Kontlang-Monadic Reflection

自作S式言語Kontlangに限定継続・マクロ・モジュールを使って「Representing Monads」ベースのモナド・ライブラリを追加した話

Transcript

1. ,POUMBOHͱ
   .POBEJD
   3FqFDUJPO
   ͋Δ͍͸
   ϚΫϩͱϞδϡʔϧͱݶఆܧଓͰͭ͘ΔϞφυϥΠϒϥϦ ![FIOQBBSE
   
2. w ϓϩάϥϚ
   w -JTQྺ̐೥
   w ͍ΖΜͳݴޠΛ৮ͬͨΓ࡞ͬͨΓ͢Δͷ͕޷͖
   w ࠷ۙ͸झຯͰ0$BNMΛ࢖͏͜ͱ͕ଟ͍
   w ͋ͻΔ͏͗͞͞ΜνʔϜʢޙظϰΟτήϯγϡλΠϯ೿ʣ
   w ϒϩάɿ
   [FIOQBBSEIBUFOBCMPHDPN
   w (JU)VC
   IUUQTHJUIVCDPN[FIOQBBSE ࣗݾ঺հ
3. ຊ೔ͷ࿩୊ w TIJGUSFTFU
   ͰϞφυΛϥΠϒϥϦͱ࣮ͯ͠૷͍ͨ͠
   w ͦͷͨΊʹඞཁͳύʔπ
   w ϚΫϩ
   w Ϟδϡʔϧ
   w ͭͬͯ͘ΈΔɾ࢖ͬͯΈΔ
4. TIJGUSFTFU
5. લճ·Ͱͷ͋Β͢͡ w ݶఆܧଓʹ͍ͭͯ஌Γ͍ͨͷͰݶఆܧଓ͕ѻ͑Δࣗ࡞ݴ ޠ,POUMBOHͷΠϯλϓϦλΛ࣮૷͍ͨ͠
   w ݶఆܧଓΛ࣮૷͢ΔͳΒɺΠϯλϓϦλΛܧଓ౉͠ελΠ ϧͰॻ͚͹ָͦ͏ʁ
   w ͍Ζ͍Ζ໘ന͔ͬͨ
   w TIJGUSFTFU࣮૷͸ؒʹ߹Θͣɾɾɾ
6. ,POUMBOH w $MPKVSFͬΆ͍ʁจ๏
   w ͍Ζ͍Ζඍົʹҧ͏
   w $MPKVSF͏Ζ͓΅͑ɾɾɾ
   w ಈతܕ෇͚
7. ,POUMBOH w ७ਮؔ਺ܕʁ
   w ݶఆܧଓҎ֎ʂ
   w ͲͪΒ͔ͱ͍͏ͱʮՄมϝϞϦͰ͋ΔετΞΛఏڙ͠ ͳ͍ʯͱݴͬͨ΄͏͕ਖ਼͍͠ʁ
8. ,POUMBOHΠϯλϓϦλ w ΠϯλϓϦλ͕$&,ந৅ػցʹ͍ۙ
   w EFGVODUJPOBMJ[F͞Εͨܧଓ౉͠ελΠϧͰॻ͔Ε͍ͯΔ
   w ΠϯλϓϦλͷ৺ଁ෦͸FWBMͱBQQMZ@DPOUͷೋؔ਺
   w ͲͪΒ΋࠶ؼͤͣ&YFDVUFUܕΛฦ͢ɿ type t = | Done of Val.t | Eval of Env.t * Cont.t * Exp.t | ApplyCont of Env.t * Cont.t * Val.t
9. ܧଓελοΫ w ΠϯλϓϦλͷঢ়ଶม਺ͷҰͭ type Execute.t = | Done of Val.t | Eval of Env.t * Cont.t * Exp.t | ApplyCont of Env.t * Cont.t * Val.t type cont = | Call of Exp.t list * Val.t list | If of Exp.t * Exp.t …… | Env type Cont.t = cont list list w ʮܧଓʯͷϦετͷϦετ
