+importData.Monoid.FromString
+#endif
+
+-- | @0@ annihilates `times`
+class(Multiplicativem,Monoidm)=>Ringoidm
+instanceRingoidInteger
+instanceRingoidInt
+instanceRingoidm=>Ringoid(Selfm)
+instanceRingoidm=>Ringoid(Dualm)
+instanceMonoidm=>Ringoid[m]
+instanceMonoidm=>Ringoid(Maybem)
+
+-- | @a * (b + c) = (a * b) + (a * c)@
+classRingoidm=>LeftSemiNearRingm
+instanceLeftSemiNearRingm=>LeftSemiNearRing(Selfm)
+instanceRightSemiNearRingm=>LeftSemiNearRing(Dualm)
+
+-- | @(a + b) * c = (a * c) + (b * c)@
+classRingoidm=>RightSemiNearRingm
+instanceRightSemiNearRingm=>RightSemiNearRing(Selfm)
+instanceLeftSemiNearRingm=>RightSemiNearRing(Dualm)
+instanceMonoidm=>RightSemiNearRing[m]
+instanceMonoidm=>RightSemiNearRing(Maybem)
+
+-- | A 'SemiRing' is an instance of both 'Multiplicative' and 'Monoid' where
+-- 'times' distributes over 'plus'.
+class(RightSemiNearRinga,LeftSemiNearRinga)=>SemiRinga
+instanceSemiRingr=>SemiRing(Selfr)
+instanceSemiRingr=>SemiRing(Dualr)
+
+class(Groupa,SemiRinga)=>Ringa
+instanceRingr=>Ring(Selfr)
+instanceRingr=>Ring(Dualr)
+
+class(Ringa,MultiplicativeGroupa)=>DivisionRinga
+instanceDivisionRingr=>DivisionRing(Selfr)
+instanceDivisionRingr=>DivisionRing(Dualr)
+
+class(Ringa,MultiplicativeGroupa)=>Fielda
+instanceFieldf=>Field(Dualf)
+instanceFieldf=>Field(Selff)
+
+#ifdef M_REFLECTION
+instanceRingoidm=>Ringoid(ReducedByms)
+instanceLeftSemiNearRingm=>LeftSemiNearRing(ReducedByms)
+instanceRightSemiNearRingm=>RightSemiNearRing(ReducedByms)
+instanceSemiRingr=>SemiRing(ReducedByrs)
+instanceRingr=>Ring(ReducedByrs)
+instanceDivisionRingr=>DivisionRing(ReducedByrs)
+instanceFieldf=>Field(ReducedByfs)
+#endif
+
+#ifdef M_PARSEC
+instance(Streamsmt,Monoida)=>Ringoid(ParsecTsuma)
+instance(Streamsmt,Monoida)=>RightSemiNearRing(ParsecTsuma)
+#endif
+
+#ifdef M_MTL
+instance(MonadPlusm,Monoidn)=>Ringoid(SState.StateTsmn)
+instance(MonadPlusm,Monoidn)=>Ringoid(LState.StateTsmn)
+instance(MonadPlusm,Monoidn)=>Ringoid(ReaderTemn)
+instance(MonadPlusm,Monoidw,Monoidn)=>Ringoid(SRWS.RWSTrwsmn)
+instance(MonadPlusm,Monoidw,Monoidn)=>Ringoid(LRWS.RWSTrwsmn)
+instance(MonadPlusm,Monoidw,Monoidn)=>Ringoid(SWriter.WriterTwmn)
+instance(MonadPlusm,Monoidw,Monoidn)=>Ringoid(LWriter.WriterTwmn)
+instance(MonadPlusm,Monoidn)=>RightSemiNearRing(SState.StateTsmn)
+instance(MonadPlusm,Monoidn)=>RightSemiNearRing(LState.StateTsmn)
+instance(MonadPlusm,Monoidn)=>RightSemiNearRing(ReaderTemn)
+instance(MonadPlusm,Monoidw,Monoidn)=>RightSemiNearRing(SRWS.RWSTrwsmn)
+instance(MonadPlusm,Monoidw,Monoidn)=>RightSemiNearRing(LRWS.RWSTrwsmn)
+instance(MonadPlusm,Monoidw,Monoidn)=>RightSemiNearRing(SWriter.WriterTwmn)
+instance(MonadPlusm,Monoidw,Monoidn)=>RightSemiNearRing(LWriter.WriterTwmn)
+#endif
+
+#ifdef M_FINGERTREE
+instance(Measuredvm,Monoidm)=>Ringoid(FingerTreevm)
+instance(Measuredvm,Monoidm)=>RightSemiNearRing(FingerTreevm)
+#endif
+
+#ifdef M_CONTAINERS
+instanceMonoidm=>Ringoid(Seqm)
+instanceMonoidm=>RightSemiNearRing(Seqm)
+#endif
+
+#ifdef X_OverloadedStrings
+instanceRingoidm=>Ringoid(FromStringm)
+instanceRightSemiNearRingm=>RightSemiNearRing(FromStringm)
+instanceLeftSemiNearRingm=>LeftSemiNearRing(FromStringm)
+instanceSemiRingr=>SemiRing(FromStringr)
+instanceRingr=>Ring(FromStringr)
+instanceDivisionRingr=>DivisionRing(FromStringr)
+instanceFieldf=>Field(FromStringf)
+#endif
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 121
-importData.Generator.Combinators(Generator,Elem,foldMap,mapReduce)
-#ifndef __GLASGOW_HASKELL__
-importData.Typeable(Typeable,typeOf,typeOfDefault)
-#endif
-importData.Typeable(Typeable1(..),TyCon,mkTyCon,mkTyConApp)
-importData.Word
-importData.Int
-
-{-
--- just for testing
-import Test.QuickCheck
-import Data.List (nub,sort)
-import qualified Data.List as List
--}
-
-#if __GLASGOW_HASKELL__
-importText.Read
-importData.Data(Data(..),mkNorepType,gcast1)
-#endif
-
-{--------------------------------------------------------------------
- Operators
---------------------------------------------------------------------}
-infixl9\\--
-
--- | /O(n+m)/. See 'difference'.
-(\\)::(USa,Orda)=>USeta->USeta->USeta
-m1\\m2=differencem1m2
-
-{--------------------------------------------------------------------
- Sets are size balanced trees
---------------------------------------------------------------------}
-typeSize=Int
-
--- | A set of values @a@.
-dataSeta=Tip
-|Bin{-# UNPACK #-}!Sizea!(USeta)!(USeta)
-
--- smart unboxed types
-classUSawhere
-dataUSeta
-view::USeta->Seta
-{-# INLINE view #-}
-tip::USeta
-{-# INLINE tip #-}
-bin::Size->a->USeta->USeta->USeta
-{-# INLINE bin #-}
-
+#ifndef __GLASGOW_HASKELL__
+importData.Typeable(Typeable,typeOf,typeOfDefault)
+#endif
+importData.Typeable(Typeable1(..),TyCon,mkTyCon,mkTyConApp)
+importData.Word
+importData.Int
+
+{-
+-- just for testing
+import Test.QuickCheck
+import Data.List (nub,sort)
+import qualified Data.List as List
+-}
+
+#if __GLASGOW_HASKELL__
+importText.Read
+importData.Data(Data(..),mkNorepType,gcast1)
+#endif
+
+{--------------------------------------------------------------------
+ Operators
+--------------------------------------------------------------------}
+infixl9\\--
+
+-- | /O(n+m)/. See 'difference'.
+(\\)::(USa,Orda)=>USeta->USeta->USeta
+m1\\m2=differencem1m2
+
+{--------------------------------------------------------------------
+ Sets are size balanced trees
+--------------------------------------------------------------------}
+typeSize=Int
+
+-- | A set of values @a@.
+dataSeta=Tip
+|Bin{-# UNPACK #-}!Sizea!(USeta)!(USeta)
+
+-- smart unboxed types
+classUSawhere
+dataUSeta
+view::USeta->Seta
+{-# INLINE view #-}
+tip::USeta
+{-# INLINE tip #-}
+bin::Size->a->USeta->USeta->USeta
+{-# INLINE bin #-}
+isTip::USeta->Bool
+{-# INLINE isTip #-}
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 178
- mapReduce _ (view -> Tip) = mempty
+ mapReduce _ (isTip -> True) = mempty
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 207
-null(view->Tip)=True
-null(view->Bin{})=False
+null(view->Bin{})=False
+null_=True
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 212
-size(view->Tip)=0
-size(view->Binsz___)=sz
+size(view->Binsz___)=sz
+size_=0
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 217
-memberx(view->Tip)=False
-memberx(view->Bin_ylr)=
-casecomparexyof
-LT->memberxl
-GT->memberxr
-EQ->True
-
--- | /O(log n)/. Is the element not in the set?
-notMember::(USa,Orda)=>a->USeta->Bool
-notMemberxt=not$memberxt
-
-{--------------------------------------------------------------------
- Construction
---------------------------------------------------------------------}
--- | /O(1)/. The empty set.
