extensible_interpreter_in_ML

֦ுՄೳΠϯλϓϦλ .-Ͱͭ͘Δ ML Day #1 1 Takahisa Watanabe @linerlock

ࠓ೔ͷ಺༰ ϞδϡϥʔͳϓϩάϥϜݴޠ։ൃ 2 ϕʔεݴޠ ֦ ு ֦ ு ໨తͷϓϩάϥϜݴޠ l.-Ͱͷ֦ுՄೳΠϯλϓϦλߏ੒ख๏

&YQSFTTJPO1SPCMFN ੩తܕ෇͖ͷϓϩάϥϜݴޠͰ ιʔείʔυΛʮฤूͤͣʯʹσʔλܕ΍खଓ͖Λ௥ՃͰ͖Δ͔ 3 The Expression Problem is
a new name for an old problem. The goal is to define a datatype by cases, where one can add new cases to the datatype and new functions over the datatype, without recompiling existing code, and while retaining static type safety (e.g., no casts). http://homepages.inf.ed.ac.uk/wadler/papers/expression/expression.txt Expression Problem Extensibility

֦ுՄೳΠϯλϓϦλ FYUFOTJCMF JOUFSQSFUFS l ΠϯλϓϦλ։ൃʹ͓͚Δ&YQSFTTJPO1SPCMFNͷղ 4 ධՁث ऴλάϨε๏ 0QFOSFDVSTJPO 0CKFDUBMHFCSB
ߏจղੳث ཱ֬͞Εͨख๏͸ͳ͍ ߏจղੳثੜ੒ܥΛ࢖͏ͱ͍͏खஈ͸͋Δ͕ ࠓճͷٞ࿦ͷର৅ʹ͸ؚΊͳ͍

֦ுՄೳΠϯλϓϦλ l ΠϯλϓϦλ։ൃʹ͓͚Δ&YQSFTTJPO1SPCMFNͷղ 5 ධՁث ऴλάϨε๏ 0QFOSFDVSTJPO 0CKFDUBMHFCSB ߏจղੳث ཱ֬͞Εͨख๏͸ͳ͍
ߏจղੳثੜ੒ܥΛ࢖͏ͱ͍͏खஈ͸͋Δ͕ ࠓճͷٞ࿦ͷର৅ʹ͸ؚΊͳ͍ ͜͜Λ΍Γ͍ͨ

ൃදͷྲྀΕ l લ൒֦ுՄೳͳධՁثͷ࣮ݱख๏ͷ঺հ n&YUFOTJCMFWBSJBOUUZQFT n &YQSFTTJPO1SPCMFNJO'1 n0QFOSFDVSTJPOΫϥεʹΑΔ֦ுΠϯλϓϦλ lޙ൒֦ுՄೳͳߏจղੳثͷ࣮ݱख๏ͷఏҊ nࣗ࡞ϥΠϒϥϦGJOBMFͷ঺հ 6

֦ுՄೳͳධՁثͷ࣮ݱ 7

֦ுՄೳΠϯλϓϦλ 8 l ର৅ݴޠΛ੩తʹ֦ுՄೳͳΠϯλϓϦλ lର৅ݴޠͷ֦ுΛͲ͏΍ͬͯදݱ͢Δ type e =
Lam of string * e | App of e * e | Var of string | Int of int ௥Ճ

֦ுՄೳΠϯλϓϦλ 9 l ର৅ݴޠΛ੩తʹ֦ுՄೳͳΠϯλϓϦλ lର৅ݴޠͷ֦ுΛͲ͏΍ͬͯදݱ͢Δ type e =
Lam of string * e | App of e * e | Var of string | Int of int ௥Ճ 0$BNMʹ͸ͦͷͨΊͷػೳ͕͋Δ

&YUFOTJCMFWBSJBOUUZQFT l։͔Εͨz୅਺తσʔλܕ ü ίϯετϥΫλΛޙ͔Β௥ՃՄೳ üྫ֎ܕexnͷҰൠԽ એݴ type t = ..
ίϯετϥΫλͷ௥Ճ ݱࡏͷείʔϓͰͷΈ༗ޮʹͳΔ type t += A type t += B of int | C 10