   w SFTFU͕ݺ͹ΕΔͱ۠੾Γͱ͠ ͯ৽͍ۭ͠Ϧετ͕௥Ճ͞Ε Δ
10. TIJGUSFTFU͕Ͱ͖ͨ
11. TIJGUSFTFUͷڍಈ w SFTFUͰܧଓΛ۠੾Δ
    w TIJGU͸ݶఆܧଓΛͱͬͯ͘Δ
    w TIJGU
    <L>
    . ͱ͢ΔͱʮݱࡏͷݶఆܧଓΛऔΓআ͖ɺͦ ΕΛؔ਺ʹͯ͠Lʹଋറ͠ɺ.Λ࣮ߦ͢ΔʯʢʮTIJGU SFTFUϓϩάϥϛϯάೖ໳ʯΑΓҾ༻ʣ http://pllab.is.ocha.ac.jp/~asai/cw2011tutorial/main-j.pdf
12. TIJGUSFTFUͷڍಈ ྦྷੵ࿨Λࢉग़͢ΔBDDVNVMBUPSɿ (letrec [(f [n] (shift [k] (cons n k))) (g [n] (g (+ n (f n)))) (accumulator [] (fn [n] (reset (g n))))]
13. TIJGUSFTFUͷڍಈ BDDVNVMBUPSΛ࢖ͬͯΈΔɿ (let* [(acc (accumulator)) (res (acc 1)) (a (car res)) (acc (cdr res)) (res (acc 2)) (b (car res)) (acc (cdr res)) (res (acc 3)) (c (car res))] (list a b c))
14. ӄཅ (reset (let [(yin ((fn [k] (do [(print "x") k])) (shift [k] (k k)))) (yang ((fn [k] (do [(print "_") k])) (shift [k] (k k))))] (yin yang))) w AY@Y@@Y@@@Y@@@@Y@@@@@YʜAͱແݶʹग़ྗ͢Δ
    w MFUSFDΛ࢖͍ͬͯͳ͍ͷʹ࠶ؼ͍ͯ͠Δ
    w ZJOͱZBOHͷఆٛ͸΄΅ಉҰͳͷʹڍಈ͕ҧ͏
    w ZBOH͚ͩݺͼग़͠ճ਺͕ϧʔϓͷ౓ʹ૿͑Δ
15. TIJGUSFTFUͷ࣮૷ w SFTFUͰܧଓελοΫʹ৽͍ۭ͠ϦετΛ௥Ճ͢Δ͜ͱͰʮܧଓ Λ۠੾Δʯ
    w SFTFU಺ͷࣜΛධՁ͢Δ࣌͸ͦͷۭϦετʹܧଓΛՃ͑Δ
    w TIJGU
    <L>
    F ͱ͍͏ࣜΛධՁ͢Δ৔߹ɿ
    w ܧଓελοΫ͔Βઌ಄ͷϦετΛ֎͠
    w ͦͷϦετΛอ࣋͢Δ7BM$POU஋ΛLͱ͍͏ม਺ʹଋറ
    w ͦͷม਺؀ڥͱܧଓελοΫͰFΛධՁ
16. TIJGUSFTFUͷ࣮૷ w 7BM$POU஋͕ؔ਺ͱͯ͠ݺͼग़͞Εͨ৔߹ɿ
    w ·ͣ͸Ҿ਺ΛධՁ
    w ܧଓελοΫʹ7BM$POUʹอ࣋͞Ε͍ͯΔܧଓͷϦετ Λ௥Ճ͢Δ
