本当はすごい newtype

ຊ౰͸͍͢͝ newtype !NS@LPOO IUUQTLPOOTBODPN 4MJEFTBSFBWBJMBCMFBUhttp://bit.ly/derivia  &YBNQMFDPEFTBSFPO(JU)VCkonn/newtype-talk-five

ࣗݾ঺հ w ੴҪେւʢ!NS@LPOOʣ ͍ ͠ ͍ ͻ Ζ Έ w
਺ֶઐ߈ത࢜՝ఔ೥ w ਺ཧ࿦ཧֶͱܭࢉػՊֶͱ͔ w ؾ͚ͮ͹)BTLFMMྺ೥

ຊ౰͸͍͢͝newtype 3PMFT 4BGF[FSPDPTUDPFSDJPOT BOE%FSJWJOH7JB ʙ.POPJE&'PMEBCMF΋͋ΔΑʙ ͍͢͝ʂ

newtype

newtype newtype Foo α = Bar α newtype Id =
MkId Word

newtype w ͨͩҰͭͷߏஙࢠͱϑΟʔϧυΛ࣋ͭσʔλܕ newtype Foo α = Bar α newtype
Id = MkId Word

newtype w ͨͩҰͭͷߏஙࢠͱϑΟʔϧυΛ࣋ͭσʔλܕ w ಺෦දݱ͕།ҰͷϑΟʔϧυͷܕͱಉҰ newtype Foo α = Bar
α newtype Id = MkId Word

newtype w ͨͩҰͭͷߏஙࢠͱϑΟʔϧυΛ࣋ͭσʔλܕ w ಺෦දݱ͕།ҰͷϑΟʔϧυͷܕͱಉҰ w ܕͷ্Ͱ͸۠ผ͞ΕΔ͕ɺϝϞϦ্Ͱͷදݱ ͸ಉҰͰɺϑΟʔϧυ΋ʮਖ਼֨ʯʹධՁ͞ΕΔ newtype Foo
α = Bar α newtype Id = MkId Word

ॳ৺ऀ͋Δ͋Δ

ॳ৺ऀ͋Δ͋Δ ʮ;ͭ͏ͷdataએݴͱԿ͕ҧ͏ͷʁʯ

ॳ৺ऀ͋Δ͋Δ ʮ;ͭ͏ͷdataએݴͱԿ͕ҧ͏ͷʁʯ ʮ಺෦දݱ͕ಉ͔ͩ͡Βޮ཰తͩΑʯ

ॳ৺ऀ͋Δ͋Δ ʮ;ͭ͏ͷdataએݴͱԿ͕ҧ͏ͷʁʯ ʮ಺෦දݱ͕ಉ͔ͩ͡Βޮ཰తͩΑʯ ʮޮ཰·ͩͲ͏Ͱ΋͍͍͠dataͰ͍͍΍ʯ

ॳ৺ऀ͋Δ͋Δ ʮ;ͭ͏ͷdataએݴͱԿ͕ҧ͏ͷʁʯ ʮ಺෦දݱ͕ಉ͔ͩ͡Βޮ཰తͩΑʯ ʮޮ཰·ͩͲ͏Ͱ΋͍͍͠dataͰ͍͍΍ʯ ʮࠓ͸VOQBDLTUSJDUpFME΋͋Δ͠ʜʜʯ

ͦΜͳ͜ͱ͸ͳ͍

newtypeͷͭͷ༻్

newtypeͷͭͷ༻్ ࣮૷ͷӅṭ module Data.Id (Id ()) where newtype Id =
MkId Word

MkId Word ܕͷ্Ͱ͸۠ผ Ͱ΋಺෦తʹ͸Word

MkId Word ܕͷ্Ͱ͸۠ผ Ͱ΋಺෦తʹ͸Word ֎෦ʹ͸σʔλߏஙࢠ MkId͸Ӆṭ

newtypeͷͭͷ༻్ ࣮૷ͷӅṭ ࣮૷ͷڞ༗ module Data.Id (Id ()) where newtype Id
= MkId Word ܕͷ্Ͱ͸۠ผ Ͱ΋಺෦తʹ͸Word {-# LANGUAGE GeneralizedNewtypeDeriving #-} newtype Id = MkId Word deriving (Num, Eq) ֎෦ʹ͸σʔλߏஙࢠ MkId͸Ӆṭ

= MkId Word ܕͷ্Ͱ͸۠ผ Ͱ΋಺෦తʹ͸Word {-# LANGUAGE GeneralizedNewtypeDeriving #-} newtype Id = MkId Word deriving (Num, Eq) ຊདྷ͸ಋग़ෆՄͰ΋ Wordͷ࣮૷͕ڞ༗Ͱ͖Δ ֎෦ʹ͸σʔλߏஙࢠ MkId͸Ӆṭ