-empty::USa=>USeta
-empty=tip
-
--- | /O(1)/. Create a singleton set.
-singleton::USa=>a->USeta
-singletonx=bin1xtiptip
-
-{--------------------------------------------------------------------
- Insertion, Deletion
---------------------------------------------------------------------}
--- | /O(log n)/. Insert an element in a set.
--- If the set already contains an element equal to the given value,
--- it is replaced with the new value.
-insert::(USa,Orda)=>a->USeta->USeta
-insertx(view->Tip)=singletonx
+memberxy=
+caseviewyof
+Bin_ylr->casecomparexyof
+LT->memberxl
+GT->memberxr
+EQ->True
+_->False
+
+-- | /O(log n)/. Is the element not in the set?
+notMember::(USa,Orda)=>a->USeta->Bool
+notMemberxt=not$memberxt
+
+{--------------------------------------------------------------------
+ Construction
+--------------------------------------------------------------------}
+-- | /O(1)/. The empty set.
+empty::USa=>USeta
+empty=tip
+
+-- | /O(1)/. Create a singleton set.
+singleton::USa=>a->USeta
+singletonx=bin1xtiptip
+
+{--------------------------------------------------------------------
+ Insertion, Deletion
+--------------------------------------------------------------------}
+-- | /O(log n)/. Insert an element in a set.
+-- If the set already contains an element equal to the given value,
+-- it is replaced with the new value.
+insert::(USa,Orda)=>a->USeta->USeta
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 251
-
--- | /O(log n)/. Delete an element from a set.
-delete::(USa,Orda)=>a->USeta->USeta
-deletex(view->Tip)=tip
+insertx_=singletonx
+
+-- | /O(log n)/. Delete an element from a set.
+delete::(USa,Orda)=>a->USeta->USeta
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 259
-
-{--------------------------------------------------------------------
- Subset
---------------------------------------------------------------------}
--- | /O(n+m)/. Is this a proper subset? (ie. a subset but not equal).
-isProperSubsetOf::(USa,Orda)=>USeta->USeta->Bool
-isProperSubsetOfs1s2
-=(sizes1<sizes2)&&(isSubsetOfs1s2)
+deletex_=tip
+
+{--------------------------------------------------------------------
+ Subset
+--------------------------------------------------------------------}
+-- | /O(n+m)/. Is this a proper subset? (ie. a subset but not equal).
+isProperSubsetOf::(USa,Orda)=>USeta->USeta->Bool
+isProperSubsetOfs1s2=(sizes1<sizes2)&&(isSubsetOfs1s2)
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 274
-isSubsetOfX(view->Tip)_=True
-isSubsetOfX_(view->Tip)=False
-isSubsetOfX(view->Bin_xlr)t=found&&isSubsetOfXllt&&isSubsetOfXrgt
-where
-(lt,found,gt)=splitMemberxt
+isSubsetOfX_(isTip->True)=False
+isSubsetOfX(view->Bin_xlr)t=found&&isSubsetOfXllt&&isSubsetOfXrgt
+where
+(lt,found,gt)=splitMemberxt
+isSubsetOfX__=True
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 286
-findMin(view->Bin_x(view->Tip)_)=x
+findMin(view->Bin_x(isTip->True)_)=x
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 288
-findMin(view->Tip)=error"Set.findMin: empty set has no minimal element"
+findMin_=error"Set.findMin: empty set has no minimal element"
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 292
-findMax(view->Bin_x_(view->Tip))=x
+findMax(view->Bin_x_(isTip->True))=x
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 294
-findMax(view->Tip)=error"Set.findMax: empty set has no maximal element"
+findMax_=error"Set.findMax: empty set has no maximal element"
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 298
-deleteMin(view->Bin__(view->Tip)r)=r
+deleteMin(view->Bin__(isTip->True)r)=r
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 300
-deleteMin(view->Tip)=tip
+deleteMin_=tip
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 304
-deleteMax(view->Bin__l(view->Tip))=l
+deleteMax(view->Bin__l(isTip->True))=l
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 306
-deleteMax(view->Tip)=tip
+deleteMax_=tip
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 322
-union(view->Tip)t2=t2
-uniont1(view->Tip)=t1
+union(isTip->True)t2=t2
+uniont1(isTip->True)=t1
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 327
-hedgeUnion__t1(view->Tip)=t1
-hedgeUnioncmplocmphi(view->Tip)(view->Bin_xlr)=joinx(filterGtcmplol)(filterLtcmphir)
+hedgeUnion__t1(isTip->True)=t1
+hedgeUnioncmplocmphi(isTip->True)(view->Bin_xlr)=joinx(filterGtcmplol)(filterLtcmphir)
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 339
-difference(view->Tip)_=tip
-differencet1(view->Tip)=t1
+difference(isTip->True)_=tip
+differencet1(isTip->True)=t1
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 344
-hedgeDiff__(view->Tip)_=tip
-hedgeDiffcmplocmphi(view->Bin_xlr)(view->Tip)=joinx(filterGtcmplol)(filterLtcmphir)
+hedgeDiff__(isTip->True)_=tip
+hedgeDiffcmplocmphi(view->Bin_xlr)(isTip->True)=joinx(filterGtcmplol)(filterLtcmphir)
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 365
-intersection(view->Tip)_=tip
-intersection_(view->Tip)=tip
+intersection(isTip->True)_=tip
+intersection_(isTip->True)=tip
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 386
-filter_(view->Tip)=tip
-filterp(view->Bin_xlr)
-|px=joinx(filterpl)(filterpr)
-|otherwise=merge(filterpl)(filterpr)
+filterp(view->Bin_xlr)
+|px=joinx(filterpl)(filterpr)
+|otherwise=merge(filterpl)(filterpr)
+filter__=tip
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 395
-partition_(view->Tip)=(tip,tip)
-partitionp(view->Bin_xlr)
-|px=(joinxl1r1,mergel2r2)
-|otherwise=(mergel1r1,joinxl2r2)
-where
-(l1,l2)=partitionpl
-(r1,r2)=partitionpr
+partitionp(view->Bin_xlr)
+|px=(joinxl1r1,mergel2r2)
+|otherwise=(mergel1r1,joinxl2r2)
+where
+(l1,l2)=partitionpl
+(r1,r2)=partitionpr
+partition__=(tip,tip)
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 427
-mapMonotonic_(view->Tip)=tip
-mapMonotonicf(view->Binszxlr)=binsz(fx)(mapMonotonicfl)(mapMonotonicfr)
+mapMonotonicf(view->Binszxlr)=binsz(fx)(mapMonotonicfl)(mapMonotonicfr)
+mapMonotonic__=tip
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 440
-foldr_z(view->Tip)=z
-foldrfz(view->Bin_xlr)=foldrf(fx(foldrfzr))l
+foldrfz(view->Bin_xlr)=foldrf(fx(foldrfzr))l
+foldr_z_=z
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 537
-{-
-XXX unused code
-
-showSet :: (Show a) => [a] -> ShowS
-showSet []
- = showString "{}"
-showSet (x:xs)
- = showChar '{' . shows x . showTail xs
- where
- showTail [] = showChar '}'
- showTail (x':xs') = showChar ',' . shows x' . showTail xs'
--}
-
-{--------------------------------------------------------------------
- Read
---------------------------------------------------------------------}
-instance(USa,Reada,Orda)=>Read(USeta)where
-#ifdef __GLASGOW_HASKELL__
-readPrec=parens$prec10$do
-Ident"fromList"<-lexP
-xs<-readPrec
-return(fromListxs)
-
-readListPrec=readListPrecDefault
-#else
-readsPrecp=readParen(p>10)$\r->do
-("fromList",s)<-lexr
-(xs,t)<-readss
-return(fromListxs,t)
-#endif
+{--------------------------------------------------------------------
+ Read
+--------------------------------------------------------------------}
+instance(USa,Reada,Orda)=>Read(USeta)where
+#ifdef __GLASGOW_HASKELL__
+readPrec=parens$prec10$do
+Ident"fromList"<-lexP
+xs<-readPrec
+return(fromListxs)
+
+readListPrec=readListPrecDefault
+#else
+readsPrecp=readParen(p>10)$\r->do
+("fromList",s)<-lexr
+(xs,t)<-readss
+return(fromListxs,t)
+#endif
+
+{--------------------------------------------------------------------
+ Typeable/Data
+--------------------------------------------------------------------}
+
+-- #include "Typeable.h"
+-- INSTANCE_TYPEABLE1(Set,setTc,"Set")
+
+{--------------------------------------------------------------------
+ Utility functions that return sub-ranges of the original
+ tree. Some functions take a comparison function as argument to
+ allow comparisons against infinite values. A function [cmplo x]
+ should be read as [compare lo x].
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 568
-{--------------------------------------------------------------------
- Typeable/Data
---------------------------------------------------------------------}
-
--- #include "Typeable.h"
--- INSTANCE_TYPEABLE1(Set,setTc,"Set")
-
-{--------------------------------------------------------------------
- Utility functions that return sub-ranges of the original
- tree. Some functions take a comparison function as argument to
- allow comparisons against infinite values. A function [cmplo x]
- should be read as [compare lo x].
