新機能で知るEgison

約1年の間に追加された主な機能についての紹介です．

Transcript

1. ৽ػೳͰ஌Δ&HJTPO Egison Workshop 2018 by @kotapiku
2. w ౦େཧ৘೥Ͱ͢
   w 7JN
   
   )BTLFMM
   
   OZBO
   w ೥લ͘Β͍͔Βָఱٕज़ݚڀॴͰ
 &HJTPOόΠτΛ͍ͯ͠·͢ Twitter & GitHub @kotapiku
3. ࠓ೔࿩͢͜ͱ w ៉ྷͳ+VQZUFSग़ྗ
   w 'VODUJPO
   4ZNCPM
   w ࢖͍΍͍͢ςϯιϧૢ࡞
   w %'4ύλʔϯ
   w ༏ઌ౓෇͖03
   w ৽ύʔαʔ࡞ͬͯ·͢ʂ
4. ៉ྷͳ+VQZUFSग़ྗ
5. +VQZUFS
   /PUFCPPLͱ͸ w 1ZUIPOͷର࿩؀ڥͱͯ͠։ൃ͞Ε͍ͯΔ
   w 1ZUIPOҎ֎ʹ΋+VMJB
   3
   3VCZͳͲ΋࢖͑Δ
   w &HJTPO΋FHJTPO@LFSOFMΛೖΕΕ͹࢖͑ΔΑ͏ʹ ͳΓ·͢
6. FHJTPO@LFSOFM IUUQTHJUIVCDPNFHJTPOFHJTPO@LFSOFM
8. .
   ΦϓγϣϯͰग़ྗΛ੾Γସ͑Δ % egison -M asciimath > [| [| 1 0 0 |] [| 0 1 0 |] [| 0 0 1 |] |] #asciimath|((1, 0, 0), (0, 1, 0), (0, 0, 1))|# % egison -M latex > [| [| 1 0 0 |] [| 0 1 0 |] [| 0 0 1 |] |]
 #latex|\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{pmatrix}|# % egison -M mathematica > [| [| 1 0 0 |] [| 0 1 0 |] [| 0 0 1 |] |] #mathematica|{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}|#
9. IUUQTHJUIVCDPNFHJTPOFHJTPOCMPCNBTUFS ITTSD-BOHVBHF&HJTPO.BUI0VUQVUIT
   w &HJTPOͷग़ྗจࣈྻΛύʔεˠม׵ˠग़ྗ
   w ύʔαʔॻ͘ͷॳΊͯͰͨ͠
   w XSJUF
   ZPVSTFMG
   B
   TDIFNF
   JO
   
   IPVST
 ΛಡΜͰؤுͬͨ ࣮૷ʹ͍ͭͯ
10. 'VODUJPO
    4ZNCPM
11. w ਺ֶ΍෺ཧͰ͸Α͘G Y
    Z Λ
    Gͱॻ͘
    w &HJTPOͰ΋؆ܿʹ਺ࣜΛ͔͖͍ͨʂ
12. 'VODUJPO
    4ZNCPM > (define $f (function [x y])) > f f > (d/d f x) f|x > (d/d (d/d f x) y) f|x|y > (define $x (* r (cos θ))) > (define $y (* r (sin θ))) > (d/d f r) (+ (* f|x (cos θ)) (* f|y (sin θ))) G Y
    Z Λఆٛ ඍ෼͕៉ྷʹ͔͚·͢ ߹੒ؔ਺ͷඍ෼΋Ͱ͖·͢
13. ඍ෼͸Ͳ͏࣮ݱ͞Ε͍ͯΔ͔ (define $∂/∂ (lambda [$f *$x] (match f math-expr { . . . [<func _ $argnames $args _> (sum (map2 (lambda[$s $r] (* (user-refs f {s}) (∂/∂ r x))) argnames args))] . . . }))) > (define $f (function [x y])) > (define $x (* r (cos θ))) > (define $y (* r (sin θ))) > (d/d f r) (+ (* f|x (cos θ)) (* f|y (sin θ))) BSHOBNFT
    
