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ͭͬͯ͋ͦ͘΅
ϥϜμܭࢉΠϯλϓϦλ
,.$ྫձߨ࠲!VUHXLL
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ࣗݾհ
w !VUHXLL ͏͕ͨΘ͖͖
w ֶ෦ใֶՊճੜ
w ϓϩάϥϛϯάݴޠʹؔ͢Δݚڀ
w &VSP5SVDL4JNVMBUPS
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ࢀߟ
<>6S[ZD[ZOFUBM-FDUVSFTPOUIF$VSSZ)PXBSE
*TPNPSQIJTN
4UVEJFTJO-PHJDBOEUIF'PVOEBUJPOTPG
.BUIFNBUJDT
&MTFWJFS4DJFODF
<>IUUQXXXLCFDFJUPIPLVBDKQdTVNJJDMBTT
LFJTBOLJTPGUXBSFLPVHBLVMBNCEBQEG
<>IUUQUUJDVDIJDBHPFEVdQMDMBTTFT$.4$
8JOUFSMFDUVSFTMFDQEG
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͓͠ͳ͕͖
w ಈػ
w Еܭࢉʹ͍ͭͯΖ͏
w ЕܭࢉͷΠϯλϓϦλΛ࣮͠Α͏
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ಈػ
w ЕܭࢉͷݟͨίϯύΫτͰ͔ͭදݱྗ͕ڧ͍
w ͔࣮͠͠Λͨ͜͠ͱ͕ͳ͍
w ΠϯλϓϦλΛ࣮ͯ͠ΈΑ͏
w จಡΉͷ͕ͩΔ͍ͱ͖ʹखΛಈ͔ͯͨ͠
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͜ͷߨ࠲ͷత
w ʮΈͳ͞Μ͕ීஈ͍ͬͯΔϓϩάϥϛϯάݴޠ ͷΠϯ
λϓϦλ
͜ͷΑ͏ʹ࣮͞Ε͍ͯΔʯͱ͍͏࣮ײΛ࣋ͬ
ͯΒ͏
w ЕܭࢉΛ࣮ͨ͠ͱ͖ͷͭ·͖ͣϙΠϯτΛڞ༗͢Δ
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͓͠ͳ͕͖
w ಈػ
w Еܭࢉʹ͍ͭͯΖ͏
w ЕܭࢉͷΠϯλϓϦλΛ࣮͠Α͏
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ܕແ͠
Еܭࢉ
w ܭࢉͷϞσϧԽͷͻͱͭ
w ؔΛͭ͘Δ ந
w ؔΛద༻͢Δ
w ͜Ε͚ͩͰͳΜͱνϡʔϦϯάશ
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Е߲
w . YcЕY.c..
w Yม
w ؔநӈ݁߹ЕYЕZ. ЕY ЕZ.
w ؔద༻ࠨ݁߹123 12
3
w దʹׅހΛՃ͑ͯΑ͍
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͞·͟·ͳЕ߲
w ЕYY
Z
w ЕYЕZY
w ЕYЕZЕ[Y[ Z[
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ଋറมͱࣗ༝ม
w ଋറม
w ؔநʹΑͬͯଋറ͞Ε͍ͯΔม
w ЕYЕZYZ[ͷଋറมY
Z
w ࣗ༝ม
w ଋറมͰͳ͍ͷ
w ЕYЕZYZ[ͷࣗ༝ม[
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มͷஔ
w .
w ߲.ʹొ͢Δࣗ༝มYΛ
w ࠩ͠ࢧ͑ͳ͍ൣғͰ
߲/ʹஔ͢Δ
w ࠩ͠ࢧ͑ͳ͍ൣғͬͯͳʹʁ
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มͷஔͷྫ
w Y ЕZZ
w Z Z Y㱠Z
w Y[ ZY
ЕXX
[ Z ЕXX
w ЕYY ЕYY
w ЕZY ЕZЕ[[ Y㱠Z
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Ћม
w ЕY. ЋЕZ.
w ࠩ͠ࢧ͑ͳ͍ൣғͰҾͷม໊ຊ࣭Ͱͳ͍
w ЕYYͱЕZZΛ۠ผ͢Δඞཁͳ͍Ͱ͢ΑͶʁ
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Ќ؆
w ͬ͘͟Γݴ͑ؔద༻
w ЕY.