-
- [trim cmplo cmphi t] A tree that is either empty or where [cmplo x == LT]
- and [cmphi x == GT] for the value [x] of the root.
- [filterGt cmp t] A tree where for all values [k]. [cmp k == LT]
- [filterLt cmp t] A tree where for all values [k]. [cmp k == GT]
-
- [split k t] Returns two trees [l] and [r] where all values
- in [l] are <[k] and all keys in [r] are >[k].
- [splitMember k t] Just like [split] but also returns whether [k]
- was found in the tree.
---------------------------------------------------------------------}
-
-{--------------------------------------------------------------------
- [trim lo hi t] trims away all subtrees that surely contain no
- values between the range [lo] to [hi]. The returned tree is either
- empty or the key of the root is between @lo@ and @hi@.
+ [trim cmplo cmphi t] A tree that is either empty or where [cmplo x == LT]
+ and [cmphi x == GT] for the value [x] of the root.
+ [filterGt cmp t] A tree where for all values [k]. [cmp k == LT]
+ [filterLt cmp t] A tree where for all values [k]. [cmp k == GT]
+
+ [split k t] Returns two trees [l] and [r] where all values
+ in [l] are <[k] and all keys in [r] are >[k].
+ [splitMember k t] Just like [split] but also returns whether [k]
+ was found in the tree.
+--------------------------------------------------------------------}
+
+{--------------------------------------------------------------------
+ [trim lo hi t] trims away all subtrees that surely contain no
+ values between the range [lo] to [hi]. The returned tree is either
+ empty or the key of the root is between @lo@ and @hi@.
+--------------------------------------------------------------------}
+trim::USa=>(a->Ordering)->(a->Ordering)->USeta->USeta
+trimcmplocmphit@(view->Bin_xlr)
+=casecmploxof
+LT->casecmphixof
+GT->t
+_->trimcmplocmphil
+_->trimcmplocmphir
+trim___=tip
+
+{--------------------------------------------------------------------
+ [filterGt x t] filter all values >[x] from tree [t]
+ [filterLt x t] filter all values <[x] from tree [t]
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 597
-trim::USa=>(a->Ordering)->(a->Ordering)->USeta->USeta
-trim__(view->Tip)=tip
-trimcmplocmphit@(view->Bin_xlr)
-=casecmploxof
-LT->casecmphixof
-GT->t
-_->trimcmplocmphil
-_->trimcmplocmphir
-
-{--------------------------------------------------------------------
- [filterGt x t] filter all values >[x] from tree [t]
- [filterLt x t] filter all values <[x] from tree [t]
---------------------------------------------------------------------}
-filterGt::USa=>(a->Ordering)->USeta->USeta
-filterGt_(view->Tip)=tip
-filterGtcmp(view->Bin_xlr)
-=casecmpxof
-LT->joinx(filterGtcmpl)r
-GT->filterGtcmpr
-EQ->r
-
-filterLt::USa=>(a->Ordering)->USeta->USeta
-filterLt_(view->Tip)=tip
-filterLtcmp(view->Bin_xlr)
-=casecmpxof
-LT->filterLtcmpl
-GT->joinxl(filterLtcmpr)
-EQ->l
-
-
-{--------------------------------------------------------------------
- Split
---------------------------------------------------------------------}
--- | /O(log n)/. The expression (@'split' x set@) is a pair @(set1,set2)@
--- where @set1@ comprises the elements of @set@ less than @x@ and @set2@
--- comprises the elements of @set@ greater than @x@.
-split::(USa,Orda)=>a->USeta->(USeta,USeta)
-split_(view->Tip)=(tip,tip)
-splitx(view->Bin_ylr)
-=casecomparexyof
-LT->let(lt,gt)=splitxlin(lt,joinygtr)
-GT->let(lt,gt)=splitxrin(joinyllt,gt)
-EQ->(l,r)
-
--- | /O(log n)/. Performs a 'split' but also returns whether the pivot
--- element was found in the original set.
-splitMember::(USa,Orda)=>a->USeta->(USeta,Bool,USeta)
-splitMemberxt=let(l,m,r)=splitLookupxtin
-(l,maybeFalse(constTrue)m,r)
-
--- | /O(log n)/. Performs a 'split' but also returns the pivot
--- element that was found in the original set.
-splitLookup::(USa,Orda)=>a->USeta->(USeta,Maybea,USeta)
-splitLookup_(view->Tip)=(tip,Nothing,tip)
-splitLookupx(view->Bin_ylr)
-=casecomparexyof
-LT->let(lt,found,gt)=splitLookupxlin(lt,found,joinygtr)
-GT->let(lt,found,gt)=splitLookupxrin(joinyllt,found,gt)
-EQ->(l,Justy,r)
-
-{--------------------------------------------------------------------
- Utility functions that maintain the balance properties of the tree.
- All constructors assume that all values in [l] < [x] and all values
- in [r] > [x], and that [l] and [r] are valid trees.
-
- In order of sophistication:
- [Bin sz x l r] The type constructor.
- [bin_ x l r] Maintains the correct size, assumes that both [l]
- and [r] are balanced with respect to each other.
- [balance x l r] Restores the balance and size.
- Assumes that the original tree was balanced and
- that [l] or [r] has changed by at most one element.
- [join x l r] Restores balance and size.
-
- Furthermore, we can construct a new tree from two trees. Both operations
- assume that all values in [l] < all values in [r] and that [l] and [r]
- are valid:
- [glue l r] Glues [l] and [r] together. Assumes that [l] and
- [r] are already balanced with respect to each other.
- [merge l r] Merges two trees and restores balance.
-
- Note: in contrast to Adam's paper, we use (<=) comparisons instead
- of (<) comparisons in [join], [merge] and [balance].
- Quickcheck (on [difference]) showed that this was necessary in order
- to maintain the invariants. It is quite unsatisfactory that I haven't
- been able to find out why this is actually the case! Fortunately, it
- doesn't hurt to be a bit more conservative.
---------------------------------------------------------------------}
-
-{--------------------------------------------------------------------
- Join
---------------------------------------------------------------------}
-join::USa=>a->USeta->USeta->USeta
-joinx(view->Tip)r=insertMinxr
-joinxl(view->Tip)=insertMaxxl
-joinxl@(view->BinsizeLylyry)r@(view->BinsizeRzlzrz)
-|delta*sizeL<=sizeR=balancez(joinxllz)rz
-|delta*sizeR<=sizeL=balanceyly(joinxryr)
-|otherwise=bin_xlr
-
-
--- insertMin and insertMax don't perform potentially expensive comparisons.
-insertMax,insertMin::USa=>a->USeta->USeta
-insertMaxxt
-=caseviewtof
-Tip->singletonx
-Bin_ylr
-->balanceyl(insertMaxxr)
-
-insertMinxt
-=caseviewtof
-Tip->singletonx
-Bin_ylr
-->balancey(insertMinxl)r
-
-{--------------------------------------------------------------------
- [merge l r]: merges two trees.
---------------------------------------------------------------------}
-merge::USa=>USeta->USeta->USeta
-merge(view->Tip)r=r
-mergel(view->Tip)=l
-mergel@(view->BinsizeLxlxrx)r@(view->BinsizeRylyry)
-|delta*sizeL<=sizeR=balancey(mergelly)ry
-|delta*sizeR<=sizeL=balancexlx(mergerxr)
-|otherwise=gluelr
-
-{--------------------------------------------------------------------
- [glue l r]: glues two trees together.
- Assumes that [l] and [r] are already balanced with respect to each other.
---------------------------------------------------------------------}
-glue::USa=>USeta->USeta->USeta
-glue(view->Tip)r=r
-gluel(view->Tip)=l
-gluelr
-|sizel>sizer=let(m,l')=deleteFindMaxlinbalanceml'r
-|otherwise=let(m,r')=deleteFindMinrinbalancemlr'
-
-
--- | /O(log n)/. Delete and find the minimal element.
---
--- > deleteFindMin set = (findMin set, deleteMin set)
-
-deleteFindMin::USa=>USeta->(a,USeta)
-deleteFindMint
-=caseviewtof
-Bin_x(view->Tip)r->(x,r)
-Bin_xlr->let(xm,l')=deleteFindMinlin(xm,balancexl'r)
-Tip->(error"Set.deleteFindMin: can not return the minimal element of an empty set",tip)
-
--- | /O(log n)/. Delete and find the maximal element.
---
--- > deleteFindMax set = (findMax set, deleteMax set)
-deleteFindMax::USa=>USeta->(a,USeta)
-deleteFindMaxt
-=caseviewtof
-Bin_xl(view->Tip)->(x,l)
-Bin_xlr->let(xm,r')=deleteFindMaxrin(xm,balancexlr')
-Tip->(error"Set.deleteFindMax: can not return the maximal element of an empty set",tip)
-
--- | /O(log n)/. Retrieves the minimal key of the set, and the set
--- stripped of that element, or 'Nothing' if passed an empty set.