    w ৽͍͠ܧଓελοΫʹҾ਺ͷධՁ݁ՌͰ͋Δ஋Λ౉͢ ʢBQQMZ@DPOUΛݺͼग़͢ʣ
17. ݶఆܧଓͱϞφυ http://pllab.is.ocha.ac.jp/~asai/cw2011tutorial/main-j.pdf
18. ϞφυΛͭ͘Ζ͏ https://www.slideshare.net/dico_leque/ss-14149810
19. ϞφυΛͭ͘Ζ͏ https://dl.acm.org/doi/pdf/10.1145/174675.178047 http://www.cs.ioc.ee/mpc-amast06/msfp/filinski-slides.pdf
20. ϥΠϒϥϦԽʹඞཁͳ΋ͷ w ϚΫϩ
    w TIJGUͱSFTFUΛผʑʹӅṭ͍ͨ͠
    w TIJGU͕SFTFU֎Ͱݺͼग़͞ΕΔͷΛආ͚ΔͨΊɺධՁΛ஗Ԇ ͍ͨ͠
    w Ϟδϡʔϧ
    w ҧ͏Ϟφυ͕ಉ͡"1*ͰڞଘͰ͖ΔΑ͏ύοέʔδԽ͍ͨ͠
    w ֎෦ϑΝΠϧʹهड़ͯ͠ϩʔυ͢Δ͜ͱͰඪ४ϥΠϒϥϦԽ ͍ͨ͠
21. ϚΫϩ
22. ϚΫϩ w ශऑͳ͕Βஔ׵ϕʔεͷୈҰڃϚΫϩ
    w ΫϩʔδϟΛ࣋ͨͳ͍ͷͰμΠφϛοΫɾείʔϓ
    w ϨΩγΧϧɾείʔϓʹ͢Δ৔߹ɺஔ׵͢ΔલʹҾ਺Λ UIVOL͢Ε͹͍͍ʁ
    w 0O
    -JTQ΍-FU
    0WFS
    -BNCEBΛಡΜͩ΄͏͕͍͍͔΋ (let [m (macro [x y] (do [y x]))] (m (println "hello") (println "goodbye")))
23. δΣωϨʔλ w ஗ԆϦετͱͯ͠ͷδΣωϨʔλ
    w ࣮૷ͱͯ͠͸ʮ஋ͱ࣍ͷؔ਺Λฦ̌͢Ҿ਺ؔ਺ʯ
    w Ϧετͱಉ͡Α͏ʹѻ͏ͨΊͷؔ਺܊Λ࣮૷Ͱ͖Δ
    w NBQ
    DPODBU
    NFSHF
    UBLF
    ESPQ
    IFBE
    UBJMͳͲͳͲ
24. δΣωϨʔλͱݶఆܧଓ w δΣωϨʔλͷ࣮૷ͷͨΊʹTIJGUSFTFUΛ࢖͏ඞཁ͸ͳ͍
    w ωετͨ͠ߴ֊ؔ਺Ͱे෼
    w ݶఆܧଓΛ࢖͏ͱZJFME͕ͭ͘ΕΔ
    w 1ZUIPO΍+BWB4DSJQUʹ͋ΔδΣωϨʔλߏจ
    w ௨ৗͷؔ਺ͱಉ͡هड़Ͱʮ్தͰఀࢭɾ࠶։ʯ͢Δؔ ਺͕ॻ͚Δ
25. δΣωϨʔλ w ϚΫϩͱݶఆܧଓͰ1ZUIPO΍+BWBTDSJQUʹ͋ΔδΣωϨʔ λߏจͷZJFMEΛͭ͘ΕΔ (define generator (macro [expr] (reset (let [result expr] (fn [] (cons result (fn [] nil))))))) (letfn [yield [x] (shift [k] (fn [] (cons x (k nil))))] ...)
