newtypeͷͭͷ༻్ ࣮ͷӅṭ ࣮ͷڞ༗ module Data.Id (Id ()) where newtype Id = MkId Word ܕͷ্Ͱ۠ผ Ͱ෦తʹWord {-# LANGUAGE GeneralizedNewtypeDeriving #-} newtype Id = MkId Word deriving (Num, Eq) ֎෦ʹσʔλߏஙࢠ MkIdӅṭ
newtypeͷͭͷ༻్ ࣮ͷӅṭ ࣮ͷڞ༗ module Data.Id (Id ()) where newtype Id = MkId Word ܕͷ্Ͱ۠ผ Ͱ෦తʹWord {-# LANGUAGE GeneralizedNewtypeDeriving #-} newtype Id = MkId Word deriving (Num, Eq) ຊདྷಋग़ෆՄͰ Wordͷ࣮͕ڞ༗Ͱ͖Δ ֎෦ʹσʔλߏஙࢠ MkIdӅṭ
newtypeͷͭͷ༻్ ࣮ͷӅṭ ࣮ͷڞ༗ module Data.Id (Id ()) where newtype Id = MkId Word ܕͷ্Ͱ۠ผ Ͱ෦తʹWord {-# LANGUAGE GeneralizedNewtypeDeriving #-} newtype Id = MkId Word deriving (Num, Eq) ຊདྷಋग़ෆՄͰ Wordͷ࣮͕ڞ༗Ͱ͖Δ %FSJWJOH7JB ͰߋʹਐԽ ֎෦ʹσʔλߏஙࢠ MkIdӅṭ
newtypeͷͭͷ༻్ ࣮ͷӅṭ ࣮ͷڞ༗ ࣮ͷબ module Data.Id (Id ()) where newtype Id = MkId Word ܕͷ্Ͱ۠ผ Ͱ෦తʹWord {-# LANGUAGE GeneralizedNewtypeDeriving #-} newtype Id = MkId Word deriving (Num, Eq) ຊདྷಋग़ෆՄͰ Wordͷ࣮͕ڞ༗Ͱ͖Δ %FSJWJOH7JB ͰߋʹਐԽ ֎෦ʹσʔλߏஙࢠ MkIdӅṭ
newtypeͷͭͷ༻్ ࣮ͷӅṭ ࣮ͷڞ༗ ࣮ͷબ {-# LANGUAGE GeneralizedNewtypeDeriving #-} newtype Id = MkId Word deriving (Num, Eq) ຊདྷಋग़ෆՄͰ Wordͷ࣮͕ڞ༗Ͱ͖Δ %FSJWJOH7JB ͰߋʹਐԽ module Data.Id (Id ()) where newtype Id = MkId Word ܕͷ্Ͱ۠ผ Ͱ෦తʹWord ֎෦ʹσʔλߏஙࢠ MkIdӅṭ
'PMEBCMFܕΫϥε ͜ͷΈʹNBY
ΛམͱͤΕΑͦ͞͏ Monoid WordΠϯελϯεߴʑҰ͔ͭ͠ॻ͚ͳ͍ʜʜ ͦ͜ͰnewtypeʹΑΔ࣮ͷબʂ class Foldable t where foldMap :: Monoid m 㱺 (a ! m) ! t a ! m … ϞϊΠυʹม
Πϯελϯεྫ newtype Sum a = Sum { getSum :: a} deriving (Num, Integral) instance Num a 㱺 Monoid (Sum a) where (<>) = (+); ε = 0 newtype Max a = Max { getMax :: a } deriving (Num, Integral, Ord) instance Ord a 㱺 Semigroup (Max a) where (<>) = max
Πϯελϯεྫ newtype Sum a = Sum { getSum :: a} deriving (Num, Integral) instance Num a 㱺 Monoid (Sum a) where (<>) = (+); ε = 0 newtype Max a = Max { getMax :: a } deriving (Num, Integral, Ord) instance Ord a 㱺 Semigroup (Max a) where (<>) = max ͷՃ๏ʹؔ͢Δ ϞϊΠυ
Πϯελϯεྫ newtype Sum a = Sum { getSum :: a} deriving (Num, Integral) instance Num a 㱺 Monoid (Sum a) where (<>) = (+); ε = 0 newtype Max a = Max { getMax :: a } deriving (Num, Integral, Ord) instance Ord a 㱺 Semigroup (Max a) where (<>) = max ͷՃ๏ʹؔ͢Δ ϞϊΠυ ࠷େݶʹؔ͢Δ ܈