-minView::USa=>USeta->Maybe(a,USeta)
-minView(view->Tip)=Nothing
-minViewx=Just(deleteFindMinx)
-
--- | /O(log n)/. Retrieves the maximal key of the set, and the set
--- stripped of that element, or 'Nothing' if passed an empty set.
-maxView::USa=>USeta->Maybe(a,USeta)
-maxView(view->Tip)=Nothing
-maxViewx=Just(deleteFindMaxx)
-
-{--------------------------------------------------------------------
- [balance x l r] balances two trees with value x.
- The sizes of the trees should balance after decreasing the
- size of one of them. (a rotation).
-
- [delta] is the maximal relative difference between the sizes of
- two trees, it corresponds with the [w] in Adams' paper,
- or equivalently, [1/delta] corresponds with the $\alpha$
- in Nievergelt's paper. Adams shows that [delta] should
- be larger than 3.745 in order to garantee that the
- rotations can always restore balance.
-
- [ratio] is the ratio between an outer and inner sibling of the
- heavier subtree in an unbalanced setting. It determines
- whether a double or single rotation should be performed
- to restore balance. It is correspondes with the inverse
- of $\alpha$ in Adam's article.
-
- Note that:
- - [delta] should be larger than 4.646 with a [ratio] of 2.
- - [delta] should be larger than 3.745 with a [ratio] of 1.534.
-
- - A lower [delta] leads to a more 'perfectly' balanced tree.
- - A higher [delta] performs less rebalancing.
-
- - Balancing is automatic for random data and a balancing
- scheme is only necessary to avoid pathological worst cases.
- Almost any choice will do in practice
-
- - Allthough it seems that a rather large [delta] may perform better
- than smaller one, measurements have shown that the smallest [delta]
- of 4 is actually the fastest on a wide range of operations. It
- especially improves performance on worst-case scenarios like
- a sequence of ordered insertions.
-
- Note: in contrast to Adams' paper, we use a ratio of (at least) 2
- to decide whether a single or double rotation is needed. Allthough
- he actually proves that this ratio is needed to maintain the
- invariants, his implementation uses a (invalid) ratio of 1.
- He is aware of the problem though since he has put a comment in his
- original source code that he doesn't care about generating a
- slightly inbalanced tree since it doesn't seem to matter in practice.
- However (since we use quickcheck :-) we will stick to strictly balanced
- trees.
---------------------------------------------------------------------}
-delta,ratio::Int
-delta=4
-ratio=2
-
-balance::USa=>a->USeta->USeta->USeta
-balancexlr
-|sizeL+sizeR<=1=binsizeXxlr
-|sizeR>=delta*sizeL=rotateLxlr
-|sizeL>=delta*sizeR=rotateRxlr
-|otherwise=binsizeXxlr
-where
-sizeL=sizel
-sizeR=sizer
-sizeX=sizeL+sizeR+1
-
--- rotate
-rotateL::USa=>a->USeta->USeta->USeta
-rotateLxlr@(view->Bin__lyry)
-|sizely<ratio*sizery=singleLxlr
-|otherwise=doubleLxlr
-rotateL__(view->Tip)=error"rotateL Tip"
-
-rotateR::USa=>a->USeta->USeta->USeta
-rotateRxl@(view->Bin__lyry)r
-|sizery<ratio*sizely=singleRxlr
-|otherwise=doubleRxlr
-rotateR_(view->Tip)_=error"rotateL Tip"
-
--- basic rotations
-singleL,singleR::USa=>a->USeta->USeta->USeta
-singleLx1t1(view->Bin_x2t2t3)=bin_x2(bin_x1t1t2)t3
-singleL__(view->Tip)=error"singleL"
-singleRx1(view->Bin_x2t1t2)t3=bin_x2t1(bin_x1t2t3)
-singleR_(view->Tip)_=error"singleR"
+filterGt::USa=>(a->Ordering)->USeta->USeta
+filterGtcmp(view->Bin_xlr)
+=casecmpxof
+LT->joinx(filterGtcmpl)r
+GT->filterGtcmpr
+EQ->r
+filterGt__=tip
+
+filterLt::USa=>(a->Ordering)->USeta->USeta
+filterLtcmp(view->Bin_xlr)
+=casecmpxof
+LT->filterLtcmpl
+GT->joinxl(filterLtcmpr)
+EQ->l
+filterLt__=tip
+
+
+{--------------------------------------------------------------------
+ Split
+--------------------------------------------------------------------}
+-- | /O(log n)/. The expression (@'split' x set@) is a pair @(set1,set2)@
+-- where @set1@ comprises the elements of @set@ less than @x@ and @set2@
+-- comprises the elements of @set@ greater than @x@.
+split::(USa,Orda)=>a->USeta->(USeta,USeta)
+splitx(view->Bin_ylr)
+=casecomparexyof
+LT->let(lt,gt)=splitxlin(lt,joinygtr)
+GT->let(lt,gt)=splitxrin(joinyllt,gt)
+EQ->(l,r)
+split__=(tip,tip)
+
+-- | /O(log n)/. Performs a 'split' but also returns whether the pivot
+-- element was found in the original set.
+splitMember::(USa,Orda)=>a->USeta->(USeta,Bool,USeta)
+splitMemberxt=let(l,m,r)=splitLookupxtin
+(l,maybeFalse(constTrue)m,r)
+
+-- | /O(log n)/. Performs a 'split' but also returns the pivot
+-- element that was found in the original set.
+splitLookup::(USa,Orda)=>a->USeta->(USeta,Maybea,USeta)
+splitLookupx(view->Bin_ylr)
+=casecomparexyof
+LT->let(lt,found,gt)=splitLookupxlin(lt,found,joinygtr)
+GT->let(lt,found,gt)=splitLookupxrin(joinyllt,found,gt)
+EQ->(l,Justy,r)
+splitLookup__=(tip,Nothing,tip)
+
+{--------------------------------------------------------------------
+ Utility functions that maintain the balance properties of the tree.
+ All constructors assume that all values in [l] < [x] and all values
+ in [r] > [x], and that [l] and [r] are valid trees.
+
+ In order of sophistication:
+ [Bin sz x l r] The type constructor.
+ [bin_ x l r] Maintains the correct size, assumes that both [l]
+ and [r] are balanced with respect to each other.
+ [balance x l r] Restores the balance and size.
+ Assumes that the original tree was balanced and
+ that [l] or [r] has changed by at most one element.
+ [join x l r] Restores balance and size.
+
+ Furthermore, we can construct a new tree from two trees. Both operations
+ assume that all values in [l] < all values in [r] and that [l] and [r]
+ are valid:
+ [glue l r] Glues [l] and [r] together. Assumes that [l] and
+ [r] are already balanced with respect to each other.
+ [merge l r] Merges two trees and restores balance.
+
+ Note: in contrast to Adam's paper, we use (<=) comparisons instead
+ of (<) comparisons in [join], [merge] and [balance].
+ Quickcheck (on [difference]) showed that this was necessary in order
+ to maintain the invariants. It is quite unsatisfactory that I haven't
+ been able to find out why this is actually the case! Fortunately, it
+ doesn't hurt to be a bit more conservative.
+--------------------------------------------------------------------}
+
+{--------------------------------------------------------------------
+ Join
+--------------------------------------------------------------------}
+join::USa=>a->USeta->USeta->USeta
+joinx(isTip->True)r=insertMinxr
+joinxl(isTip->True)=insertMaxxl
+joinxl@(view->BinsizeLylyry)r@(view->BinsizeRzlzrz)
+|delta*sizeL<=sizeR=balancez(joinxllz)rz
+|delta*sizeR<=sizeL=balanceyly(joinxryr)
+|otherwise=bin_xlr
+
+
+-- insertMin and insertMax don't perform potentially expensive comparisons.
+insertMax,insertMin::USa=>a->USeta->USeta
+insertMaxxt
+=caseviewtof
+Bin_ylr->balanceyl(insertMaxxr)
+_->singletonx
+
+insertMinxt
+=caseviewtof
+Bin_ylr->balancey(insertMinxl)r
+_->singletonx
+
+{--------------------------------------------------------------------
+ [merge l r]: merges two trees.
+--------------------------------------------------------------------}
+merge::USa=>USeta->USeta->USeta
+merge(isTip->True)r=r
+mergel(isTip->True)=l
+mergel@(view->BinsizeLxlxrx)r@(view->BinsizeRylyry)
+|delta*sizeL<=sizeR=balancey(mergelly)ry
+|delta*sizeR<=sizeL=balancexlx(mergerxr)
+|otherwise=gluelr
+
+{--------------------------------------------------------------------
+ [glue l r]: glues two trees together.
+ Assumes that [l] and [r] are already balanced with respect to each other.
+--------------------------------------------------------------------}
+glue::USa=>USeta->USeta->USeta
+glue(isTip->True)r=r
+gluel(isTip->True)=l
+gluelr
+|sizel>sizer=let(m,l')=deleteFindMaxlinbalanceml'r
+|otherwise=let(m,r')=deleteFindMinrinbalancemlr'
+
+
+-- | /O(log n)/. Delete and find the minimal element.