ສࣄղܾ͔ l /0 lίϯετϥΫλ͕଍ͤΔ͚ͩͰ͸ &YQSFTTJPO1SPCMFNͷղʹ͸ͳΒͳ͍ 11

&YQSFTTJPO1SPCMFNJO'1 12 データ型の追加手続きの追加 FP OOP l ୅਺తσʔλܕίϯετϥΫλΛ૿΍͢ͱ ؔ܎͢ΔશͯͷύλʔϯϚονʹʮฤूʯ͕ඞཁ l
खଓ͖ͷ௥Ճ͸؆୯ ؔ਺Λ৽͘͠ఆٛ͢Δ͚ͩ '1ʹ͓͚Δ&YQSFTTJPO1SPCMFN

ྫ୊ type e = .. type e += Int of
int | Add of e * e let rec eval = function | Int n -> n | Add (n, m) -> eval n + eval m 13

ྫ୊σʔλܕͷ௥Ճ type e = .. type e += Int of
int | Add of e * e type e += Sub of e * e let rec eval = function | Int n -> n | Add (n, m) -> eval n + eval m | Sub (n, m) -> eval n – eval m let rec show = function | Int n -> sprintf “%d” n | Add (n, m) -> sprintf “(%s + %s)” (show n) (show m) | Sub (n, m) -> sprintf “(%s - %s)” (show n) (show m) 15 ੺ࣈͷ෦෼͸ιʔείʔυͷ ฤूʹΑΔରԠ͕ඞཁ

΍Γ͍ͨ͜ͱ 16 let rec eval = function | Int n
-> n | Add (n, m) -> eval n + eval m let rec eval_sub = function | Sub (n, m) -> eval_sub n – eval_sub m | e -> eval e • ֦ுͨ͠෦෼͚ͩΛॲཧ͢Δखଓ͖Λ௥Ճ • ֦ுͨ͠෦෼Ҏ֎ͷॲཧ͸طଘͷखଓ͖ʹॲཧΛҕৡ ҕৡ

໰୊ 17 let rec eval = function | Int n
-> n | Add (n, m) -> eval n + eval m let rec eval_sub = function | Sub (n, m) -> eval_sub n – eval_sub m | e -> eval e • evalؔ਺ͷ࠶ؼݺͼग़͠Ҏ߱, eval_subؔ਺͕ݺ͹Εͳ͍ • ໰୊ͱͳΔྫAdd (Sub (Int 1, Int 2), Int 3) ҕৡ

PQFOSFDVSTJPOʹΑΔղܾ ll։͔Εͨz࠶ؼؔ਺ l࠶ؼݺͼग़͠ͷෆಈ఺Λύϥϝʔλͱͯ͠ड͚ͱΔ 18 let eval_open = fun eval ->
| Int n -> n | Add (n, m) -> eval n + eval m

ྫ୊΁ͷద༻ let eval_open = fun eval -> | Int n
-> n | Add (n, m) -> eval n + eval m let eval_sub_open = fun eval -> | Sub (n, m) -> eval n – eval m | e -> eval_open eval e 19

5ZJOHUIFLOPU l࠷ޙʹ։͔Εͨ࠶ؼؔ਺Λlด͡Δzఆ͕ٛඞཁ 20 let rec eval e = eval_sub_open eval
e PQFOSFDVSTJPOؔ਺ͷ࠶ؼݺͼग़͕͠ શͯ͜ͷevalΛࢦ͢Α͏ʹͳΔ

໰୊ l PQFOSFDVSTJPO͸ॻ͘ͷ͕ͭΒ͍ lྫ૬ޓ࠶ؼؔ਺ෆಈ఺ͷ਺͚ͩҾ਺͕૿͑Δ 21

ผղΫϥεʹΑΔ࣮ݱ l खଓ͖ΛΫϥεͷϝιουͱͯ͠දݱ lखଓ͖ͷ௥Ճ͸ܧঝʹΑ࣮ͬͯݱ l ࣗݾࢀর UIJT ͸ৗʹܧঝπϦʔͷ༿Λࢦ͢ n ஗ԆόΠϯσΟϯά
n PQFOSFDVSTJPOͱಉ༷ͷ࢓૊ΈΛ࣮ݱͰ͖Δ 22

ྫ୊ΫϥεʹΑΔ࣮ݱ 23 class add_or_int = object (this) method eval =
function | Int n -> n | Add (n, m) -> this#eval n + this#eval m end class sub = object (this) inherit add_or_sub as super method eval = function | Sub (n, m) -> this#eval n – this#eval m | e -> super#eval e end ݱࡏͷखଓ͖ͰΧόʔ͠ͳ͍ཁૉ͸਌ʹॲཧΛҕৡ