26. δΣωϨʔλ (letfn [count [] (letrec [f [n] (do [(yield n) (f (+ n 1))])] (generator (f 0)))] ...) w HFOFSBUPSͱZJFMEΛ࢖ͬͯ͢΂ͯͷࣗવ਺ͷ஗ԆϦετɿ
27. ͳͥϚΫϩ͕ඞཁʁ w HFOFSBUPSͷҾ਺ͷධՁΛ஗Ԇ͢ΔͨΊ
    w Ҿ਺಺ͰZJFME͕࢖ΘΕΔͷͰɺධՁΛ஗Ԇ͠ͳ͍ͱTIJGU͕SFTFU֎Ͱݺ ͼग़͞Εͯ͠·͏
    w UIVOLͰ΋Մೳ
    w Ҿ਺ͷؔ਺ʹแΉ͜ͱͰධՁΛ஗Ԇ͢Δ
    w 0DIB$BNMͰ͸ϚΫϩ͕ͳ͍ͨΊUIVOLΛ࢖͍ͬͯΔ
    w ه๏తʹ͸ϚΫϩͷ΄͏͕͖ͬ͢Γ͍ͯ͠Δ
    w Ϟφυ࡞੒Ͱ΋ಉ͡खΛ࢖͏ʢϚΫϩʹΑΔධՁ஗Ԇʣ
28. Ϟδϡʔϧ
29. Ϟδϡʔϧͱ͸ w ಠࣗͷ໊લۭؒ
    w ֎෦ϑΝΠϧΛಡΈࠐΜͰϞδϡʔϧʹͰ͖Δ
    w NPEVMF
    <ʜ> ͰϞδϡʔϧΦϒδΣΫτΛ࡞੒
    w ʜͷதʹ͸ EFpOF
    Y
    ʜ ͔ଞͷ͕ࣜೖΔ
    w .YͰϞδϡʔϧ.಺ͰEFpOF͞Εͨม਺YʹΞΫηεͰ͖ Δ
30. ֎෦Ϟδϡʔϧ w ֎෦ϑΝΠϧʹ EFpOF
    ʜ ͰϞδϡʔϧม਺Λఆ͍ٛͯ͘͠
    w JNQPSU
    lpMFOBNFz Ͱ֎෦ϑΝΠϧΛಡΈࠐΈϞδϡʔϧΦϒδΣ ΫτΛ࡞੒ (let [List (import "list.ktl")] (List.map (fn [x] (* x x)) (List.range 5)))
31. ϞδϡʔϧΛ։͘ w Ϟδϡʔϧ.ͷม਺Λ.YͰ͸ͳ͘Yͱ௚઀࢖͍͍ͨ
    w ී௨ͷࣜͷதͰ࢖͑Δ PQFO
    .
    ʜ
    w ϞδϡʔϧఆٛͰ࢖͑Δ NPEVMF
    < JODMVEF
    .
    ʜ> ͱ NPEVMF
    < VTJOH
    .
    ʜ>
    w JODMVEF
    . ͸ఆٛ͞Ε͍ͯΔϞδϡʔϧͷม਺ͱͳΔ
    w VTJOH
    . ͸ɿ
    w Ϟδϡʔϧఆٛத͚ͩ.ͷม਺͕ΞΫηεͰ͖Δ
    w Ϟδϡʔϧ֎෦͔Β͸͜ΕΒม਺ʹΞΫηεͰ͖ͳ͍
32. ϞφυϥΠϒϥϦ
33. .BZCFϞφυ (define reify (macro [expr] (reset expr))) (define reflect (letfn [reflect [m] (shift [k] (if (nil? m) m (k m)))] reflect)) w ʮϞφυΛͭ͘Ζ͏ʯͰग़ͯͨྫ
    w ͨͩ͠4PNF
    B
    c
    /POFͱ͍ͬͨܕ͸࢖͍ͬͯͳ͍
    w -JTQFSͳΒ໧ͬͯOJMΛฦ͢
    w LPOUMBOHʹ୅਺తσʔλܕ͕ͳ͍ͱ͍͏ͷ΋ཧ༝ɾɾɾ
34. .BZCFϞφυ࢖༻ྫ (let [(M Stdlib.MaybeMonad) (L Stdlib.List)] (M.reify (let [(x (M.reflect (L.find (fn [x] (= x 2)) (list 1 0 3)))) (y (M.reflect (L.find (fn [x] (= x 3)) (list 1 2 3))))] (cons x y)))) w ඪ४ϥΠϒϥϦͷϞδϡʔϧΛ࢖͍ͬͯΔ
    w EPͳͲͷಛघߏจ͸࢖ΘͣEJSFDU
    TUZMFͰॻ͍͍ͯΔ͕ɺӅ ṭ͞ΕͨTIJGUSFTFUʹΑͬͯ .SFqFDU ͷதͷ͕ࣜOJMͱධ Ձ͞Εͨ৔߹ɺ.SFJGZશମͷ஋͕OJMʹͳΔ
35. 4UBUFϞφυ (define reify (macro [expr] (reset (let [result expr] (fn [state] (cons result state)))))) (define reflect (letfn [reflect [f] (shift [k] (fn [state] (let* [(val-state (f state)) (val (car val-state)) (state1 (cdr val-state))] ((k val) state1))))] reflect)) (define get (letfn [get [] (reflect (fn [state] (cons state state)))] get)) (define put (letfn [put [val] (reflect (fn [state] (cons nil val)))] put)) (define run_state (letfn [run_state [m state] (m state)] run_state)) w ʮTIJGUSFTFUϓϩάϥϛϯάೖ໳ʯͰ΋ݴٴ͞Ε͍ͯͨ