+--
+-- > deleteFindMin set = (findMin set, deleteMin set)
+
+deleteFindMin::USa=>USeta->(a,USeta)
+deleteFindMint
+=caseviewtof
+Bin_x(isTip->True)r->(x,r)
+Bin_xlr->let(xm,l')=deleteFindMinlin(xm,balancexl'r)
+Tip->(error"Set.deleteFindMin: can not return the minimal element of an empty set",tip)
+
+-- | /O(log n)/. Delete and find the maximal element.
+--
+-- > deleteFindMax set = (findMax set, deleteMax set)
+deleteFindMax::USa=>USeta->(a,USeta)
+deleteFindMaxt
+=caseviewtof
+Bin_xl(isTip->True)->(x,l)
+Bin_xlr->let(xm,r')=deleteFindMaxrin(xm,balancexlr')
+_->(error"Set.deleteFindMax: can not return the maximal element of an empty set",tip)
+
+-- | /O(log n)/. Retrieves the minimal key of the set, and the set
+-- stripped of that element, or 'Nothing' if passed an empty set.
+minView::USa=>USeta->Maybe(a,USeta)
+minView(isTip->True)=Nothing
+minViewx=Just(deleteFindMinx)
+
+-- | /O(log n)/. Retrieves the maximal key of the set, and the set
+-- stripped of that element, or 'Nothing' if passed an empty set.
+maxView::USa=>USeta->Maybe(a,USeta)
+maxView(isTip->True)=Nothing
+maxViewx=Just(deleteFindMaxx)
+
+{--------------------------------------------------------------------
+ [balance x l r] balances two trees with value x.
+ The sizes of the trees should balance after decreasing the
+ size of one of them. (a rotation).
+
+ [delta] is the maximal relative difference between the sizes of
+ two trees, it corresponds with the [w] in Adams' paper,
+ or equivalently, [1/delta] corresponds with the $\alpha$
+ in Nievergelt's paper. Adams shows that [delta] should
+ be larger than 3.745 in order to garantee that the
+ rotations can always restore balance.
+
+ [ratio] is the ratio between an outer and inner sibling of the
+ heavier subtree in an unbalanced setting. It determines
+ whether a double or single rotation should be performed
+ to restore balance. It is correspondes with the inverse
+ of $\alpha$ in Adam's article.
+
+ Note that:
+ - [delta] should be larger than 4.646 with a [ratio] of 2.
+ - [delta] should be larger than 3.745 with a [ratio] of 1.534.
+
+ - A lower [delta] leads to a more 'perfectly' balanced tree.
+ - A higher [delta] performs less rebalancing.
+
+ - Balancing is automatic for random data and a balancing
+ scheme is only necessary to avoid pathological worst cases.
+ Almost any choice will do in practice
+
+ - Allthough it seems that a rather large [delta] may perform better
+ than smaller one, measurements have shown that the smallest [delta]
+ of 4 is actually the fastest on a wide range of operations. It
+ especially improves performance on worst-case scenarios like
+ a sequence of ordered insertions.
+
+ Note: in contrast to Adams' paper, we use a ratio of (at least) 2
+ to decide whether a single or double rotation is needed. Allthough
+ he actually proves that this ratio is needed to maintain the
+ invariants, his implementation uses a (invalid) ratio of 1.
+ He is aware of the problem though since he has put a comment in his
+ original source code that he doesn't care about generating a
+ slightly inbalanced tree since it doesn't seem to matter in practice.
+ However (since we use quickcheck :-) we will stick to strictly balanced
+ trees.
+--------------------------------------------------------------------}
+delta,ratio::Int
+delta=4
+ratio=2
+
+balance::USa=>a->USeta->USeta->USeta
+balancexlr
+|sizeL+sizeR<=1=binsizeXxlr
+|sizeR>=delta*sizeL=rotateLxlr
+|sizeL>=delta*sizeR=rotateRxlr
+|otherwise=binsizeXxlr
+where
+sizeL=sizel
+sizeR=sizer
+sizeX=sizeL+sizeR+1
+
+-- rotate
+rotateL::USa=>a->USeta->USeta->USeta
+rotateLxlr@(view->Bin__lyry)
+|sizely<ratio*sizery=singleLxlr
+|otherwise=doubleLxlr
+rotateL___=error"rotateL Tip"
+
+rotateR::USa=>a->USeta->USeta->USeta
+rotateRxl@(view->Bin__lyry)r
+|sizery<ratio*sizely=singleRxlr
+|otherwise=doubleRxlr
+rotateR___=error"rotateL Tip"
+
+-- basic rotations
+singleL,singleR::USa=>a->USeta->USeta->USeta
+singleLx1t1(view->Bin_x2t2t3)=bin_x2(bin_x1t1t2)t3
+singleL___=error"singleL"
+singleRx1(view->Bin_x2t1t2)t3=bin_x2t1(bin_x1t2t3)
+singleR___=error"singleR"
+
+doubleL,doubleR::USa=>a->USeta->USeta->USeta
+doubleLx1t1(view->Bin_x2(view->Bin_x3t2t3)t4)=bin_x3(bin_x1t1t2)(bin_x2t3t4)
+doubleL___=error"doubleL"
+doubleRx1(view->Bin_x2t1(view->Bin_x3t2t3))t4=bin_x3(bin_x2t1t2)(bin_x1t3t4)
+doubleR___=error"doubleR"
+
+
+{--------------------------------------------------------------------
+ The bin constructor maintains the size of the tree
+--------------------------------------------------------------------}
+bin_::USa=>a->USeta->USeta->USeta
+bin_xlr
+=bin(sizel+sizer+1)xlr
+
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 848
-doubleL,doubleR::USa=>a->USeta->USeta->USeta
-doubleLx1t1(view->Bin_x2(view->Bin_x3t2t3)t4)=bin_x3(bin_x1t1t2)(bin_x2t3t4)
-doubleL___=error"doubleL"
-doubleRx1(view->Bin_x2t1(view->Bin_x3t2t3))t4=bin_x3(bin_x2t1t2)(bin_x1t3t4)
-doubleR___=error"doubleR"
-
-
-{--------------------------------------------------------------------
- The bin constructor maintains the size of the tree
---------------------------------------------------------------------}
-bin_::USa=>a->USeta->USeta->USeta
-bin_xlr
-=bin(sizel+sizer+1)xlr
-
-
-{--------------------------------------------------------------------
- Utilities
---------------------------------------------------------------------}
-foldlStrict::(a->b->a)->a->[b]->a
-foldlStrictfzxs
-=casexsof
-[]->z
-(x:xx)->letz'=fzxinseqz'(foldlStrictfz'xx)
-
+{--------------------------------------------------------------------
+ Utilities
+--------------------------------------------------------------------}
+foldlStrict::(a->b->a)->a->[b]->a
+foldlStrictfzxs
+=casexsof
+[]->z
+(x:xx)->letz'=fzxinseqz'(foldlStrictfz'xx)
+
+
+{--------------------------------------------------------------------
+ Debugging
+--------------------------------------------------------------------}
+-- | /O(n)/. Show the tree that implements the set. The tree is shown
+-- in a compressed, hanging format.
+showTree::(USa,Showa)=>USeta->String
+showTrees
+=showTreeWithTrueFalses
+
+
+{- | /O(n)/. The expression (@showTreeWith hang wide map@) shows
+ the tree that implements the set. If @hang@ is
+ @True@, a /hanging/ tree is shown otherwise a rotated tree is shown. If
+ @wide@ is 'True', an extra wide version is shown.
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 873
-{--------------------------------------------------------------------
- Debugging
---------------------------------------------------------------------}
--- | /O(n)/. Show the tree that implements the set. The tree is shown
--- in a compressed, hanging format.
-showTree::(USa,Showa)=>USeta->String
-showTrees
-=showTreeWithTrueFalses
-
-
-{- | /O(n)/. The expression (@showTreeWith hang wide map@) shows
- the tree that implements the set. If @hang@ is
- @True@, a /hanging/ tree is shown otherwise a rotated tree is shown. If
- @wide@ is 'True', an extra wide version is shown.