= MkId Word ܕͷ্Ͱ͸۠ผ Ͱ΋಺෦తʹ͸Word {-# LANGUAGE GeneralizedNewtypeDeriving #-} newtype Id = MkId Word deriving (Num, Eq) ຊདྷ͸ಋग़ෆՄͰ΋ Wordͷ࣮૷͕ڞ༗Ͱ͖Δ %FSJWJOH7JB ͰߋʹਐԽ ֎෦ʹ͸σʔλߏஙࢠ MkId͸Ӆṭ

newtypeͷͭͷ༻్ ࣮૷ͷӅṭ ࣮૷ͷڞ༗ ࣮૷ͷબ୒ module Data.Id (Id ()) where newtype
Id = MkId Word ܕͷ্Ͱ͸۠ผ Ͱ΋಺෦తʹ͸Word {-# LANGUAGE GeneralizedNewtypeDeriving #-} newtype Id = MkId Word deriving (Num, Eq) ຊདྷ͸ಋग़ෆՄͰ΋ Wordͷ࣮૷͕ڞ༗Ͱ͖Δ %FSJWJOH7JB ͰߋʹਐԽ ֎෦ʹ͸σʔλߏஙࢠ MkId͸Ӆṭ

newtypeͷͭͷ༻్ ࣮૷ͷӅṭ ࣮૷ͷڞ༗ ࣮૷ͷબ୒ {-# LANGUAGE GeneralizedNewtypeDeriving #-} newtype Id
= MkId Word deriving (Num, Eq) ຊདྷ͸ಋग़ෆՄͰ΋ Wordͷ࣮૷͕ڞ༗Ͱ͖Δ %FSJWJOH7JB ͰߋʹਐԽ module Data.Id (Id ()) where newtype Id = MkId Word ܕͷ্Ͱ͸۠ผ Ͱ΋಺෦తʹ͸Word ֎෦ʹ͸σʔλߏஙࢠ MkId͸Ӆṭ

࣮૷ͷબ୒

࣮૷ͷબ୒ .POPJEͱ'PMEBCMFΛྫʹ

ྫ୊ɿϦετͷ૸ࠪ ໰ ੔਺ͷϦετ͕༩͑ΒΕͨ࣌ɺͦͷ࠷େ஋ͱ ૯࿨ΛҰճͷ૸ࠪͰٻΊΑɻ ˞foldl͓Αͼfoldsύοέʔδ͸Έͳ͔ͬͨࣄʹ͍ͯͩ͘͠͞

ղ౴ྫ

ղ౴ྫ ৞ΈࠐΈͩʂ

ղ౴ྫ ৞ΈࠐΈͩʂ aggregate :: [ℕ] ! (Maybe ℕ, ℕ) aggregate
= foldr (λ a (m, s) ! (Just a `max` m, a + s)) (Nothing, 0) ˞ℕ͸*OUFHFSͷུͩͱࢥ͍ͬͯͩ͘͞

= foldr (λ a (m, s) ! (Just a `max` m, a + s)) (Nothing, 0) Կ͔ࣅͨΑ͏ͳ͜ͱ΍ͬͯΜͳʜʜ ˞ℕ͸*OUFHFSͷུͩͱࢥ͍ͬͯͩ͘͞

= foldr (λ a (m, s) ! (Just a `max` m, a + s)) (Nothing, 0) Կ͔ࣅͨΑ͏ͳ͜ͱ΍ͬͯΜͳʜʜ ม׵ʴೋ߲ԋࢉ ˞ℕ͸*OUFHFSͷུͩͱࢥ͍ͬͯͩ͘͞

= foldr (λ a (m, s) ! (Just a `max` m, a + s)) (Nothing, 0) Կ͔ࣅͨΑ͏ͳ͜ͱ΍ͬͯΜͳʜʜ ม׵ʴೋ߲ԋࢉ ୯Ґݩ ˞ℕ͸*OUFHFSͷུͩͱࢥ͍ͬͯͩ͘͞

= foldr (λ a (m, s) ! (Just a `max` m, a + s)) (Nothing, 0) Կ͔ࣅͨΑ͏ͳ͜ͱ΍ͬͯΜͳʜʜ .POPJEͩʂ ม׵ʴೋ߲ԋࢉ ୯Ґݩ ˞ℕ͸*OUFHFSͷུͩͱࢥ͍ͬͯͩ͘͞

.POPJE w ࠨӈͷผͳ͘ܭࢉͰ͖ͯɺ୯Ґݩ͕͋Δ΍ͭ • max ΋ + ΋…… • ࠨ͔Β΍ͬͯ΋ӈ͔Β΍ͬͯ΋ಉ͡
• Nothing (࠷େ஋ແ͠) ͱ 0 ͕୯Ґݩ (ɛ) • ϞϊΠυม׵ʴ৞ΈࠐΈ ⤳ Foldable! x ∙ (y ∙ z) = (x ∙ y) ∙ z x ∙ ε = x = ε ∙ x

'PMEBCMFܕΫϥε class Foldable t where foldMap :: Monoid m 㱺
(a ! m) ! t a ! m …

'PMEBCMFܕΫϥε class Foldable t where foldMap :: Monoid m 㱺
(a ! m) ! t a ! m … ϞϊΠυʹม׵  ࠨ͔Β৞ΈࠐΈ

'PMEBCMFܕΫϥε ͜ͷ࿮૊ΈʹNBY ΛམͱͤΕ͹Αͦ͞͏ class Foldable t where foldMap ::
Monoid m 㱺 (a ! m) ! t a ! m … ϞϊΠυʹม׵  ࠨ͔Β৞ΈࠐΈ