Πϯελϯεྫ newtype Sum a = Sum { getSum :: a} deriving (Num, Integral) instance Num a 㱺 Monoid (Sum a) where (<>) = (+); ε = 0 newtype Max a = Max { getMax :: a } deriving (Num, Integral, Ord) instance Ord a 㱺 Semigroup (Max a) where (<>) = max ͷՃ๏ʹؔ͢Δ ϞϊΠυ ࠷େݶʹؔ͢Δ ܈ (/%ʹΑΔ ࣮ͷڞ༗
࣮ࡍ্ͷҙ w ༗քͳܕ͔͠ϞϊΠυʹͳΒͳ͍ʂʢ࠷େখݩ͕ͳ͍ͱ୯ ҐݩʹͳΒͳ͍ͷͰʣ w ୯Ґݩͷͳ͍܈ʹͳΔ w ܈͔ΒϞϊΠυʹม͠ͳ͍ͱ'PMEBCMF͑ͳ͍ʂ newtype Max a = Max a instance Ord a 㱺 Semigroup (Max a) instance Bounded a 㱺 Monoid (Max a)
࣮ࡍ্ͷҙ 0QUJPO܈ʹ୯ҐݩΛ͚ͯ͠ϞϊΠυʹ͢Δ ʙ()$ɿ.BZCF੍ͱͯ͠.POPJEBΛཁٻʂ newtype Option a = Option (Maybe a) instance Semigroup a 㱺 Monoid (Option a) instance Monoid a 㱺 Monoid (Maybe a)
࣮ࡍ্ͷҙ 0QUJPO܈ʹ୯ҐݩΛ͚ͯ͠ϞϊΠυʹ͢Δ ʙ()$ɿ.BZCF੍ͱͯ͠.POPJEBΛཁٻʂ ()$ʙɿ4FNJHSPVQBʹͳΓɺ0QUJPOෆཁʹʂ newtype Option a = Option (Maybe a) instance Semigroup a 㱺 Monoid (Option a) instance Monoid a 㱺 Monoid (Maybe a) instance Semigroup a 㱺 Monoid (Maybe a)
࣮ࡍ্ͷҙ 0QUJPO܈ʹ୯ҐݩΛ͚ͯ͠ϞϊΠυʹ͢Δ ʙ()$ɿ.BZCF੍ͱͯ͠.POPJEBΛཁٻʂ ()$ʙɿ4FNJHSPVQBʹͳΓɺ0QUJPOෆཁʹʂ ͱ͍͑ɺϙʔλϒϧͳίʔυΛॻ͜͏ͱࢥͬͨΒ0QUJPOʹཔΔ ඞཁ͋Γʜʜɻ newtype Option a = Option (Maybe a) instance Semigroup a 㱺 Monoid (Option a) instance Monoid a 㱺 Monoid (Maybe a) instance Semigroup a 㱺 Monoid (Maybe a)
;FSP$PTU$PFSDJPO w $PFSDJCMF෦දݱ͕ಉ͡ܕಉ࢜Λؔ࿈͚ͮΔܕ੍ w ҰݟܕΫϥε͕ͩɺ࣮ࡍʹ()$͕ίϯύΠϧ࣌ʹใΛੜ ͠ɺউखʹΠϯελϯεΛՃͰ͖ͳ͍ import Data.Coerce (coerce) coerce :: Coercible a b 㱺 a ! b
;FSP$PTU$PFSDJPO w $PFSDJCMF෦දݱ͕ಉ͡ܕಉ࢜Λؔ࿈͚ͮΔܕ੍ w ҰݟܕΫϥε͕ͩɺ࣮ࡍʹ()$͕ίϯύΠϧ࣌ʹใΛੜ ͠ɺউखʹΠϯελϯεΛՃͰ͖ͳ͍ w Data.CoerceͷcoerceؔͰθϩίετͷΩϟετ͕Ͱ͖Δʂ import Data.Coerce (coerce) coerce :: Coercible a b 㱺 a ! b
;FSP$PTU$PFSDJPO w $PFSDJCMF෦දݱ͕ಉ͡ܕಉ࢜Λؔ࿈͚ͮΔܕ੍ w ҰݟܕΫϥε͕ͩɺ࣮ࡍʹ()$͕ίϯύΠϧ࣌ʹใΛੜ ͠ɺউखʹΠϯελϯεΛՃͰ͖ͳ͍ w Data.CoerceͷcoerceؔͰθϩίετͷΩϟετ͕Ͱ͖Δʂ w Ϟδϡʔϧຖʹਪɺcoerceʹσʔλߏஙࢠͷใ͕ඞཁ import Data.Coerce (coerce) coerce :: Coercible a b 㱺 a ! b
ωετܕͷม ͲΜͳίϯςφதͷܕมͰ͖ͯศརʂ ຊʹʁ newtype Down a = Down a instance Ord a 㱺 Ord (Down a) where a ≤ b = b ≤ a data Heap a minView :: Heap a ! Maybe a ٯॱΛೖΕΔ