    \lYz
    lZz^
    BSHT
    
    \
    S
    DPT
    В
    
    S
    TJO
    В ^
    
14. ࢖͍΍͍͢ςϯιϧૢ࡞
15. Λ͍ͨ͠
    
    Ͱ΋ʜ
    
    'VODUJPO
    4ZNCPM͸ࣗ਎ͷ໊લΛ࣋ͨͳ͚Ε͹ͳΒͳ͍
    ˠ
    τοϓϨϕϧͰ͔͠ѻ͑ͳ͍
    (define $g_i_j [| [| (function [x y]) 0 0 |] [| 0 (function [x y]) 0 |] [| 0 0 (function [x y]) |] |]_i_j)
16. 'VODUJPO
    4ZNCPM > (define $f (function [x y])) > f f > (d/d f x) f|x > (d/d (d/d f x) y) f|x|y > (define $x (* r (cos θ))) > (define $y (* r (sin θ))) > (d/d f r) (+ (* f|x (cos θ)) (* f|y (sin θ))) ධՁ஋Ͱ͸ͳ໊͘લΛग़ྗ͢Δ
17. (define $g11 (function [x y])) (define $g22 (function [x y])) (define $g33 (function [x y])) (define $g_i_j [| [| g11 0 0 |] [| 0 g22 0 |] [| 0 0 g33 |] |]_i_j) (d/d g_i_j x) ͜ͷ··Ͱ͸ʜ w ֤ཁૉʹ͍ͭͯॻ͘ͷ͕໘౗
    w H͕H@@ͳͷ͔Hddͳͷ͔෼͔Βͳ͍
18. ͜͏ॻ͚ΔΑ͏ʹ͠·ͨ͠ > (define $g__ (generate-tensor ɹ(match-lambda [integer integer] ɹɹ{[[$n ,n] (function [x y z])] [[_ _] 0]}) {3 3})) > g_i_j [| [| g_1_1 0 0 |] [| 0 g_2_2 0 |] [| 0 0 g_3_3 |] |]_i_j > (d/d g_i_j x) [| [| g_1_1|x 0 0 |] [| 0 g_2_2|x 0 |] [| 0 0 g_3_3|x |] |]_i_j ςϯιϧͷ໊લ
    