'PMEBCMFܕΫϥε ͜ͷ࿮૊ΈʹNBY ΛམͱͤΕ͹Αͦ͞͏ Monoid WordΠϯελϯε͸ߴʑҰ͔ͭ͠ॻ͚ͳ͍ʜʜ class Foldable t where
foldMap :: Monoid m 㱺 (a ! m) ! t a ! m … ϞϊΠυʹม׵  ࠨ͔Β৞ΈࠐΈ

'PMEBCMFܕΫϥε ͜ͷ࿮૊ΈʹNBY ΛམͱͤΕ͹Αͦ͞͏ Monoid WordΠϯελϯε͸ߴʑҰ͔ͭ͠ॻ͚ͳ͍ʜʜ ͦ͜ͰnewtypeʹΑΔ࣮૷ͷબ୒ʂ class Foldable t
where foldMap :: Monoid m 㱺 (a ! m) ! t a ! m … ϞϊΠυʹม׵  ࠨ͔Β৞ΈࠐΈ

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

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

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  ൒܈

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༗

࣮ࡍ্ͷ஫ҙ w ༗քͳܕ͔͠ϞϊΠυʹͳΒͳ͍ʂʢ࠷େখݩ͕ͳ͍ͱ୯ ҐݩʹͳΒͳ͍ͷͰʣ w ୯Ґݩͷͳ͍൒܈ʹ͸ͳΔ w ൒܈͔ΒϞϊΠυʹม׵͠ͳ͍ͱ'PMEBCMF͸࢖͑ͳ͍ʂ newtype Max
a = Max a instance Ord a 㱺 Semigroup (Max a) instance Bounded a 㱺 Monoid (Max a)

࣮ࡍ্ͷ஫ҙ newtype Option a = Option (Maybe a) instance Semigroup
a 㱺 Monoid (Option a)

࣮ࡍ্ͷ஫ҙ 0QUJPO͸൒܈ʹ୯ҐݩΛ෇͚଍ͯ͠ϞϊΠυʹ͢Δ newtype Option a = Option (Maybe a) instance
Semigroup a 㱺 Monoid (Option a)

࣮ࡍ্ͷ஫ҙ 0QUJPO͸൒܈ʹ୯ҐݩΛ෇͚଍ͯ͠ϞϊΠυʹ͢Δ ʙ()$ɿ.BZCF͸੍໿ͱͯ͠.POPJEBΛཁٻʂ newtype Option a = Option (Maybe a)
instance Semigroup a 㱺 Monoid (Option a) instance Monoid a 㱺 Monoid (Maybe a)

࣮ࡍ্ͷ஫ҙ 0QUJPO͸൒܈ʹ୯ҐݩΛ෇͚଍ͯ͠ϞϊΠυʹ͢Δ ʙ()$ɿ.BZCF͸੍໿ͱͯ͠.POPJEBΛཁٻʂ ()$ʙɿ4FNJHSPVQBʹͳΓɺ0QUJPO͸ෆཁʹʂ 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)

࣮ࡍ্ͷ஫ҙ 0QUJPO͸൒܈ʹ୯ҐݩΛ෇͚଍ͯ͠ϞϊΠυʹ͢Δ ʙ()$ɿ.BZCF͸੍໿ͱͯ͠.POPJEBΛཁٻʂ ()$ʙɿ4FNJHSPVQBʹͳΓɺ0QUJPO͸ෆཁʹʂ ͱ͸͍͑ɺϙʔλϒϧͳίʔυΛॻ͜͏ͱࢥͬͨΒ0QUJPOʹཔΔ 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)

'PMEBCMF/FXUZQF൛ import Control.Arrow aggregate :: [ℕ] ! (Maybe ℕ, ℕ)
aggregate = fmap getMax *** getSum ◦ foldMap (Just . Max &&& Sum)

'PMEBCMF/FXUZQF൛ ਵ෼͖ͬ͢Γʂ import Control.Arrow aggregate :: [ℕ] ! (Maybe ℕ,
ℕ) aggregate = fmap getMax *** getSum ◦ foldMap (Just . Max &&& Sum)

'PMEBCMF/FXUZQF൛ ਵ෼͖ͬ͢Γʂ Ͱ΋Ұʑ.BY 4VNΛണ͢ͷ͸μϧ͍ͳ͋ʜʜωε τͯ͠Δ͠ʜʜ import Control.Arrow aggregate :: [ℕ]
! (Maybe ℕ, ℕ) aggregate = fmap getMax *** getSum ◦ foldMap (Just . Max &&& Sum)

'PMEBCMF/FXUZQF൛ ਵ෼͖ͬ͢Γʂ Ͱ΋Ұʑ.BY 4VNΛണ͢ͷ͸μϧ͍ͳ͋ʜʜωε τͯ͠Δ͠ʜʜ import Control.Arrow aggregate :: [ℕ]
! (Maybe ℕ, ℕ) aggregate = fmap getMax *** getSum ◦ foldMap (Just . Max &&& Sum) ‎;FSP$PTU$PFSDJPOT