-
-> Set> putStrLn $ showTreeWith True False $ fromDistinctAscList [1..5]
-> 4
-> +--2
-> | +--1
-> | +--3
-> +--5
->
-> Set> putStrLn $ showTreeWith True True $ fromDistinctAscList [1..5]
-> 4
-> |
+> Set> putStrLn $ showTreeWith True False $ fromDistinctAscList [1..5]
+> 4
+> +--2
+> | +--1
+> | +--3
+> +--5
+>
+> Set> putStrLn $ showTreeWith True True $ fromDistinctAscList [1..5]
+> 4
+> |
+> +--2
+> | |
+> | +--1
+> | |
+> | +--3
+> |
+> +--5
+>
+> Set> putStrLn $ showTreeWith False True $ fromDistinctAscList [1..5]
+> +--5
+> |
+> 4
+> |
+> | +--3
+> | |
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 899
-> | |
-> | +--1
-> | |
-> | +--3
-> |
-> +--5
->
-> Set> putStrLn $ showTreeWith False True $ fromDistinctAscList [1..5]
-> +--5
-> |
-> 4
-> |
-> | +--3
-> | |
-> +--2
-> |
-> +--1
-
--}
-showTreeWith::(USa,Showa)=>Bool->Bool->USeta->String
-showTreeWithhangwidet
-|hang=(showsTreeHangwide[]t)""
-|otherwise=(showsTreewide[][]t)""
-
-showsTree::(USa,Showa)=>Bool->[String]->[String]->USeta->ShowS
-showsTreewidelbarsrbarst
-=caseviewtof
-Tip->showsBarslbars.showString"|\n"
-Bin_x(view->Tip)(view->Tip)
-->showsBarslbars.showsx.showString"\n"
-Bin_xlr
-->showsTreewide(withBarrbars)(withEmptyrbars)r.
-showWidewiderbars.
-showsBarslbars.showsx.showString"\n".
-showWidewidelbars.
-showsTreewide(withEmptylbars)(withBarlbars)l
-
-showsTreeHang::(USa,Showa)=>Bool->[String]->USeta->ShowS
-showsTreeHangwidebarst
-=caseviewtof
-Tip->showsBarsbars.showString"|\n"
-Bin_x(view->Tip)(view->Tip)
-->showsBarsbars.showsx.showString"\n"
-Bin_xlr
-->showsBarsbars.showsx.showString"\n".
-showWidewidebars.
-showsTreeHangwide(withBarbars)l.
-showWidewidebars.
-showsTreeHangwide(withEmptybars)r
-
-showWide::Bool->[String]->String->String
-showWidewidebars
-|wide=showString(concat(reversebars)).showString"|\n"
-|otherwise=id
-
-showsBars::[String]->ShowS
-showsBarsbars
-=casebarsof
-[]->id
-_->showString(concat(reverse(tailbars))).showStringnode
+> |
+> +--1
+
+-}
+showTreeWith::(USa,Showa)=>Bool->Bool->USeta->String
+showTreeWithhangwidet
+|hang=(showsTreeHangwide[]t)""
+|otherwise=(showsTreewide[][]t)""
+
+showsTree::(USa,Showa)=>Bool->[String]->[String]->USeta->ShowS
+showsTreewidelbarsrbarst
+=caseviewtof
+Tip->showsBarslbars.showString"|\n"
+Bin_x(isTip->True)(isTip->True)
+->showsBarslbars.showsx.showString"\n"
+Bin_xlr
+->showsTreewide(withBarrbars)(withEmptyrbars)r.
+showWidewiderbars.
+showsBarslbars.showsx.showString"\n".
+showWidewidelbars.
+showsTreewide(withEmptylbars)(withBarlbars)l
+
+showsTreeHang::(USa,Showa)=>Bool->[String]->USeta->ShowS
+showsTreeHangwidebarst
+=caseviewtof
+Tip->showsBarsbars.showString"|\n"
+Bin_x(isTip->True)(isTip->True)
+->showsBarsbars.showsx.showString"\n"
+Bin_xlr
+->showsBarsbars.showsx.showString"\n".
+showWidewidebars.
+showsTreeHangwide(withBarbars)l.
+showWidewidebars.
+showsTreeHangwide(withEmptybars)r
+
+showWide::Bool->[String]->String->String
+showWidewidebars
+|wide=showString(concat(reversebars)).showString"|\n"
+|otherwise=id
+
+showsBars::[String]->ShowS
+showsBarsbars
+=casebarsof
+[]->id
+_->showString(concat(reverse(tailbars))).showStringnode
+
+node::String
+node="+--"
+
+withBar,withEmpty::[String]->[String]
+withBarbars="| ":bars
+withEmptybars=" ":bars
+
+{--------------------------------------------------------------------
+ Assertions
+--------------------------------------------------------------------}
+-- | /O(n)/. Test if the internal set structure is valid.
+valid::(USa,Orda)=>USeta->Bool
+validt
+=balancedt&&orderedt&&validsizet
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 960
-node::String
-node="+--"
-
-withBar,withEmpty::[String]->[String]
-withBarbars="| ":bars
-withEmptybars=" ":bars
-
-{--------------------------------------------------------------------
- Assertions
---------------------------------------------------------------------}
--- | /O(n)/. Test if the internal set structure is valid.
-valid::(USa,Orda)=>USeta->Bool
-validt
-=balancedt&&orderedt&&validsizet
-
-ordered::(USa,Orda)=>USeta->Bool
-orderedt
-=bounded(constTrue)(constTrue)t
-where
-boundedlohit'
-=caseviewt'of
-Tip->True
-Bin_xlr->(lox)&&(hix)&&boundedlo(<x)l&&bounded(>x)hir
-
-balanced::USa=>USeta->Bool
-balancedt
-=caseviewtof
-Tip->True
-Bin__lr->(sizel+sizer<=1||(sizel<=delta*sizer&&sizer<=delta*sizel))&&
-balancedl&&balancedr
-
-validsize::USa=>USeta->Bool
-validsizet
-=(realsizet==Just(sizet))
-where
-realsizet'
-=caseviewt'of
-Tip->Just0
-Binsz_lr->case(realsizel,realsizer)of
-(Justn,Justm)|n+m+1==sz->Justsz
-_->Nothing
-
-{-
-{--------------------------------------------------------------------
- Testing
---------------------------------------------------------------------}
-testTree :: [Int] -> USet Int
-testTree xs = fromList xs
-test1 = testTree [1..20]
-test2 = testTree [30,29..10]
-test3 = testTree [1,4,6,89,2323,53,43,234,5,79,12,9,24,9,8,423,8,42,4,8,9,3]
-
-{--------------------------------------------------------------------
- QuickCheck
---------------------------------------------------------------------}
-
-{-
-qcheck prop
- = check config prop
- where
- config = Config
- { configMaxTest = 500
- , configMaxFail = 5000
- , configSize = \n -> (div n 2 + 3)
- , configEvery = \n args -> let s = show n in s ++ [ '\b' | _ <- s ]
- }
--}
-
-
-{--------------------------------------------------------------------
- Arbitrary, reasonably balanced trees
---------------------------------------------------------------------}
-instance (US a, Enum a) => Arbitrary (USet a) where
- arbitrary = sized (arbtree 0 maxkey)
- where maxkey = 10000
+ordered::(USa,Orda)=>USeta->Bool
+orderedt
+=bounded(constTrue)(constTrue)t
+where
+boundedlohit'
+=caseviewt'of
+Bin_xlr->(lox)&&(hix)&&boundedlo(<x)l&&bounded(>x)hir
+_->True
+
+balanced::USa=>USeta->Bool
+balancedt
+=caseviewtof
+Bin__lr->(sizel+sizer<=1||(sizel<=delta*sizer&&sizer<=delta*sizel))&&
+balancedl&&balancedr
+_->True
+
+validsize::USa=>USeta->Bool
+validsizet
+=(realsizet==Just(sizet))
+where
+realsizet'
+=caseviewt'of
+Binsz_lr->case(realsizel,realsizer)of
+(Justn,Justm)|n+m+1==sz->Justsz
+_->Nothing
+_->Just0
+
+{-
+{--------------------------------------------------------------------
+ Testing
+--------------------------------------------------------------------}
+testTree :: [Int] -> USet Int
+testTree xs = fromList xs
+test1 = testTree [1..20]
+test2 = testTree [30,29..10]
+test3 = testTree [1,4,6,89,2323,53,43,234,5,79,12,9,24,9,8,423,8,42,4,8,9,3]
+
+{--------------------------------------------------------------------
+ QuickCheck
+--------------------------------------------------------------------}
+
+{-
+qcheck prop
+ = check config prop
+ where
+ config = Config
+ { configMaxTest = 500
+ , configMaxFail = 5000
+ , configSize = \n -> (div n 2 + 3)
+ , configEvery = \n args -> let s = show n in s ++ [ '\b' | _ <- s ]
+ }
+-}
+
+