    ఴࣈͷ্Լ ໊લΛࣗಈͰ͚ͭͯ͘ΕΔ ඍ෼΋ͪΌΜͱදࣔ͞ΕΔ
19. w ςϯιϧΛlϵ@@@z
    lϵd@@zͷΑ͏ͳ໊લʹ
 ఆٛͰ͖Δ
    w 'VODUJPO
    4ZNCPM͸جຊτοϓϨϕϧͰѻ͏
 ʜ EFpOF
    G
    GVODUJPO
    ʜ ͳͲ
    w ςϯιϧͷத਎ͳΒ'VODUJPO
    4ZNCPMΛ࢖͑Δ
20. %'4
    QBUUFSO
21. %'4
    QBUUFSO > (take 10 (match-all nats (set integer) [(dfs <cons $m <cons $n <cons $l _>>>) [m n l]])) {[1 1 1] [1 1 2] [1 1 3] [1 1 4] [1 1 5] [1 1 6] [1 1 7] [1 1 8] [1 1 9] [1 1 10]} > (take 10 (match-all nats (set integer) [<cons $m (dfs <cons $n <cons $l _>>)> [m n l]])) {[1 1 1] [2 1 1] [3 1 1] [4 1 1] [5 1 1] [6 1 1] [7 1 1] [8 1 1] [9 1 1] [10 1 1]} > (take 10 (match-all nats (set integer) [(dfs <cons $m (bfs <cons $n <cons $l _>>)>) [m n l]])) {[1 1 1] [1 1 2] [1 2 1] [1 1 3] [1 2 2] [1 3 1] [1 1 4] [1 2 3] [1 3 2] [1 4 1]} > (take 10 (match-all nats (set integer) [(dfs <cons $m <cons $n (bfs <cons $l _>)>>) [m n l]])) {[1 1 1] [1 1 2] [1 1 3] [1 1 4] [1 1 5] [1 1 6] [1 1 7] [1 1 8] [1 1 9] [1 1 10]}
22. → MState{[<cons $m <cons $n _>> nats (multiset integer)]} env {} → MState{[$m 1 integer] [<cons $n _> {2 3 4 ...} (multiset integer)]} env {} MState{[$m 2 integer] [<cons $n _> {1 3 4 ...} (multiset integer)]} env {} … → MState{[$m 1 something] [<cons $n _> {2 3 4 ...} (multiset integer)]} env {} → MState{[<cons $n _> {2 3 4 ...} (multiset integer)]} env {[m 1]} → MState{[$n 2 integer] [_ {3 4 ...} (multiset integer)]} env {[m 1]} MState{[$n 3 integer] [_ {2 4 ...} (multiset integer)]} env {[m 1]} … → MState{[$n 2 something] [_ {3 4 ...} (multiset integer)]} env {[m 1]} → MState{[_ {3 4 ...} (multiset integer)]} env {[m 1] [n 2]} → MState{} env {[m 1] [n 2]} ύλʔϯϚονͷ༷ࢠ লུͯ͠
 Ұͭ໨ͷ.4UBUFͷΈ
 ਐΊ͍ͯ·͢ (match-all nats (multiset integer) [<cons $m <cons $n _>> {m n}])
23. ύλʔϯϚονશମͷ༷ࢠ
24. શମΛ%'4͢Δͷ͸؆୯
25. ͜ͷํ๏ͰҰ෦%'4ʹ͢Δͱμϝ
26. ղܾࡦ w ύλʔϯͷ൪্ʹEGT
    QBUUFSO͕དྷͨΒɼ
 ͦΕҎ߱͸൪໨Ҏ߱ͷ.4UBUFΛޙճ͠ʹ͢Δ
    w ޙճ͠ʹͨ͠.4UBUFΛύλʔϯ͝ͱʹूΊͯ
 ໦Λ࡞Δ
    w ޙճ͠ʹͨ͠໦ͨͪΛɼ͕ࠜਂ͍ॱʹॲཧ͢Δ
27. ෦෼తʹ%'4͢Δͷ͕ՄೳʹͳΔ
28. ༏ઌ౓෇͖03
29. 0SEFSFE
    03
    1BUUFSO > (match-all (between 1 9) (multiset integer) [<cons (& (|* ,1 ,2 ,3) $x) <cons (& (|* ,4 ,5 ,6) $y) <cons (& (|* ,7 ,8 ,9) $z) _>>> {x y z}]) {{1 4 7} {1 4 8} {1 4 9} {1 5 7} {1 5 8} {1 5 9} {1 6 7} {1 6 8} {1 6 9} {2 4 7} {2 4 8} {2 4 9} {2 5 7} {2 5 8} {2 5 9} {2 6 7} {2 6 8} {2 6 9} {3 4 7} {3 4 8} {3 4 9} {3 5 7} {3 5 8} {3 5 9} {3 6 7} {3 6 8} {3 6 9}}
30. 0SEFSFE
    03
    1BUUFSOΛ࢖͏ྫ w #FTU
    TIV⒐F SPTFUUB
    DPEF 
 IUUQXXXSPTFUUBDPEFPSHXJLJ#FTU@TIV⒐F
    w จࣈྻ͕༩͑ΒΕɼͦͷจࣈྻΛฒ΂ସ͑ͯ
 ݩͷҐஔͱҟͳΔ৔ॴʹ͋Δจࣈͷ਺Λ࠷େԽ͢Δ
    w FH
    USFF
    ˠ
    FFUS
    
    HSSS
    ˠ
    SHSS
31. #FTU
    TIVGqFͷղ౴ྫ (define $shuffle-string (lambda [$s] (pack (shuffle (unpack s))))) (define $shuffle (lambda [$lst] (match [lst (randomize lst)] [(list eq) (multiset eq)] {[[(loop $i [1 $n] <cons $x_i ...> <nil>) (loop $i [1 n] (dfs <cons (& (|* !,x_i ,x_i) $y_i) ...>) <nil>)] (map 1#y_%1 (between 1 n))]}))) (shuffle-string “tree”) ; “eetr” γϟοϑϧલͷจࣈ
    