4BGF;FSP$PTU $PFSDJPOTBOE3PMFT

4BGF;FSP$PTU $PFSDJPOTBOE3PMFT [1] Breitner, Eisenberg, Peyton Jones and Weirich, 2014
ʙOFXUZQFͷະདྷΛ੾Γ୓͍ͨେൃ໌ʙ

೥Ҏલͷ )BTLFMMFSͷ΅΍͖ɿ

͔ͨ͠ʹ࣮૷ͷબ୒ʹ OFXUZQF͸ศར͚ͩͲ͞ʜʜ

݁ہҰຕҰຕണͯ͠  ͍͔ͳ͍ͱ͍͚ͳ͍͠

ͦ͏͢Δͱޮ཰͸  ѱ͍͡ΌΜ

҆શ͔ͩΒVOTBGF$PFSDF ࢖͏ख΋͋Δ͚Ͳ

͋Μ·៉ྷ͡Όͳ͍ʜʜ

͔͠͠

ɹ೥ɺ OFXUZQFʹ ֵ໋͕ى͖ͨ

;FSP$PTU$PFSDJPO

;FSP$PTU$PFSDJPO import Data.Coerce (coerce) coerce :: Coercible a b 㱺
a ! b

;FSP$PTU$PFSDJPO w $PFSDJCMF͸಺෦දݱ͕ಉ͡ܕಉ࢜Λؔ࿈͚ͮΔܕ੍໿ import Data.Coerce (coerce) coerce :: Coercible a
b 㱺 a ! b

;FSP$PTU$PFSDJPO w $PFSDJCMF͸಺෦දݱ͕ಉ͡ܕಉ࢜Λؔ࿈͚ͮΔܕ੍໿ w ҰݟܕΫϥε͕ͩɺ࣮ࡍʹ͸()$͕ίϯύΠϧ࣌ʹ৘ใΛੜ੒ ͠ɺউखʹΠϯελϯεΛ௥ՃͰ͖ͳ͍ import Data.Coerce (coerce) coerce
:: Coercible a b 㱺 a ! b

;FSP$PTU$PFSDJPO w $PFSDJCMF͸಺෦දݱ͕ಉ͡ܕಉ࢜Λؔ࿈͚ͮΔܕ੍໿ w ҰݟܕΫϥε͕ͩɺ࣮ࡍʹ͸()$͕ίϯύΠϧ࣌ʹ৘ใΛੜ੒ ͠ɺউखʹΠϯελϯεΛ௥ՃͰ͖ͳ͍ w Data.Coerceͷcoerceؔ਺ͰθϩίετͷΩϟετ͕Ͱ͖Δʂ import Data.Coerce
(coerce) coerce :: Coercible a b 㱺 a ! b

;FSP$PTU$PFSDJPO w $PFSDJCMF͸಺෦දݱ͕ಉ͡ܕಉ࢜Λؔ࿈͚ͮΔܕ੍໿ w ҰݟܕΫϥε͕ͩɺ࣮ࡍʹ͸()$͕ίϯύΠϧ࣌ʹ৘ใΛੜ੒ ͠ɺউखʹΠϯελϯεΛ௥ՃͰ͖ͳ͍ w Data.Coerceͷcoerceؔ਺ͰθϩίετͷΩϟετ͕Ͱ͖Δʂ w Ϟδϡʔϧຖʹਪ࿦ɺcoerceʹ͸σʔλߏஙࢠͷ৘ใ͕ඞཁ
import Data.Coerce (coerce) coerce :: Coercible a b 㱺 a ! b

͜ΕΛ࢖͑͹ʜʜ import Control.Arrow aggregate :: [ℕ] ! (Maybe ℕ, ℕ)
aggregate = fmap getMax *** getSum ◦ foldMap (Just . Max &&& Sum)

͜͏ͳΓ·͢ import Control.Arrow import Data.Coerce aggregate :: [ℕ] ! (Maybe
ℕ, ℕ) aggregate = coerce ◦ foldMap (Just . Max &&& Sum)

ℕ, ℕ) aggregate = coerce ◦ foldMap (Just . Max &&& Sum) ω ε τ ܕ ΋ θ ϩ ί ε τ Ͱ ม ׵ ʂ

ℕ, ℕ) aggregate = coerce ◦ foldMap (Just . Max &&& Sum) coerce :: (Maybe (Max ), Sum ) → (Maybe , ) ω ε τ ܕ ΋ θ ϩ ί ε τ Ͱ ม ׵ ʂ

ℕ, ℕ) aggregate = coerce ◦ foldMap (Just . Max &&& Sum) w θϩίετͳͷͰɺ૸ࠪ͸Ұճ͚ͩ coerce :: (Maybe (Max ), Sum ) → (Maybe , ) ω ε τ ܕ ΋ θ ϩ ί ε τ Ͱ ม ׵ ʂ

ℕ, ℕ) aggregate = coerce ◦ foldMap (Just . Max &&& Sum) w θϩίετͳͷͰɺ૸ࠪ͸Ұճ͚ͩ w લޙͷܕ͕͔ͬ͠Γܾ·͍ͬͯΔͷͰDPFSDFҰൃͰऴྃ coerce :: (Maybe (Max ), Sum ) → (Maybe , ) ω ε τ ܕ ΋ θ ϩ ί ε τ Ͱ ม ׵ ʂ