/ .
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Ќ؆Λମײ͢Δ
w EFGG Y
SFUVSOY Y
w G
w ͜Ε͋͘·ͰମײͰ͢
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Ќ؆
ЕYЕZЕ[Y[ Z[
ЕYЕZY
ЕYЕZY
ЕZЕ[ ЕYЕZY
[ Z[
ЕYЕZY
Е[ ЕYЕZY
[ ЕYЕZY
[
Е[ ЕZ[
ЕYЕZY
[
Е[ ЕZ[
ЕZ[
Е[[
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ਖ਼نܗ
w ͜ΕҎ্Ќ؆Ͱ͖ͳ͍߲
w ྫ
w Y
w ЕYY
w ЕYЕZY
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͓͠ͳ͕͖
w ಈػ
w Еܭࢉʹ͍ͭͯΖ͏
w ЕܭࢉͷΠϯλϓϦλΛ࣮͠Α͏
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༷
w ೖྗЕ߲ͷจࣈྻදݱ
w ग़ྗЌ؆ͷεςοϓͱਖ਼نܗ ͷΑ͏ͳͷ
w ͭ͡ඞͣ͠ਖ਼نܗʹ؆͞ΕΔΘ͚Ͱͳ͍
w Ќ؆ͯ͠Έͯɼ߲͕มԽ͠ͳ͔ͬͨΒఀࢭ͢Δ
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࣮ݴޠ
w ݴޠ0$BNMΛ͏
w ͦͦ͜͜πʔϧνΣʔϯ͕͋Δ
w Θ͕ͨ͠Α͘৮͍ͬͯΔ
w ͍͜ͳ͍ͤͯͳ͍ͱࢥ͏ʜʜ
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؆·ͰͷྲྀΕ
τʔΫϯྻ -".#%"*%%05
ߏจ 'VO Y
%F#SVJKOJOEFY 'VO
ЕYЕZЕ[Y[ Z[
ЕYЕZY
ЕYЕZY
ЕYY
ࣈ۟ղੳ
ߏจղੳ
%F#SVJKOJOEFYม
Ќ؆
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࣮ͷྲྀΕ
τʔΫϯྻ -".#%"*%%05
ߏจ 'VO Y
%F#SVJKOJOEFY 'VO
ЕYЕZЕ[Y[ Z[
ЕYЕZY
ЕYЕZY
ЕYY
ࣈ۟ղੳ
ߏจղੳ
%F#SVJKOJOEFYม
Ќ؆
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DGΠϯλϓϦλ
τʔΫϯྻ *% Y
&2/6.
ߏจ 45.5 <"44*(/ Y
>
Ծػցίʔυ -0"%
4503&
Y Y
ࣈ۟ղੳ
ߏจղੳ
Ծػցίʔυͷม
ධՁ
˞ͲΕ͘Β͍σʔλߏΛม͢Δ͔ઃܭʹΑΔ
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Е߲ͷσʔλܕΛఆٛ͠Α͏
w . YcЕY.c..
w ࣮ʹམͱ͜͠Ή
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Е߲ͷσʔλܕΛఆٛ͠Α͏
type id = string
type term =
| Var of id
| Fun of id * term
| App of term * term
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࣮ͷྲྀΕ
τʔΫϯྻ -".#%"*%%05
ߏจ 'VO Y
%F#SVJKOJOEFY 'VO
ЕYЕZЕ[Y[ Z[
ЕYЕZY
ЕYЕZY
ЕYY
ࣈ۟ղੳ
ߏจղੳ
%F#SVJKOJOEFYม
Ќ؆
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ߏจղੳ
w ЕYYͷΑ͏ͳه߸ྻʹҙຯΛ࣋ͨͤΔ࡞ۀ
w ЕYY 'VO Y
7BSY
w ݫີʹ͜ͷه߸ྻΛͦͷ··ѻ͏Θ͚Ͱͳ͍
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ߏจղੳثΛ࣮͠Α͏
w NFOIJSΛ͏Α
w ZBDDͷ0$BNM൛ͷ͍ͭ͢͝
w PDBNMZBDDͱ͍͏ͷ͋Δ
w จ๏Λ#/'෩ͷͷͰهड़
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τʔΫϯΛఆٛ͢Δ
w . YcЕY.c..