ΫϥεʹΑΔ࣮ݱ͸ྑ͍ղ͔ 001ݴޠͰॻ͘ͷͱԿ͕ҧ͏ͷ l001Ͱ͸ΫϥεΛ༻͍ͯσʔλܕͷදݱ΋ߦ͏ &YUFOTJCMFWBSJBOUUZQFT Ϋϥε l'1σʔλܕ 001ʹΑΔखଓ͖ͷ֦ு lهड़ੑ͸ߴ͍ l001ͷ&YQSFTTJPO1SPCMFN͕࠶೩͢Δ
24

લ൒ͷ·ͱΊ l l։͔Εͨzσʔλܕͱ࠶ؼؔ਺͕͋Ε͹ ΠϯλϓϦλ ධՁث ͸֦ுͰ͖Δ lσʔλܕFYUFOTJCMFUZQFWBSJBOUT l࠶ؼؔ਺ lPQFOSFDVSTJPO lΫϥε
25

֦ுՄೳͳߏจղੳثͷ࣮ݱ 26

֦ுՄೳΠϯλϓϦλ l ΠϯλϓϦλ։ൃʹ͓͚Δ&YQSFTTJPO1SPCMFNͷղ 27 ධՁث ऴλάϨε๏ 0QFOSFDVSTJPO 0CKFDUBMHFCSB ߏจղੳث ཱ֬͞Εͨख๏͸ͳ͍
ߏจղੳثੜ੒ܥΛ࢖͏ͱ͍͏खஈ͸͋Δ͕ ࠓճͷٞ࿦ͷର৅ʹ͸ؚΊͳ͍ ͜͜Λ΍Γ͍ͨ

࣮ݱͷΞΠσΞ ϓϦϯλ͸֦ுՄೳΠϯλϓϦλʹج͍ͮͯఆٛՄೳ ϓϦϯλͱߏจղੳث͸ରͷؔ܎ʹ͋Δ Parse x = Parse (Print (Parse x))
28 ֦ுՄೳΠϯλϓϦλͱͯ͠ఆٛͨ͠ϓϦϯλ͔Β ֦ுߏจثΛಋग़Ͱ͖ͳ͍͔

ߏจղੳثͱϓϦϯλ 29 ߏจղੳث ϓϦϯλ ԋࢉࢠͷ༏ઌॱҐ ԋࢉࢠͷ݁߹ํ޲ º ߏจղੳث೚ҙͷೖྗ͔Βߏจ໦Λ࡞Δ ϓϦϯλ༩͑ΒΕͨߏจ໦Λ୧ͬͯจࣈྻΛ࡞Δ ߏจ໦ͷ૊ΈཱͯํΛ஌͓ͬͯ͘ඞཁ͕ͳ͍
ϓϦϯλʹରͯ͠ߏจղੳʹඞཁͳ৘ใΛ෇͚Ճ͍͑ͯ͘ ߏจղੳث ϓϦϯλ

ߏจղੳثͱϓϦϯλ 30 ߏจղੳث ϓϦϯλ ԋࢉࢠͷ༏ઌॱҐ ԋࢉࢠͷ݁߹ํ޲ *OWFSUJCMF4ZOUBYߏจղੳثͱϓϦϯλΛಉ࣌ʹఆٛ <Rendel+; 2010] ߏจنଇ
ΠϯλϑΣΠε ϓϦϯλ ղऍ ߏจղੳث ղऍ º

finale : *OWFSUJCMF4ZOUBYGPS.- 31 http://github.com/takahisa/finale ߏจղੳثͱϓϦϯλΛಉ࣌ʹఆٛՄೳ "QQMJDBUJWF1BSTFSDPNCJOBUPSͬΆ͍ελΠϧ let jboolean =
jbooleanE <$> (text "true" *> pure (=) true) <|> jbooleanE <$> (text "false" *> pure (=) false) ྫ+40/ਅِ஋Ϧςϥϧͷߏจఆٛ • ऴλάϨε๏ʹΑΔܕ҆શͳݴޠ಺%4-ͱ࣮ͯ͠૷ • ϞδϡϥʔͳߏจղੳϓϦϯτͷͨΊͷػೳΛఏڙ