ωετܕͷม׵

ωετܕͷม׵ ͲΜͳίϯςφதͷܕ΋ม׵Ͱ͖ͯศརʂ

ωετܕͷม׵ ͲΜͳίϯςφதͷܕ΋ม׵Ͱ͖ͯศརʂ ຊ౰ʹʁ

ωετܕͷม׵ ͲΜͳίϯςφதͷܕ΋ม׵Ͱ͖ͯศརʂ ຊ౰ʹʁ 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

Ord a 㱺 Ord (Down a) where a ≤ b = b ≤ a data Heap a minView :: Heap a ! Maybe a ٯॱΛೖΕΔ

Ord a 㱺 Ord (Down a) where a ≤ b = b ≤ a data Heap a minView :: Heap a ! Maybe a ٯॱΛೖΕΔ ώʔϓ

Ord a 㱺 Ord (Down a) where a ≤ b = b ≤ a data Heap a minView :: Heap a ! Maybe a ٯॱΛೖΕΔ ώʔϓ ࠷খݩ0

Ord a 㱺 Ord (Down a) where a ≤ b = b ≤ a data Heap a minView :: Heap a ! Maybe a ҙຯ࿦తʹ Heap aͱHeap (Down a)͸Ωϟετग़དྷͳ͍΂͖ ٯॱΛೖΕΔ ώʔϓ ࠷খݩ0

ͦ͜Ͱ3PMFT

ͦ͜Ͱ3PMFT w ͜ͷ··Ͱ͸DPFSDFͰม׵ग़དྷͯ͠·͏ʂ

ͦ͜Ͱ3PMFT w ͜ͷ··Ͱ͸DPFSDFͰม׵ग़དྷͯ͠·͏ʂ ghci> h = fromList [1,2,3] :: Heap
Int ghci> minView (coerce h :: Heap (Down Int)) Just 1

Int ghci> minView (coerce h :: Heap (Down Int)) Just 1 Just 3Ͱ͋Δ΂͖ʂ

Int ghci> minView (coerce h :: Heap (Down Int)) Just 1 w ͦ͜Ͱ3PMFΛࢦఆɿ Just 3Ͱ͋Δ΂͖ʂ

ͦ͜Ͱ3PMFT w ͜ͷ··Ͱ͸DPFSDFͰม׵ग़དྷͯ͠·͏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 3Ͱ͋Δ΂͖ʂ

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 3Ͱ͋Δ΂͖ʂ

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 3Ͱ͋Δ΂͖ʂ w σʔλߏஙࢠΛ࿐ग़͠ͳ͚Ε͹ɺଞͷϞδϡʔϧͰ͸OPNJOBMʹਪ࿦͞ΕΔഺ

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 3Ͱ͋Δ΂͖ʂ w σʔλߏஙࢠΛ࿐ग़͠ͳ͚Ε͹ɺଞͷϞδϡʔϧͰ͸OPNJOBMʹਪ࿦͞ΕΔഺ w OFXUZQFߏஙࢠͷ৘ใΛJNQPSU͠ͳ͍ͱDPFSDFͰ͖ͳ͍

3PMFTৄࡉ

3PMFTৄࡉ w 3PMFʮ͜ͷܕม਺͸͜͏͍͏ౕͰ͢ʯ

3PMFTৄࡉ w 3PMFʮ͜ͷܕม਺͸͜͏͍͏ౕͰ͢ʯ w ࡾछɿrepresentational / nominal / phantom

3PMFTৄࡉ w 3PMFʮ͜ͷܕม਺͸͜͏͍͏ౕͰ͢ʯ w ࡾछɿrepresentational / nominal / phantom w
SFQSʮ͜͜͸಺෦දݱ͕ಉ͡ͳΒಉ஋ʯ

SFQSʮ͜͜͸಺෦දݱ͕ಉ͡ͳΒಉ஋ʯ w OPNJOBMʮ׬શʹಉ͡ܕ͡Όͳ͍ͱͩΊʯ

SFQSʮ͜͜͸಺෦දݱ͕ಉ͡ͳΒಉ஋ʯ w OPNJOBMʮ׬શʹಉ͡ܕ͡Όͳ͍ͱͩΊʯ w QIBOUPNʮλμͷ০Γʂத਎ʹؔ܎ͳ͠ʯ

SFQSʮ͜͜͸಺෦දݱ͕ಉ͡ͳΒಉ஋ʯ w OPNJOBMʮ׬શʹಉ͡ܕ͡Όͳ͍ͱͩΊʯ w QIBOUPNʮλμͷ০Γʂத਎ʹؔ܎ͳ͠ʯ w ()$͸దٓ࠷΋ҰൠతͳSPMFΛਪ࿦ͯ͘͠ΕΔ

SFQSʮ͜͜͸಺෦දݱ͕ಉ͡ͳΒಉ஋ʯ w OPNJOBMʮ׬શʹಉ͡ܕ͡Όͳ͍ͱͩΊʯ w QIBOUPNʮλμͷ০Γʂத਎ʹؔ܎ͳ͠ʯ w ()$͸దٓ࠷΋ҰൠతͳSPMFΛਪ࿦ͯ͘͠ΕΔ w σʔλܕݻ༗ͷҙຯ࿦͸Ϣʔβ͔͠஌Βͳ͍ͷͰɺࠓճͷΑ ͏ͳέʔεͰ͸ϥΠϒϥϦ࣮૷ऀ͕ࢦఆ