    \
    Y
    Y
    
    Y
    ʜ
    YO
    ^ γϟοϑϧޙͷจࣈ
    
    \
    Z
    Z
    
    Z
    ʜ
    ZO
    ^
32. w c
    QBU
    QBU Λॲཧ͢Δͱ͖QBUΛ
 ޙճ͠ʹ͢Δ
    ˠ
    ύλʔϯ͝ͱʹ໦͕ͨ͘͞ΜͰ͖Δ
    w ਤඳ͘ͷେมͩͬͨͷͰ࣮૷ͨ͠ͱ͖ʹॻ͍͍ͯͨ ΋ͷΛͦͷ··ࡌͤ·͢ ͍ͩͿద౰Ͱ͢ʣ ࣮૷ͷৄࡉ
34. ৽ύʔαʔ࡞ͬͯ·͢ʂ
35. 4͍ࣜ΍ͩͳ͋ʜಡΈͮΒ͍Α͏ʜ
36. (define $list (lambda [$a] (matcher {[<nil> [] {[{} {[]}] [_ {}]}] [<cons $ $> [a (list a)] {[{$x @$xs} {[x xs]}] [_ {}]}] [<snoc $ $> [a (list a)] {[{@$xs $x} {[x xs]}] [_ {}]}] [<join $ $> [(list a) (list a)] {[$tgt (match-all tgt (list a) [(loop $i [1 $n] <cons $xa_i ...> $rs) [(foldr (lambda [%i %r] {xa_i @r}) {} (between 1 n)) rs]])]}] [<nioj $ $> [(list a) (list a)] {[$tgt (match-all tgt (list a) [(loop $i [1 $n] <snoc $xa_i ...> $rs) [(foldr (lambda [%i %r] {@r xa_i}) {} (between 1 n)) rs]])]}] [,$val [] {[$tgt (if (eq? val tgt) {[]} {})]}] [$ [something] {[$tgt {tgt}]}] }))) Before
37. list(a) = matcher | <nil> as () -> | [] -> {()} | _ -> {} | <cons $ $> as (a, list(a)) -> | [$x, @$xs] -> {(x, xs)} | _ -> {} | <snoc $ $> as (a, list(a)) -> | [@$xs, $x] -> {(x, xs)} | _ -> {} | <join $ $> as (list(a), list(a)) -> | $tgt -> matchAll tgt as list(a) | loop($i, [1, $n], <cons $xa_i ...>, $rs) -> (foldr((%i %r -> [xa_i, @r]), [], 1..n), rs) | <nioj $ $> as (list(a), list(a)) -> | $tgt -> matchAll tgt as list(a) | loop($i, [1, $n], <snoc $xa_i ...>, $rs) -> (foldr((%i %r -> [@r, xa_i]), [], 1..n), rs) | $val as () -> | $tgt -> if val == tgt then {()} else {} | $ as (something) -> | $tgt -> {tgt} After
38. (define $twin-primes (match-all primes (list integer) [<join _ <cons $p <cons ,(+ p 2) _>>> [p (+ p 2)]])) (take 10 twin-primes) twinPrimes = matchAll primes as list(integer) | _ <++> p <:> (p + 2) <:> _ -> [p, p + 2] take(10, twinPrimes) Before After
39. w IUUQTHJUIVCDPNFHJTPOFHJTPOCMPCNBTUFS ITTSD-BOHVBHF&HJTPO1BSTFS/PO4IT
    w ݩͷύʔαʔʹͳΒͬͯ1BSTFDͰॻ͍ͯ·͢
    w ࠓͷͱ͜ΖFHJTPO
    /Ͱ࢖͑·͢
    w SFQMͩͱվߦͰ͙͢ࢮ͵ͷͰ͓ࢼ͠ͳΒϑΝΠϧͰ
 ࣮ߦ͍ͯͩ͘͠͞ʜ
    w OPOTUFTUͷԼʹTBNQMF͕͍Ζ͍Ζ͋Γ·͢ ࣮૷ͷৄࡉ