ωετܕͷม ͲΜͳίϯςφதͷܕมͰ͖ͯศརʂ ຊʹʁ newtype Down a = Down a instance Ord a 㱺 Ord (Down a) where a ≤ b = b ≤ a data Heap a minView :: Heap a ! Maybe a ٯॱΛೖΕΔ ώʔϓ
ωετܕͷม ͲΜͳίϯςφதͷܕมͰ͖ͯศརʂ ຊʹʁ newtype Down a = Down a instance Ord a 㱺 Ord (Down a) where a ≤ b = b ≤ a data Heap a minView :: Heap a ! Maybe a ٯॱΛೖΕΔ ώʔϓ ࠷খݩ0
ωετܕͷม ͲΜͳίϯςφதͷܕมͰ͖ͯศརʂ ຊʹʁ newtype Down a = Down a instance Ord a 㱺 Ord (Down a) where a ≤ b = b ≤ a data Heap a minView :: Heap a ! Maybe a ҙຯతʹ Heap aͱHeap (Down a)Ωϟετग़དྷͳ͍͖ ٯॱΛೖΕΔ ώʔϓ ࠷খݩ0
ͦ͜Ͱ3PMFT w ͜ͷ··ͰDPFSDFͰมग़དྷͯ͠·͏ʂ type role Heap nominal ghci> h = fromList [1,2,3] :: Heap Int ghci> minView (coerce h :: Heap (Down Int)) Just 1 w ͦ͜Ͱ3PMFΛࢦఆɿ Just 3Ͱ͋Δ͖ʂ
ͦ͜Ͱ3PMFT w ͜ͷ··ͰDPFSDFͰมग़དྷͯ͠·͏ʂ type role Heap nominal ghci> h = fromList [1,2,3] :: Heap Int ghci> minView (coerce h :: Heap (Down Int)) Just 1 w ͦ͜Ͱ3PMFΛࢦఆɿ ghci> minView (coerce h :: Heap (Down Int)) error: Couldn't match type ‘Int’ with ‘Down Int’ Just 3Ͱ͋Δ͖ʂ
ͦ͜Ͱ3PMFT w ͜ͷ··ͰDPFSDFͰมग़དྷͯ͠·͏ʂ type role Heap nominal ghci> h = fromList [1,2,3] :: Heap Int ghci> minView (coerce h :: Heap (Down Int)) Just 1 w ͦ͜Ͱ3PMFΛࢦఆɿ ghci> minView (coerce h :: Heap (Down Int)) error: Couldn't match type ‘Int’ with ‘Down Int’ Just 3Ͱ͋Δ͖ʂ w σʔλߏஙࢠΛ࿐ग़͠ͳ͚ΕɺଞͷϞδϡʔϧͰOPNJOBMʹਪ͞ΕΔഺ
ͦ͜Ͱ3PMFT w ͜ͷ··ͰDPFSDFͰมग़དྷͯ͠·͏ʂ type role Heap nominal ghci> h = fromList [1,2,3] :: Heap Int ghci> minView (coerce h :: Heap (Down Int)) Just 1 w ͦ͜Ͱ3PMFΛࢦఆɿ ghci> minView (coerce h :: Heap (Down Int)) error: Couldn't match type ‘Int’ with ‘Down Int’ Just 3Ͱ͋Δ͖ʂ w σʔλߏஙࢠΛ࿐ग़͠ͳ͚ΕɺଞͷϞδϡʔϧͰOPNJOBMʹਪ͞ΕΔഺ w OFXUZQFߏஙࢠͷใΛJNQPSU͠ͳ͍ͱDPFSDFͰ͖ͳ͍
3PMFTৄࡉ w 3PMFʮ͜ͷܕม͜͏͍͏ౕͰ͢ʯ w ࡾछɿrepresentational / nominal / phantom w SFQSʮ͜͜෦දݱ͕ಉ͡ͳΒಉʯ w OPNJOBMʮશʹಉ͡ܕ͡Όͳ͍ͱͩΊʯ w QIBOUPNʮλμͷ০Γʂதʹؔͳ͠ʯ w ()$దٓ࠷ҰൠతͳSPMFΛਪͯ͘͠ΕΔ
3PMFTৄࡉ w 3PMFʮ͜ͷܕม͜͏͍͏ౕͰ͢ʯ w ࡾछɿrepresentational / nominal / phantom w SFQSʮ͜͜෦දݱ͕ಉ͡ͳΒಉʯ w OPNJOBMʮશʹಉ͡ܕ͡Όͳ͍ͱͩΊʯ w QIBOUPNʮλμͷ০Γʂதʹؔͳ͠ʯ w ()$దٓ࠷ҰൠతͳSPMFΛਪͯ͘͠ΕΔ w σʔλܕݻ༗ͷҙຯϢʔβ͔͠Βͳ͍ͷͰɺࠓճͷΑ ͏ͳέʔεͰϥΠϒϥϦ࣮ऀ͕ࢦఆ