SFQSʮ͜͜͸಺෦දݱ͕ಉ͡ͳΒಉ஋ʯ w OPNJOBMʮ׬શʹಉ͡ܕ͡Όͳ͍ͱͩΊʯ w QIBOUPNʮλμͷ০Γʂத਎ʹؔ܎ͳ͠ʯ w ()$͸దٓ࠷΋ҰൠతͳSPMFΛਪ࿦ͯ͘͠ΕΔ w σʔλܕݻ༗ͷҙຯ࿦͸Ϣʔβ͔͠஌Βͳ͍ͷͰɺࠓճͷΑ ͏ͳέʔεͰ͸ϥΠϒϥϦ࣮૷ऀ͕ࢦఆ w OFXUZQFߏஙࢠͷ৘ใ͕ͳ͍ͱcoerce͸ෆՄೳ

$PFSDJPO3PMFT·ͱΊ w DPFSDFؔ਺Λ࢖͏ͱ಺෦දݱͷಉ͡ܕ͸ωε τ͍ͯͯ͠΋θϩίετͰม׵Մೳ w OFXUZQFͷར༻͕ΑΓ҆શɾ؆୯ʹʂ w ࡉ͔ͳม׵Մೳੑ͸3PMFΛࢦఆ੍ͯ͠ޚ w ීஈ͸3PMF͸ਪ࿦͞ΕΔͷͰ໰୊ͳ͠
w ҙຯ࿦্ม׵͞ΕΔͱࠔΔʗม׵ग़དྷͯ΄͠ ͍΋ͷ͸ࣗ෼Ͱࢦఆ

͜Ε͜Εɺ  ͜͏͍͏ͷཉ͔ͬͨ͠

͔ͯͳΜͰͳ͔ͬͨͷʁ

;FSP$PTU$PFSDJPOલ࢙ɿ (/%ͷड೉ w (FOFSBMJ[FE/FXUZQF%FSJWJOH (/% ͸()$ ͷࠒʹ͸طʹ͋ͬͨ w ͜ͷࠒ͸()$͸ܕγεςϜ͕߇͑໨Ͱɺશͯ ͸্ख͘ճ͍ͬͯͨ
w ͦͷޙɺܕ଒΍("%5TͳͲ͕ೖΓʜʜ w ؾ෇͘ͱ(/%͸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))

= 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)) (/%

= 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

͜Ε͸·͍ͣʜʜ

(/%Λٹ͍͍ͨʜʜ

ʜʜͱ͍͏ܦҢͰ 3PMF͕ݱΕͨ

= 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))

= 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

= 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࿦

= 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

3PMFTͷొ৔Ͱ OFXUZQF͸  ໾ׂΛՌͤΔΑ͏ʹ

໾ׂɿ

࣮૷ͷӅṭ

࣮૷ͷڞ༗

࣮૷ͷબ୒

͜Ε͕ݱࡏͷ  ͍ · OFXUZQF

͔͜͜Β͸ ະདྷͷOFXUZQF ͷ࿩ ͋ͨ͠

OFXUZQFͷະདྷ ·ͨ͸ɺ%FSJWJOH7JB ͋ͨ͠

OFXUZQFͷະདྷ ·ͨ͸ɺ%FSJWJOH7JB ʙ࣮૷ͷڞ༗ͱબ୒͕Ͱ͋͏ͱ͖ʙ [2] Blöndal, Löh and Scott, 2018 ͋ͨ͠

%FSJWJOH7JBΑΓॊೈͳ ࣮૷ͷڞ༗

%FSJWJOH7JBΑΓॊೈͳ ࣮૷ͷڞ༗ w ()$͔ΒೖΔ৽ػೳ

%FSJWJOH7JBΑΓॊೈͳ ࣮૷ͷڞ༗ w ()$͔ΒೖΔ৽ػೳ w ݱ࣌఺Ͱ()$BMQIB͕ग़͍ͯΔ

%FSJWJOH7JBΑΓॊೈͳ ࣮૷ͷڞ༗ w ()$͔ΒೖΔ৽ػೳ w ݱ࣌఺Ͱ()$BMQIB͕ग़͍ͯΔ w OFXUZQFΛEFSJWJOHઅͷώϯτͱͯ͠༻͍Δ ͜ͱ͕Ͱ͖ΔΑ͏ʹͳΔ

ྫɿ*EͷϞϊΠυߏ଄ {-# LANGUAGE DerivingVia #-} newtype Id = MkId Word
deriving (Semigroup, Monoid) via Max Word

ྫɿ*EͷϞϊΠυߏ଄ w લʹݟͨΑ͏ʹɺ8PSEͷϞϊΠυ࣮૷͸ෳ਺͋Δ {-# LANGUAGE DerivingVia #-} newtype Id =
MkId Word deriving (Semigroup, Monoid) via Max Word