w άοͱᛀΜͰඞཁͦ͏ͳτʔΫϯΛఆٛ͠Α͏
w *% ม
w -".#%"
%05 Е
w -1"3&/
31"3&/ ׅހ
w &0- Е߲ͷऴ
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τʔΫϯΛఆٛ͢Δ
%{
open Syntax
%}
%token ID
%token LAMBDA DOT
%token LPAREN RPAREN
%token EOL
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จ๏Λఆٛ͢Δ
w . YcЕY.c..
w άοͱᛀΜͰจ๏Λॻ͘
w NBJO &YQS &0-
w &YQS -".#%"*%%05 &YQS c "QQ&YQS
w "QQ&YQS "QQ&YQS "&YQS c "&YQS
w "&YQS *%c-1"3&/ &YQS 31"3&/
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จ๏Λఆٛ͢Δ
%start main
%type main
%%
main:
Expr EOL { $1 }
Expr:
| LAMBDA i=ID DOT e=Expr { Fun (i, e) }
| AppExpr { $1 }
AppExpr:
| e1=AppExpr e2=AExpr { App (e1, e2) }
| AExpr { $1 }
AExpr:
| i=ID { Var i }
| LPAREN e=Expr RPAREN { e }
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࣮ͷྲྀΕ
τʔΫϯྻ -".#%"*%%05
ߏจ 'VO Y
%F#SVJKOJOEFY 'VO
ЕYЕZЕ[Y[ Z[
ЕYЕZY
ЕYЕZY
ЕYY
ࣈ۟ղੳ
ߏจղੳ
%F#SVJKOJOEFYม
Ќ؆
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ࣈ۟ղੳ
w ͦͦЕYYͷΑ͏ͳจࣈྻͷ··ͩͱѻ͍ͮΒ͍
w ۭനจࣈΛແࢹ͢Δͱ͔
w ίϝϯτ͜͜ͰऔΓআ͔ΕΔ
w -".#%"*% Y
%05*% Y
͙Β͍ʹ໌֬ͳྻͩͱΑ͍
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ࣈ۟ղੳثΛ࣮͠Α͏
w PDBNMMFYΛ͏Α
w MFYͷ0$BNM൛
w ϧʔϧΛਖ਼نදݱͰهड़
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ࣈ۟ղੳϧʔϧΛఆٛ͢Δ
{
open Parser
}
rule main = parse
[' ' '\t']+ { main lexbuf }
| ['\n'] { EOL }
| ['a'-'z'] { ID (Lexing.lexeme lexbuf) }
| '\\' { LAMBDA }
| '.' { DOT }
| '(' { LPAREN }
| ')' { RPAREN }
| eof { exit 0 }
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࣮ͷྲྀΕ
τʔΫϯྻ -".#%"*%%05
ߏจ 'VO Y
%F#SVJKOJOEFY 'VO
ЕYЕZЕ[Y[ Z[
ЕYЕZY
ЕYЕZY
ЕYY
ࣈ۟ղੳ
ߏจղੳ
%F#SVJKOJOEFYม
Ќ؆
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%F#SVJKOJOEFYʹม͠Α͏
w ʜʜͬͯͳʹʁ
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Ћม ࢥ͍ग़͢
w ʮଋറมͷ໊લຊ࣭Ͱͳ͍ʯ