3PMFTৄࡉ w 3PMFʮ͜ͷܕม͜͏͍͏ౕͰ͢ʯ w ࡾछɿrepresentational / nominal / phantom w SFQSʮ͜͜෦දݱ͕ಉ͡ͳΒಉʯ w OPNJOBMʮશʹಉ͡ܕ͡Όͳ͍ͱͩΊʯ w QIBOUPNʮλμͷ০Γʂதʹؔͳ͠ʯ w ()$దٓ࠷ҰൠతͳSPMFΛਪͯ͘͠ΕΔ w σʔλܕݻ༗ͷҙຯϢʔβ͔͠Βͳ͍ͷͰɺࠓճͷΑ ͏ͳέʔεͰϥΠϒϥϦ࣮ऀ͕ࢦఆ w OFXUZQFߏஙࢠͷใ͕ͳ͍ͱcoerceෆՄೳ
$PFSDJPO3PMFT·ͱΊ w DPFSDFؔΛ͏ͱ෦දݱͷಉ͡ܕωε τ͍ͯͯ͠θϩίετͰมՄೳ w OFXUZQFͷར༻͕ΑΓ҆શɾ؆୯ʹʂ w ࡉ͔ͳมՄೳੑ3PMFΛࢦఆ੍ͯ͠ޚ w ීஈ3PMFਪ͞ΕΔͷͰͳ͠ w ҙຯ্ม͞ΕΔͱࠔΔʗมग़དྷͯ΄͠ ͍ͷࣗͰࢦఆ
;FSP$PTU$PFSDJPOલ࢙ɿ (/%ͷड w (FOFSBMJ[FE/FXUZQF%FSJWJOH (/% ()$ ͷࠒʹطʹ͋ͬͨ w ͜ͷࠒ()$ܕγεςϜ͕߇͑Ͱɺશͯ ্ख͘ճ͍ͬͯͨ w ͦͷޙɺܕ("%5TͳͲ͕ೖΓʜʜ w ؾ͘ͱ(/%ෆ݈શʹͳ͍ͬͯͨʂ
(/%ෆ݈શ newtype Id1 a = MkId1 a newtype Id2 a = MkId2 (Id1 a) deriving (UnsafeCast b) type family Discern a b type instance Discern (Id1 a) b = a type instance Discern (Id2 a) b = b class UnsafeCast to from where unsafe :: from ! Discern from to instance UnsafeCast b (Id1 a) where unsafe (MkId1 x) = x unsafeCoerce :: a ! b unsafeCoerce x = unsafe (MkId2 (MkId1 x))
(/%ෆ݈શ newtype Id1 a = MkId1 a newtype Id2 a = MkId2 (Id1 a) deriving (UnsafeCast b) type family Discern a b type instance Discern (Id1 a) b = a type instance Discern (Id2 a) b = b class UnsafeCast to from where unsafe :: from ! Discern from to instance UnsafeCast b (Id1 a) where unsafe (MkId1 x) = x unsafeCoerce :: a ! b unsafeCoerce x = unsafe (MkId2 (MkId1 x)) (/%
(/%ෆ݈શ newtype Id1 a = MkId1 a newtype Id2 a = MkId2 (Id1 a) deriving (UnsafeCast b) type family Discern a b type instance Discern (Id1 a) b = a type instance Discern (Id2 a) b = b class UnsafeCast to from where unsafe :: from ! Discern from to instance UnsafeCast b (Id1 a) where unsafe (MkId1 x) = x unsafeCoerce :: a ! b unsafeCoerce x = unsafe (MkId2 (MkId1 x)) (/% ҙͷܕؒͷΩϟετʂ
(/%ෆ݈શ newtype Id1 a = MkId1 a newtype Id2 a = MkId2 (Id1 a) deriving (UnsafeCast b) type family Discern a b type instance Discern (Id1 a) b = a type instance Discern (Id2 a) b = b class UnsafeCast to from where unsafe :: from ! Discern from to instance UnsafeCast b (Id1 a) where unsafe (MkId1 x) = x unsafeCoerce :: a ! b unsafeCoerce x = unsafe (MkId2 (MkId1 x))