+{--------------------------------------------------------------------
+ Arbitrary, reasonably balanced trees
+--------------------------------------------------------------------}
+instance (US a, Enum a) => Arbitrary (USet a) where
+ arbitrary = sized (arbtree 0 maxkey)
+ where maxkey = 10000
+
+arbtree :: (US a, Enum a) => Int -> Int -> Int -> Gen (USet a)
+arbtree lo hi n
+ | n <= 0 = return tip
+ | lo >= hi = return tip
+ | otherwise = do{ i <- choose (lo,hi)
+ ; m <- choose (1,30)
+ ; let (ml,mr) | m==(1::Int)= (1,2)
+ | m==2 = (2,1)
+ | m==3 = (1,1)
+ | otherwise = (2,2)
+ ; l <- arbtree lo (i-1) (n `div` ml)
+ ; r <- arbtree (i+1) hi (n `div` mr)
+ ; return (bin_ (toEnum i) l r)
+ }
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 1036
-arbtree :: (US a, Enum a) => Int -> Int -> Int -> Gen (USet a)
-arbtree lo hi n
- | n <= 0 = return tip
- | lo >= hi = return tip
- | otherwise = do{ i <- choose (lo,hi)
- ; m <- choose (1,30)
- ; let (ml,mr) | m==(1::Int)= (1,2)
- | m==2 = (2,1)
- | m==3 = (1,1)
- | otherwise = (2,2)
- ; l <- arbtree lo (i-1) (n `div` ml)
- ; r <- arbtree (i+1) hi (n `div` mr)
- ; return (bin_ (toEnum i) l r)
- }
-
-
-{--------------------------------------------------------------------
- Valid tree's
---------------------------------------------------------------------}
-forValid :: (US a, Enum a,Show a,Testable b) => (USet a -> b) -> Property
-forValid f
- = forAll arbitrary $ \t ->
--- classify (balanced t) "balanced" $
- classify (size t == 0) "empty" $
- classify (size t > 0 && size t <= 10) "small" $
- classify (size t > 10 && size t <= 64) "medium" $
- classify (size t > 64) "large" $
- balanced t ==> f t
-
-forValidIntTree :: Testable a => (USet Int -> a) -> Property
-forValidIntTree f
- = forValid f
+
+{--------------------------------------------------------------------
+ Valid tree's
+--------------------------------------------------------------------}
+forValid :: (US a, Enum a,Show a,Testable b) => (USet a -> b) -> Property
+forValid f
+ = forAll arbitrary $ \t ->
+-- classify (balanced t) "balanced" $
+ classify (size t == 0) "empty" $
+ classify (size t > 0 && size t <= 10) "small" $
+ classify (size t > 10 && size t <= 64) "medium" $
+ classify (size t > 64) "large" $
+ balanced t ==> f t
+
+forValidIntTree :: Testable a => (USet Int -> a) -> Property
+forValidIntTree f
+ = forValid f
+
+forValidUnitTree :: Testable a => (USet Int -> a) -> Property
+forValidUnitTree f
+ = forValid f
+
+
+prop_Valid
+ = forValidUnitTree $ \t -> valid t
+
+{--------------------------------------------------------------------
+ Single, Insert, Delete
+--------------------------------------------------------------------}
+prop_Single :: Int -> Bool
+prop_Single x
+ = (insert x empty == singleton x)
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 1069
-forValidUnitTree :: Testable a => (USet Int -> a) -> Property
-forValidUnitTree f
- = forValid f
+prop_InsertValid :: Int -> Property
+prop_InsertValid k
+ = forValidUnitTree $ \t -> valid (insert k t)
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 1073
-
-prop_Valid
- = forValidUnitTree $ \t -> valid t
+prop_InsertDelete :: Int -> USet Int -> Property
+prop_InsertDelete k t
+ = not (member k t) ==> delete k (insert k t) == t
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 1077
-{--------------------------------------------------------------------
- Single, Insert, Delete
---------------------------------------------------------------------}
-prop_Single :: Int -> Bool
-prop_Single x
- = (insert x empty == singleton x)
-
-prop_InsertValid :: Int -> Property
-prop_InsertValid k
- = forValidUnitTree $ \t -> valid (insert k t)
-
-prop_InsertDelete :: Int -> USet Int -> Property
-prop_InsertDelete k t
- = not (member k t) ==> delete k (insert k t) == t
-
-prop_DeleteValid :: Int -> Property
-prop_DeleteValid k
- = forValidUnitTree $ \t ->
- valid (delete k (insert k t))
+prop_DeleteValid :: Int -> Property
+prop_DeleteValid k
+ = forValidUnitTree $ \t ->
+ valid (delete k (insert k t))
+
+{--------------------------------------------------------------------
+ Balance
+--------------------------------------------------------------------}
+prop_Join :: Int -> Property
+prop_Join x
+ = forValidUnitTree $ \t ->
+ let (l,r) = split x t
+ in valid (join x l r)
+
+prop_Merge :: Int -> Property
+prop_Merge x
+ = forValidUnitTree $ \t ->
+ let (l,r) = split x t
+ in valid (merge l r)
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 1097
-{--------------------------------------------------------------------
- Balance
---------------------------------------------------------------------}
-prop_Join :: Int -> Property
-prop_Join x
- = forValidUnitTree $ \t ->
- let (l,r) = split x t
- in valid (join x l r)
-
-prop_Merge :: Int -> Property
-prop_Merge x
- = forValidUnitTree $ \t ->
- let (l,r) = split x t
- in valid (merge l r)
-
-
-{--------------------------------------------------------------------
- Union
---------------------------------------------------------------------}
-prop_UnionValid :: Property
-prop_UnionValid
- = forValidUnitTree $ \t1 ->
- forValidUnitTree $ \t2 ->
- valid (union t1 t2)
-
-prop_UnionInsert :: Int -> USet Int -> Bool
-prop_UnionInsert x t
- = union t (singleton x) == insert x t
-
-prop_UnionAssoc :: USet Int -> USet Int -> USet Int -> Bool
-prop_UnionAssoc t1 t2 t3
- = union t1 (union t2 t3) == union (union t1 t2) t3
+
+{--------------------------------------------------------------------
+ Union
+--------------------------------------------------------------------}
+prop_UnionValid :: Property
+prop_UnionValid
+ = forValidUnitTree $ \t1 ->
+ forValidUnitTree $ \t2 ->
+ valid (union t1 t2)
+
+prop_UnionInsert :: Int -> USet Int -> Bool
+prop_UnionInsert x t
+ = union t (singleton x) == insert x t
+
+prop_UnionAssoc :: USet Int -> USet Int -> USet Int -> Bool
+prop_UnionAssoc t1 t2 t3
+ = union t1 (union t2 t3) == union (union t1 t2) t3
+
+prop_UnionComm :: USet Int -> USet Int -> Bool
+prop_UnionComm t1 t2
+ = (union t1 t2 == union t2 t1)
+
+
+prop_DiffValid
+ = forValidUnitTree $ \t1 ->
+ forValidUnitTree $ \t2 ->
+ valid (difference t1 t2)
+
+prop_Diff :: [Int] -> [Int] -> Bool
+prop_Diff xs ys
+ = toAscList (difference (fromList xs) (fromList ys))
+ == List.sort ((List.\\) (nub xs) (nub ys))
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 1130
-prop_UnionComm :: USet Int -> USet Int -> Bool
-prop_UnionComm t1 t2
- = (union t1 t2 == union t2 t1)
-
+prop_IntValid
+ = forValidUnitTree $ \t1 ->
+ forValidUnitTree $ \t2 ->
+ valid (intersection t1 t2)
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 1135
-prop_DiffValid
- = forValidUnitTree $ \t1 ->
- forValidUnitTree $ \t2 ->
- valid (difference t1 t2)
+prop_Int :: [Int] -> [Int] -> Bool
+prop_Int xs ys
+ = toAscList (intersection (fromList xs) (fromList ys))
+ == List.sort (nub ((List.intersect) (xs) (ys)))