w ͍ͬΆ͏ߏจʹଋറมͷ໊લ͕͋Δ
w దʹมͷ໊લͷ͜ͱΛߟ͑ͳ͍ͱ
؆݁Ռ͕ΊͪΌͪ͘ΌʹͳΔ
w ଋറมͷ໊લʹଋറ͞Εͨ͘ͳ͍ʂʂʂʂ
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Ќ؆ ·͕͍ͪ
ЕYЕZЕ[Y[ Z[
ЕYЕ[Y
ЕYЕZY
ЕZЕ[ ЕYЕ[Y
[ Z[
ЕYЕZY
Е[ ЕYЕ[Y
[ ЕYЕZY
[
Е[ Е[[
ЕYЕZY
[
Е[ Е[[
ЕZ[
Е[ЕZ[
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%F#SVJKOJOEFYʹม͠Α͏
w ؔநʹΑΔଋറ͔Βͷωετͷਂ͞Ͱม͕Ұҙʹ
ఆ·Δ
w ͜͜ͰJOEFYͱ͢Δ
w ЕYЕZY ЕЕ
w ЕYЕZЕ[Y[ Z[
ЕЕЕ
w ͨͩࣗ͠༝ม์͓ͬͯ͘
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%F#SVJKOJOEFYͷڧΈ
w มͷ໊લΛߏจ͔ΒऔΓআ͘͜ͱ͕Ͱ͖Δ
w ؆ͷաఔͰͷЋมΛߟ͑ͳͯ͘Α͍
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%F#SVJKOJOEFYͷม
w % ϵ
/
Y
/ϵ Y
ϵ Y
͕ఆٛ͞Ε͍ͯΔ
w % ϵ
/
Y
Y ϵ Y
͕ఆٛ͞Εͳ͍ɼࣗ༝มͰ͋Δ
w % ϵ
/
ЕY.
Е % ϵ\Y/ ^
/
.
w % ϵ
/
12
% ϵ
/
1
% ϵ
/
2
w %NBJO .
% \^
.
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%F#SVJKOJOEFYͷม
w ྫ
w %NBJO ЕYЕZY
w % \^
ЕYЕZY
w Е % \Y^
ЕZY
w ЕЕ % \Y
Z^
Y
w ЕЕ
ЕЕ
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࣮ͷྲྀΕ
τʔΫϯྻ -".#%"*%%05
ߏจ 'VO Y
%F#SVJKOJOEFY 'VO
ЕYЕZЕ[Y[ Z[
ЕYЕZY
ЕYЕZY
ЕYY
ࣈ۟ղੳ
ߏจղੳ
%F#SVJKOJOEFYม
Ќ؆
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%F#SVJKOJOEFYͷЌ؆
w ػցతͳJOEFYͷૢ࡞ͱஔ͚ͩͰЌ؆͕࣮ߦ͞ΕΔ
w ͳΜ͔͍ࣜ͢͝
w ࢿྉ<>Λࢀর
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࣮ͷྲྀΕ
τʔΫϯྻ -".#%"*%%05
ߏจ 'VO Y
%F#SVJKOJOEFY 'VO
ЕYЕZЕ[Y[ Z[
ЕYЕZY
ЕYЕZY
ЕYY
ࣈ۟ղੳ
ߏจղੳ
%F#SVJKOJOEFYม
Ќ؆
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࣮ͨ͠ͷ
w IUUQTHJUIVCDPNVUHXLLMBNCEBDIBNB
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σϞ
w aYaZa[Y[ Z[
aYaZY
aYaZY
w aYaZa[Y[ Z[
aYa[Y
aYaZY
ม໊Λม͚͑ͨͩ
w aG aYG YY
aYG YY
ఀࢭ͠ͳ͍
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ࠓޙͷ՝
w ܕΛ͚Δ
w ࣮͕ͨ͠ߨ࠲Ͱলུ
w ࣗ༝มͷѻ͍Λ͏·͘Γ͍ͨ
Slide 52
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·ͱΊ
w Еܭࢉʹ͍ͭͯͳΜͱͳ͔͖ͬͯͨ͘
w ЕܭࢉͷΠϯλϓϦλΛ࣮ͨ͠