Ϟδϡϥʔͳߏจղੳʹ޲͚ͯ lύʔαϓϦϯλͷ֦ு๏͸લ൒ͱಉ͡ lͨͩ͠ lਖ਼͍݁͠ՌzΛಘΔͨΊʹ͸޻෉͕ඞཁ 32 • Modular parsers
should support left-recursion. • Modular parsers should use a longest match composition operator 5ZQF4BGF.PEVMBS1BSTJOH<;IBOH > • ࠨ࠶ؼ • ࠷௕Ұக

Ϟδϡϥʔͳߏจղੳͷ໰୊ 33 ॱ൪ʹؔ͢Δ໰୊ FYQ JOU Լʹ௥Ճ نଇͷ௥ՃΛߦ͏ͱʜ FYQ JOU c
JOU b `FYQ FYQ JOU b `FYQ cJOU ্ʹ௥Ճ

Ϟδϡϥʔͳߏจղੳͷ໰୊ 34 ॱ൪ʹؔ͢Δ໰୊ FYQ JOU Լʹ௥Ճ نଇͷ௥ՃΛߦ͏ͱʜ FYQ JOU c
JOU b `FYQ FYQ JOU b `FYQ cJOU ্ʹ௥Ճ Լͷنଇʹ ӬԕʹભҠ͠ͳ͍

Ϟδϡϥʔͳߏจղੳͷ໰୊ l֦ுͷ૊Έ߹ΘͤํʹΑͬͯ݁Ռ͕มΘΔ lDPNQPTBCJMJUZͷ؍఺͔Β޷·͘͠ͳ͍ lFSSPSQSPOF l࠷௕Ұக๏ʹΑΔղ l શ෦ࢼ͢࠷΋ೖྗΛফඅͨ͠نଇΛબͿ lޮ཰͸ѱ͍DPNQPTBCJMJUZͱͷτϨʔυΦϑ 35

ࠨ࠶ؼͷ໰୊ l QBSTFSDPNCJOBUPSҰൠͷ໰୊ lԋࢉࢠͷ༏ઌॱҐ෇͖QBSTJOHͳͲͰසग़ l֦ுʹΑͬͯ༧ظͤ͵ࠨ࠶ؼ͕ൃੜ͕ͪ͠ lଈࢮ 36

ࠨ࠶ؼ΁ͷରॲ l -FGUSFDVSTJPOFMJNJOBUJPO l ΍Γ͍͕ͨʜ l ࠓճ͸සग़ύλʔϯͰ͋ΔԋࢉࢠͷॱҐ෇͖จ๏ͷ QBSTJOHʹϐϘοτ 37

ԋࢉࢠॱҐղੳ l ԋࢉࢠͷ༏ઌॱҐɾ݁߹ํ޲ͷςʔϒϧ͔Β ࣜͷߏจղੳΛߦ͏ lࠓ͸JOWFSUJCMFTZOUBYͷ্Ͱ΍͍ͬͯΔ lԋࢉࢠॱҐϓϦϯλͬͯԿͩʜ lߟ͑ͨ͘ͳ͍ͷͰ ࠶ؼԼ߱ߏจղੳثΛ ,OPUΛด͡ΔλΠϛϯάͰੜ੒
38

,FOOFM IUUQTHJUIVCDPNUBLBIJTBLFOOFM l ຊ೔঺հͨ͠಺༰ͷ૊Έ߹ΘͤʹΑΔ ֦ுՄೳͳΠϯλϓϦλ։ൃϑϨʔϜϫʔΫ lݱࡏϥϜμܭࢉ਺஋ܕਅِ஋ܕԋࢉͳͲΛ૊Έ ߹Θͤͯͪΐͬͱͨ͠࠶ؼؔ਺͕ॻ͚Δ 39

·ͱΊ l ֦ுՄೳΠϯλϓϦλͷߏஙख๏ʹ͍ͭͯ঺հ lࣗ࡞ϥΠϒϥϦGJOBMFʹ͍ͭͯͷ঺հ lJOWFSUJCMFTZOUBY NPEVMBSQBSTJOH 40 ໺๬ • ϓϩάϥϜݴޠॲཧܥશମΛ֦ுՄೳʹ͍ͨ͠
• ΧόʔͰ͖͍ͯͳ͍෦෼ܕݕࠪثϓϩάϥϜม׵ ࠷దԽث ͳͲ • ͓஌ܙΛ͓ି͍ͩ͘͠͞

extensible_interpreter_in_ML

extensible_interpreter_in_ML

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