ྫɿ*EͷϞϊΠυߏ଄ w લʹݟͨΑ͏ʹɺ8PSEͷϞϊΠυ࣮૷͸ෳ਺͋Δ w *EͰ͸ʮҰ൪৽͍͠*E ࠷େͷ*E ΛબͿʯԋࢉΛϞϊΠυԋ ࢉͱͯ͠࢖͍͔ͨͬͨͱ͢Δ {-# LANGUAGE
DerivingVia #-} newtype Id = MkId Word deriving (Semigroup, Monoid) via Max Word

ྫɿ*EͷϞϊΠυߏ଄ w લʹݟͨΑ͏ʹɺ8PSEͷϞϊΠυ࣮૷͸ෳ਺͋Δ w *EͰ͸ʮҰ൪৽͍͠*E ࠷େͷ*E ΛબͿʯԋࢉΛϞϊΠυԋ ࢉͱͯ͠࢖͍͔ͨͬͨͱ͢Δ w Max
Word͸IdͱಉҰදݱɺ NBY ʹؔ͠ϞϊΠυ {-# LANGUAGE DerivingVia #-} newtype Id = MkId Word deriving (Semigroup, Monoid) via Max Word

ྫɿ*EͷϞϊΠυߏ଄ w લʹݟͨΑ͏ʹɺ8PSEͷϞϊΠυ࣮૷͸ෳ਺͋Δ w *EͰ͸ʮҰ൪৽͍͠*E ࠷େͷ*E ΛબͿʯԋࢉΛϞϊΠυԋ ࢉͱͯ͠࢖͍͔ͨͬͨͱ͢Δ w Max
Word͸IdͱಉҰදݱɺ NBY ʹؔ͠ϞϊΠυ w %FSJWJOH7JB͸͜ͷ࣮૷Λࣗಈతʹ*Eʹ্࣋ͪ͛ͯ͘ΕΔʂ {-# LANGUAGE DerivingVia #-} newtype Id = MkId Word deriving (Semigroup, Monoid) via Max Word

%FSJWJOH7JBWT(/%

%FSJWJOH7JBWT(/% w %FSJWJOH7JB͸(/%ͷεʔύʔηοτ

%FSJWJOH7JBWT(/% w %FSJWJOH7JB͸(/%ͷεʔύʔηοτ w (/%͸แ·ΕΔҰ൪಺ଆͷܕͷ࣮૷ΛݟΔ

%FSJWJOH7JBWT(/% w %FSJWJOH7JB͸(/%ͷεʔύʔηοτ w (/%͸แ·ΕΔҰ൪಺ଆͷܕͷ࣮૷ΛݟΔ w %FSJWJOH7JB͸$PFSDJCMFͳ೚ҙͷܕͷ࣮ ૷ΛɺίετθϩͰ࠶ར༻͢Δ͜ͱ͕Ͱ͖Δʂ

%FSJWJOH7JBͷࣹఔ͸ OFXUZQFʹݶΒͳ͍

%FSJWJOH7JBͷࣹఔ͸ OFXUZQFʹݶΒͳ͍ w ݪ࿦จͰ͸೚ҙͷಉܕͳܕͷؒͰ࣮૷Λڞ༗ ͢Δํ๏΋ఏҊ͞Ε͍ͯΔ ˞͜ͷlಉܕz͸ਖ਼֬ʹ͸ʮ૯শతͳදݱ͕$PFSDJCMFʯͱ͍͏΍΍ڧ͍৚݅

%FSJWJOH7JBͷࣹఔ͸ OFXUZQFʹݶΒͳ͍ w ݪ࿦จͰ͸೚ҙͷಉܕͳܕͷؒͰ࣮૷Λڞ༗ ͢Δํ๏΋ఏҊ͞Ε͍ͯΔ ૯শϓϩάϥϛϯάͱ$PFSDJPOͷ߹Θٕͤ ˞͜ͷlಉܕz͸ਖ਼֬ʹ͸ʮ૯শతͳදݱ͕$PFSDJCMFʯͱ͍͏΍΍ڧ͍৚݅

%FNP +40/ม׵Πϯελϯεͷ੩తఆٛ ಉܕͳܕͷؒͰͷ࣮૷ͷڞ༗ ˞$PNQMFUFDPEFJTBWBJMBCMFBUhttp://bit.ly/derivia

ෳࡶͳྫ w ܕϨϕϧͰΤϯίʔυͷ࢓༷Λࢦఆ w 'SPN+40/5P+40/Ͱ࢓༷͕ڞ༗͞ΕΔ͜ͱΛ੩తʹอূ data OtherConfig = OtherConfig {
otrNameOfProcess :: Maybe String , otrArgsToProcess :: [String] } deriving (Read, Show, Eq, Ord, Generic) deriving (ToJSON, FromJSON) via WithOptions '[ FieldLabelModifier '[CamelTo2 "-"] , ConstructorTagModifier '[CamelTo2 "-"] , OmitNothingFields 'True ] OtherConfig

ಉܕͷྫ data Blog = Blog { authors :: [Author] ,
articles :: [Article] } deriving (Generic) deriving (Semigroup, Monoid) via Blog `SameRepAs` ([Author], Dual [Article]) {- ghci> mconcat [Blog ["1"] ["1"], Blog ["2"] ["3","4"]] Blog {authors = ["1","2"], articles = ["3","4","1"]} -}