    w "1*͸SFJGZSFqFDUΑΓʹมߋ
36. -JTUϞφυ w όοΫτϥοΫ͢Δඇܾఆੑϓϩάϥϛϯά (define reify (macro [expr] (reset (list expr)))) (define reflect (letfn [reflect [m] (shift [k] (List.merge (List.map k m)))] reflect)) (define fail (letfn [fail [] (reflect nil)] fail)) (define assert (letfn [assert [x] (if x nil (fail))] assert))
37. (FOFSBUPSϞφυ w -JTUͱಉ͘͡ඇܾఆੑϓϩάϥϛϯά (define reify (macro [expr] (reset (let [result expr] (fn [] (cons result (fn [] nil))))))) (define reflect (letfn [reflect [m] (shift [k] (Generator.merge (Generator.map k m)))] reflect)) (define fail (letfn [fail [] (reflect (fn [] nil))] fail)) (define assert (letfn [assert [x] (if x nil (fail))] assert))
38. όοΫτϥοΫ୳ࡧ (let* [(G Stdlib.Generator) (GM Stdlib.GeneratorMonad) (g (GM.reify (let* [(gen (G.from_list (list 1 2 3 4 5)) (x (GM.reflect gen)) (y (GM.reflect gen)) (z (GM.reflect gen)) (_ (GM.assert (= (* z z) (+ (* x x) (* y y)))))] (list x y z))))] (G.head g))
39. Ϟφυɾɾɾʁ w ͜͜·Ͱ࣮૷͖ͯͨ͠΋ͷ͸ຊ౰ʹϞφυͳͷ͔ʁ
    w SFqFDUͱSFJGZʁSFUVSOͱCJOE͸ʁ
    w SFqFDUSFJGZͰSFUVSOCJOE͸ॻ͚Δ
    w SFUVSOCJOEͱTIJGUSFTFUͰSFqFDUSFJGZ͸ॻ͚Δ
40. SFqFDUSFJGZˠSFUVSOCJOE w SFqFDUSFJGZͰSFUVSOCJOE͸ॻ͚Δ (letfn [return [a] (reify a)] ...) (let [bind (macro [m f] (reify (reflect (f (reflect m)))))] ...)
41. SFUVSOCJOEˠSFqFDUSFJGZ w SFUVSOCJOEͰSFqFDUSFJGZΛॻ͘ʹ͸TIJGUSFTFU͕ඞཁ
    w ʮϞφυΛͭ͘Ζ͏ʯʮ3FQSFTFOUJOH
    .POBETʯࢀর
    w TIJGUSFTFUΛ࢖͏͜ͱͰEPͷΑ͏ͳಛघߏจͳ͠ʹEJSFDU
    TUZMFͰهड़Ͱ͖Δ
42. ࠓޙ΍Γ͍ͨ͜ͱ w ͍ΖΜͳϞφυʹձ͍ʹ͍͘
    w 1PPS
    NBO`T
    DPODVSSFODZ
    NPOBEͰڠௐతεϨουΛ࣮૷ͯ͠Έ͍ͨ
    w $PSPVUJOF͸(FOFSBUPSͱ΄΅ಉ࣮͡૷Ͱ࡞Εͦ͏
    w ͪΌΜͱͨ͠3&1-Λͭ͘Δ
    w 3&1-ೖྗΛϞδϡʔϧ಺ఆٛͩͱೝࣝͤ͞Ε͹͍͚ͦ͏
    w λΠϜτϥϕϧՄೳͳΠϯλϓϦλ
    w Τϥʔ࣌ʹҰ୴ఀࢭɾר͖໭ͯ͠͠ධՁதͷࣜɺม਺؀ڥɺܧଓελοΫͷத਎Λ ฤूͰ͖ΔΑ͏ʹ͍ͨ͠
    w $14ม׵ʹΑΔίϯύΠϥ