(/%ෆ݈શ newtype Id1 a = MkId1 a newtype Id2 a = MkId2 (Id1 a) deriving (UnsafeCast b) type family Discern a b type instance Discern (Id1 a) b = a type instance Discern (Id2 a) b = b class UnsafeCast to from where unsafe :: from ! Discern from to instance UnsafeCast b (Id1 a) where unsafe (MkId1 x) = x unsafeCoerce :: a ! b unsafeCoerce x = unsafe (MkId2 (MkId1 x)) (/%DPFSDF Λܦ༝͢ΔΑ͏ʹ
(/%ෆ݈શ newtype Id1 a = MkId1 a newtype Id2 a = MkId2 (Id1 a) deriving (UnsafeCast b) type family Discern a b type instance Discern (Id1 a) b = a type instance Discern (Id2 a) b = b class UnsafeCast to from where unsafe :: from ! Discern from to instance UnsafeCast b (Id1 a) where unsafe (MkId1 x) = x unsafeCoerce :: a ! b unsafeCoerce x = unsafe (MkId2 (MkId1 x)) (/%DPFSDF Λܦ༝͢ΔΑ͏ʹ ()$ݡ͍ͷͰ BΛOPNJOBMʹਪ
(/%ෆ݈શ newtype Id1 a = MkId1 a newtype Id2 a = MkId2 (Id1 a) deriving (UnsafeCast b) type family Discern a b type instance Discern (Id1 a) b = a type instance Discern (Id2 a) b = b class UnsafeCast to from where unsafe :: from ! Discern from to instance UnsafeCast b (Id1 a) where unsafe (MkId1 x) = x unsafeCoerce :: a ! b unsafeCoerce x = unsafe (MkId2 (MkId1 x)) (/%DPFSDF Λܦ༝͢ΔΑ͏ʹ ()$ݡ͍ͷͰ BΛOPNJOBMʹਪ 3FKFDU
ྫɿ*EͷϞϊΠυߏ w લʹݟͨΑ͏ʹɺ8PSEͷϞϊΠυ࣮ෳ͋Δ w *EͰʮҰ൪৽͍͠*E ࠷େͷ*E ΛબͿʯԋࢉΛϞϊΠυԋ ࢉͱ͍͔ͯͨͬͨ͠ͱ͢Δ {-# LANGUAGE DerivingVia #-} newtype Id = MkId Word deriving (Semigroup, Monoid) via Max Word
ྫɿ*EͷϞϊΠυߏ w લʹݟͨΑ͏ʹɺ8PSEͷϞϊΠυ࣮ෳ͋Δ w *EͰʮҰ൪৽͍͠*E ࠷େͷ*E ΛબͿʯԋࢉΛϞϊΠυԋ ࢉͱ͍͔ͯͨͬͨ͠ͱ͢Δ w Max WordIdͱಉҰදݱɺ NBY
ʹؔ͠ϞϊΠυ {-# LANGUAGE DerivingVia #-} newtype Id = MkId Word deriving (Semigroup, Monoid) via Max Word
ྫɿ*EͷϞϊΠυߏ w લʹݟͨΑ͏ʹɺ8PSEͷϞϊΠυ࣮ෳ͋Δ w *EͰʮҰ൪৽͍͠*E ࠷େͷ*E ΛબͿʯԋࢉΛϞϊΠυԋ ࢉͱ͍͔ͯͨͬͨ͠ͱ͢Δ w Max WordIdͱಉҰදݱɺ NBY
ʹؔ͠ϞϊΠυ w %FSJWJOH7JB͜ͷ࣮Λࣗಈతʹ*Eʹ্࣋ͪ͛ͯ͘ΕΔʂ {-# LANGUAGE DerivingVia #-} newtype Id = MkId Word deriving (Semigroup, Monoid) via Max Word