ಉܕͷྫ DPOU 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

%FSJWJOH7JB·ͱΊ

%FSJWJOH7JB·ͱΊ w ()$͔Βར༻Մೳ

%FSJWJOH7JB·ͱΊ w ()$͔Βར༻Մೳ w OFXUZQFΛ࢖ͬͯEFSJWJOHʹ࢖͏࣮૷Λબ୒ ग़དྷΔ

%FSJWJOH7JB·ͱΊ w ()$͔Βར༻Մೳ w OFXUZQFΛ࢖ͬͯEFSJWJOHʹ࢖͏࣮૷Λબ୒ ग़དྷΔ w DPFSDFͱ(FOFSJDTͱ૊Έ߹ΘͤΕ͹ɺදݱ͕ ಉ͡ͱ͸ݶΒͳ͍͕ಉܕͳܕͷ࣮૷΋ಋग़Մೳ

%FSJWJOH7JB·ͱΊ w ()$͔Βར༻Մೳ w OFXUZQFΛ࢖ͬͯEFSJWJOHʹ࢖͏࣮૷Λબ୒ ग़དྷΔ w DPFSDFͱ(FOFSJDTͱ૊Έ߹ΘͤΕ͹ɺදݱ͕ ಉ͡ͱ͸ݶΒͳ͍͕ಉܕͳܕͷ࣮૷΋ಋग़Մೳ w
੍໿ͰදݱͰ͖ΔಉܕͳΒଞʹ΋ద༻Մೳ

·ͱΊ

·ͱΊ w OFXUZQFͷ༻్͸ࡾͭ

·ͱΊ w OFXUZQFͷ༻్͸ࡾͭ w ࣮૷ͷӅṭʗ࣮૷ͷڞ༗ʗ࣮૷ͷબ୒

·ͱΊ w OFXUZQFͷ༻్͸ࡾͭ w ࣮૷ͷӅṭʗ࣮૷ͷڞ༗ʗ࣮૷ͷબ୒ w %BUB$PFSDFΛ࢖͏ͱ಺෦දݱ͕ಉ͡ܕಉ࢜Λθϩ ίετͰΩϟετՄೳ

·ͱΊ w OFXUZQFͷ༻్͸ࡾͭ w ࣮૷ͷӅṭʗ࣮૷ͷڞ༗ʗ࣮૷ͷબ୒ w %BUB$PFSDFΛ࢖͏ͱ಺෦දݱ͕ಉ͡ܕಉ࢜Λθϩ ίετͰΩϟετՄೳ w OFXUZQFͷग़ੈ͸͔͜͜Β࢝·ͬͨ

w ෳ߹ܕ΋3PMFਪ࿦ɾḼऍͰద੾ʹѻ͑Δ

w ෳ߹ܕ΋3PMFਪ࿦ɾḼऍͰద੾ʹѻ͑Δ 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.

ޚਗ਼ௌ  ͋Γ͕ͱ͏͍͟͝·ͨ͠

"OZ2VFTUJPO w OFXUZQFͷ༻్͸ࡾͭ w ࣮૷ͷӅṭʗ࣮૷ͷڞ༗ʗ࣮૷ͷબ୒ w %BUB$PFSDFΛ࢖͏ͱ಺෦දݱ͕ಉ͡ܕಉ࢜Λθϩ ίετͰΩϟετՄೳ w OFXUZQFͷग़ੈ͸͔͜͜Β࢝·ͬͨ
w ෳ߹ܕ΋3PMFਪ࿦ɾḼऍͰద੾ʹѻ͑Δ w ()$͔Β%FSJWJOH7JBͰOFXUZQFʹΑΓ  ಋग़અΛΧελϚΠζՄೳʹʂ

͓·͚

ͳͥ.POPJEͱ'PMEBCMF͸  ஥͕͍͍ͷ͔ʁ w 'PMEBCMFͷ࠷খఆٛ w ࣮͸͜Ε͸ࣗ༝ϞϊΠυͷීวੑͷҰ෦͕༝དྷ class Foldable t where
foldMap :: Monoid m 㱺 (a ! m) ! t a ! m

7 ↵ M ↵ ' [ · ] 9! 7QH/JT
' <latexit 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<latexit 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<latexit 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<latexit 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<latexit 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<latexit 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ࣗ༝Ϟφυͷීวੑ w ࣗ༝ϞϊΠυവखͷఆ͔ٛΒ w α͔ΒGα΁ͷೖࣹ w G͕വखͰ͋Δ͜ͱ w Gαࣗ਎͕ϞϊΠυͰ͋Δࣄ w ʜʜΛআ͘ͱ'PMEBCMFʹͳΔ w ௚઀࡞Δํ๏͕ͳͯ͘΋͍͍ w Hask ݍͷവखͱ͸ݶΒͳ͍ w ϞϊΠυͱ͸ݶΒͳ͍ɺ୯ͳΔ ໦ߏ଄Ͱ΋৞ΈࠐΈ͍ͨ

'PMEBCMFͱ5SBWFSTBCMF w 5SBWFSTBCMF͸ࣗ༝ϞϊΠυͱ'PMEBCMFͷதؒ w USBWFSTF͸ࣗ༝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

本当はすごい newtype

本当はすごい newtype

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