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 1140
-prop_Diff :: [Int] -> [Int] -> Bool
-prop_Diff xs ys
- = toAscList (difference (fromList xs) (fromList ys))
- == List.sort ((List.\\) (nub xs) (nub ys))
-
-prop_IntValid
- = forValidUnitTree $ \t1 ->
- forValidUnitTree $ \t2 ->
- valid (intersection t1 t2)
-
-prop_Int :: [Int] -> [Int] -> Bool
-prop_Int xs ys
- = toAscList (intersection (fromList xs) (fromList ys))
- == List.sort (nub ((List.intersect) (xs) (ys)))
-
-{--------------------------------------------------------------------
- Lists
---------------------------------------------------------------------}
-prop_Ordered
- = forAll (choose (5,100)) $ \n ->
- let xs = [0..n::Int]
- in fromAscList xs == fromList xs
-
-prop_List :: [Int] -> Bool
-prop_List xs
- = (sort (nub xs) == toList (fromList xs))
--}
-
-
-newtypeBoxeda=Boxeda
-instanceUS(Boxeda)where
-dataUSet(Boxeda)=BoxedTip|BoxedBin{-# UNPACK #-}!Size(Boxeda)!(USet(Boxeda))!(USet(Boxeda))
-viewBoxedTip=Tip
-view(BoxedBinsilr)=Binsilr
-tip=BoxedTip
-bin=BoxedBin
-
-instanceUSCharwhere
-dataUSetChar=CharTip|CharBin{-# UNPACK #-}!Size{-# UNPACK #-}!Char!(USetChar)!(USetChar)
-viewCharTip=Tip
-view(CharBinsilr)=Binsilr
-tip=CharTip
-bin=CharBin
-instanceUSIntwhere
-dataUSetInt=IntTip|IntBin{-# UNPACK #-}!Size{-# UNPACK #-}!Int!(USetInt)!(USetInt)
-viewIntTip=Tip
-view(IntBinsilr)=Binsilr
-tip=IntTip
-bin=IntBin
-
-instanceUSIntegerwhere
-dataUSetInteger=IntegerTip|IntegerBin{-# UNPACK #-}!Size{-# UNPACK #-}!Integer!(USetInteger)!(USetInteger)
-viewIntegerTip=Tip
-view(IntegerBinsilr)=Binsilr
-tip=IntegerTip
-bin=IntegerBin
-
-instanceUSInt8where
-dataUSetInt8=Int8Tip|Int8Bin{-# UNPACK #-}!Size{-# UNPACK #-}!Int8!(USetInt8)!(USetInt8)
-viewInt8Tip=Tip
-view(Int8Binsilr)=Binsilr
-tip=Int8Tip
-bin=Int8Bin
-
-instanceUSInt16where
-dataUSetInt16=Int16Tip|Int16Bin{-# UNPACK #-}!Size{-# UNPACK #-}!Int16!(USetInt16)!(USetInt16)
-viewInt16Tip=Tip
-view(Int16Binsilr)=Binsilr
-tip=Int16Tip
-bin=Int16Bin
-
-instanceUSInt32where
-dataUSetInt32=Int32Tip|Int32Bin{-# UNPACK #-}!Size{-# UNPACK #-}!Int32!(USetInt32)!(USetInt32)
-viewInt32Tip=Tip
-view(Int32Binsilr)=Binsilr
-tip=Int32Tip
-bin=Int32Bin
+{--------------------------------------------------------------------
+ Lists
+--------------------------------------------------------------------}
+prop_Ordered
+ = forAll (choose (5,100)) $ \n ->
+ let xs = [0..n::Int]
+ in fromAscList xs == fromList xs
+
+prop_List :: [Int] -> Bool
+prop_List xs
+ = (sort (nub xs) == toList (fromList xs))
+-}
+
+
+newtypeBoxeda=Boxeda
+instanceUS(Boxeda)where
+dataUSet(Boxeda)=BoxedTip|BoxedBin{-# UNPACK #-}!Size(Boxeda)!(USet(Boxeda))!(USet(Boxeda))
+viewBoxedTip=Tip
+view(BoxedBinsilr)=Binsilr
+tip=BoxedTip
+bin=BoxedBin
+isTipBoxedTip=True
+isTip_=False
+
+instanceUSCharwhere
+dataUSetChar=CharTip|CharBin{-# UNPACK #-}!Size{-# UNPACK #-}!Char!(USetChar)!(USetChar)
+viewCharTip=Tip
+view(CharBinsilr)=Binsilr
+tip=CharTip
+bin=CharBin
+isTipCharTip=True
+isTip_=False
+
+instanceUSIntwhere
+dataUSetInt=IntTip|IntBin{-# UNPACK #-}!Size{-# UNPACK #-}!Int!(USetInt)!(USetInt)
+viewIntTip=Tip
+view(IntBinsilr)=Binsilr
+tip=IntTip
+bin=IntBin
+isTipIntTip=True
+isTip_=False
+
+instanceUSIntegerwhere
+dataUSetInteger=IntegerTip|IntegerBin{-# UNPACK #-}!Size{-# UNPACK #-}!Integer!(USetInteger)!(USetInteger)
+viewIntegerTip=Tip
+view(IntegerBinsilr)=Binsilr
+tip=IntegerTip
+bin=IntegerBin
+isTipIntegerTip=True
+isTip_=False
+
+instanceUSInt8where
+dataUSetInt8=Int8Tip|Int8Bin{-# UNPACK #-}!Size{-# UNPACK #-}!Int8!(USetInt8)!(USetInt8)
+viewInt8Tip=Tip
+view(Int8Binsilr)=Binsilr
+tip=Int8Tip
+bin=Int8Bin
+isTipInt8Tip=True
+isTip_=False
+
+instanceUSInt16where
+dataUSetInt16=Int16Tip|Int16Bin{-# UNPACK #-}!Size{-# UNPACK #-}!Int16!(USetInt16)!(USetInt16)
+viewInt16Tip=Tip
+view(Int16Binsilr)=Binsilr
+tip=Int16Tip
+bin=Int16Bin
+isTipInt16Tip=True
+isTip_=False
+
+instanceUSInt32where
+dataUSetInt32=Int32Tip|Int32Bin{-# UNPACK #-}!Size{-# UNPACK #-}!Int32!(USetInt32)!(USetInt32)
+viewInt32Tip=Tip
+view(Int32Binsilr)=Binsilr
+tip=Int32Tip
+bin=Int32Bin
+isTipInt32Tip=True
+isTip_=False
hunk ./doc/html/monoids/src/Data-Set-Unboxed.html 1224
-
-instanceUSWord8where
-dataUSetWord8=Word8Tip|Word8Bin{-# UNPACK #-}!Size{-# UNPACK #-}!Word8!(USetWord8)!(USetWord8)
-viewWord8Tip=Tip
-view(Word8Binsilr)=Binsilr
-tip=Word8Tip
-bin=Word8Bin
-
-instanceUSWord16where
-dataUSetWord16=Word16Tip|Word16Bin{-# UNPACK #-}!Size{-# UNPACK #-}!Word16!(USetWord16)!(USetWord16)
-viewWord16Tip=Tip
-view(Word16Binsilr)=Binsilr
-tip=Word16Tip
-bin=Word16Bin
-
-instanceUSWord32where
-dataUSetWord32=Word32Tip|Word32Bin{-# UNPACK #-}!Size{-# UNPACK #-}!Word32!(USetWord32)!(USetWord32)
-viewWord32Tip=Tip
-view(Word32Binsilr)=Binsilr
-tip=Word32Tip
-bin=Word32Bin
-
-instanceUSWord64where
-dataUSetWord64=Word64Tip|Word64Bin{-# UNPACK #-}!Size{-# UNPACK #-}!Word64!(USetWord64)!(USetWord64)
-viewWord64Tip=Tip
-view(Word64Binsilr)=Binsilr
-tip=Word64Tip
-bin=Word64Bin
-
-instanceUSDoublewhere
-dataUSetDouble=DoubleTip|DoubleBin{-# UNPACK #-}!Size{-# UNPACK #-}!Double!(USetDouble)!(USetDouble)
-viewDoubleTip=Tip
-view(DoubleBinsilr)=Binsilr
-tip=DoubleTip
-bin=DoubleBin
-
-instanceUSFloatwhere
-dataUSetFloat=FloatTip|FloatBin{-# UNPACK #-}!Size{-# UNPACK #-}!Float!(USetFloat)!(USetFloat)
-viewFloatTip=Tip
-view(FloatBinsilr)=Binsilr
-tip=FloatTip
-bin=FloatBin
-
+isTipInt64Tip=True
+isTip_=False
+
+instanceUSWord8where
+dataUSetWord8=Word8Tip|Word8Bin{-# UNPACK #-}!Size{-# UNPACK #-}!Word8!(USetWord8)!(USetWord8)
+viewWord8Tip=Tip
+view(Word8Binsilr)=Binsilr
+tip=Word8Tip
+bin=Word8Bin
+isTipWord8Tip=True
+isTip_=False
+
+instanceUSWord16where
+dataUSetWord16=Word16Tip|Word16Bin{-# UNPACK #-}!Size{-# UNPACK #-}!Word16!(USetWord16)!(USetWord16)
+viewWord16Tip=Tip
+view(Word16Binsilr)=Binsilr
+bin=Word16Bin
+tip=Word16Tip
+isTipWord16Tip=True
+isTip_=False
+
+instanceUSWord32where
+dataUSetWord32=Word32Tip|Word32Bin{-# UNPACK #-}!Size{-# UNPACK #-}!Word32!(USetWord32)!(USetWord32)
+viewWord32Tip=Tip
+view(Word32Binsilr)=Binsilr
+tip=Word32Tip
+bin=Word32Bin
+isTipWord32Tip=True
+isTip_=False
+
+instanceUSWord64where
+dataUSetWord64=Word64Tip|Word64Bin{-# UNPACK #-}!Size{-# UNPACK #-}!Word64!(USetWord64)!(USetWord64)
+viewWord64Tip=Tip
+view(Word64Binsilr)=Binsilr
+tip=Word64Tip
+bin=Word64Bin
+isTipWord64Tip=True
+isTip_=False
+
+instanceUSDoublewhere
+dataUSetDouble=DoubleTip|DoubleBin{-# UNPACK #-}!Size{-# UNPACK #-}!Double!(USetDouble)!(USetDouble)
+viewDoubleTip=Tip
+view(DoubleBinsilr)=Binsilr
+tip=DoubleTip
+bin=DoubleBin
+isTipDoubleTip=True
+isTip_=False
+
+instanceUSFloatwhere
+dataUSetFloat=FloatTip|FloatBin{-# UNPACK #-}!Size{-# UNPACK #-}!Float!(USetFloat)!(USetFloat)
+viewFloatTip=Tip
+view(FloatBinsilr)=Binsilr
+tip=FloatTip
+bin=FloatBin
+isTipFloatTip=True
+isTip_=False
+
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Instances