newtype SameRepAs a b = SameRepAs { runSameRepAs :: a } type Iso a b = (Generic a, Generic b, Coercible (Rep a ()) (Rep b ())) instance (Semigroup b, Iso a b) 㱺 Semigroup (SameRepAs a b) where SameRepAs a <> SameRepAs b = ... instance (Monoid b, Iso a b) 㱺 Monoid (SameRepAs a b) where mempty = SameRepAs $ toA mempty where toA :: b -> a toA = to . (coerce :: Rep b () -> Rep a ()) . from
·ͱΊ w OFXUZQFͷ༻్ࡾͭ w ࣮ͷӅṭʗ࣮ͷڞ༗ʗ࣮ͷબ w %BUB$PFSDFΛ͏ͱ෦දݱ͕ಉ͡ܕಉ࢜Λθϩ ίετͰΩϟετՄೳ w OFXUZQFͷग़ੈ͔͜͜Β࢝·ͬͨ w ෳ߹ܕ3PMFਪɾḼऍͰదʹѻ͑Δ w ()$͔Β%FSJWJOH7JBͰOFXUZQFʹΑΓ ಋग़અΛΧελϚΠζՄೳʹʂ
ࢀߟจݙ 1. J. Breitner, R. A. Eisenberg, S. P. Jones and S. Weirich, Safe Zero-cost Coercions for Haskell, ICFP 2014. 2. Baldur Blöndal, Andres Löh and Ryan Scott, Deriving Via: How to Turn Hand-Written Instances into an Anti-Pattern, ICFP18.
"OZ2VFTUJPO w OFXUZQFͷ༻్ࡾͭ w ࣮ͷӅṭʗ࣮ͷڞ༗ʗ࣮ͷબ w %BUB$PFSDFΛ͏ͱ෦දݱ͕ಉ͡ܕಉ࢜Λθϩ ίετͰΩϟετՄೳ w OFXUZQFͷग़ੈ͔͜͜Β࢝·ͬͨ w ෳ߹ܕ3PMFਪɾḼऍͰదʹѻ͑Δ w ()$͔Β%FSJWJOH7JBͰOFXUZQFʹΑΓ ಋग़અΛΧελϚΠζՄೳʹʂ
7 ↵ M ↵ ' [ · ] 9! 7QH/JT ' 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ࣗ༝Ϟφυͷීวੑ w ࣗ༝ϞϊΠυവखͷఆ͔ٛΒ w α͔ΒGαͷೖࣹ w G͕വखͰ͋Δ͜ͱ w Gα͕ࣗϞϊΠυͰ͋Δࣄ w ʜʜΛআ͘ͱ'PMEBCMFʹͳΔ w ࡞Δํ๏͕ͳ͍͍ͯ͘ w Hask ݍͷവखͱݶΒͳ͍ w ϞϊΠυͱݶΒͳ͍ɺ୯ͳΔ ߏͰΈࠐΈ͍ͨ
'PMEBCMFͱ5SBWFSTBCMF w 5SBWFSTBCMFࣗ༝ϞϊΠυͱ'PMEBCMFͷதؒ w USBWFSTFࣗ༝ϞϊΠυͳΒ؆୯ʹॻ͚Δ class (Pointed f, Foldable f, ∀a. Monoid (f a)) 㱺 FreeMonoid f instance (Pointed f, Foldable f, ∀a. Monoid (f a)) 㱺 FreeMonoid f fold :: (FreeMonoid f) 㱺 (a ! b ! b) ! b ! f a ! b fold g n xs = appEndo (foldMap (Endo . g) xs) n traverseF :: (FreeMonoid f, Applicative t) 㱺 (a ! t b) ! f a ! t (f b) traverseF f = fold (λa tb ! (<>) <$> (iota <$> f a) <*> tb) (pure mempty) ͔ΒೖΔ QuantifiedConstraints $PNQMFUFDPEFɿsrc/Data/Foldable/Monoid.hs
konn
shumpei0111
poteboy
_tanako
gmvalentino8
tapompom
akarin
tomokusaba
tsukushi
chobishiba
daisukeshinoku
iimokoy
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brad_frost
tammielis
swwweet
mojombo
tenderlove
mongodb
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deanohume
matthewcrist
hursman