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ຑ੃ͷ఺਺ܕ͔ΒֶͿ 5ZQF4DSJQU

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໊લງా༗࠸ ೥݄.ೖࣾ ௚ۙͷϓϩδΣΫτ.1BZɺ৺ଁ܅ UZQFDIBMMFOHFTΛগͣͭ͠΍͍ͬͯΔ NFEJVNͷޙ൒͘Β͍·ͰEPOF લ৬͸αΠόʔΤʔδΣϯτ ຑ੃෦͕͋Γॴଐͯͨ͠ ్த͔Β༓ྶ෦һʹ IUUQTHJUIVCDPNUZQFDIBMMFOHFTUZQFDIBMMFOHFT

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खṛͷຕͷṛͰ໾Λ࡞Ε͹0,ɺ఺਺͕໯͑Δ👍 ͔ͳΓͬ͘͟ΓɺҰݴͰຑ੃ϧʔϧͷ঺հ ͭͷṛͷ૊ΈΛηοτ ਺ࣈ֊ஈλΠϓ ຕಉ͡λΠϓ ຕಉ͡λΠϓ ͭͷṛͷ૊ΈΛηοτ

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ࠓ೔࿩͢͜ͱ ຑ੃ͷखṛΛೖྗͯ͠ɺͦͷखṛͷ఺਺ͷϦςϥϧܕΛฦ͢ܕΛ ࡞ͬͨɻ ௨শຑ੃܅BMQIB൛ ຑ੃܅࡞੒ͷաఔͱ5ZQF4DSJQUͷػೳɾ஌ݟΛ঺հ͍ͨ͠ IUUQTHJUIVCDPNIPSJUBZVZBNBIKPOHLVO ࠓ೔͸ɺ͜ͷลΓͷύϥϝʔλͷ࿩͸ׂѪ

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ṛͷܕఆٛ खṛͷܕఆٛ ͭͷṛ͕ಉ͡ṛ͔νΣοΫ͢Δ ·ͱΊ ໨࣍

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ṛͷఆٛ w -JUFSBM5ZQF w 5FNQMBUF-JUFSBM5ZQF

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ṛͷܕఆٛ -JUFSBMܕ͸ɺͦͷ஋ࣗ਎͔͠ड͚෇͚ͳ͍ܕ lPzͱ͍͏-JUFSBMܕʹ͸zPz͔͠୅ೖͰ͖ͳ͍ ܗؙ͕͍ͷͰʮPʯ -JUFSBM5ZQF

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ṛͷܕఆٛ શ෦खಈͰఆٛʁ 5FNQMBUF-JUFSBM5ZQF ܕΛ5FNQMBUF-JUFSBMͷೖྗʹ࢖͑Δɻ ਺ࣈͷṛ͸̍ʙ·Ͱͷ͋Δɻ

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ṛͷܕఆٛ w 5FNQMBUF-JUFSBM5ZQFʹ6OJPOܕΛ౉͢ͱ෼഑ͯ͠ධՁ͞Εͨ݁Ռͷ6OJPOʹͳΔ 6OJPOͷશ௨Γͷ૊Έ߹Θ͕ͤఆٛ͞ΕΔ 5FNQMBUF-JUFSBM5ZQF w ਺ṛ͸छྨ͋ΔͷͰɺ࣮ࡍ͸b.BSL`ܕ΋6OJPOʹͳΔ͕ɺׂѪ

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खṛͷܕఆٛ w "SSBZ5ZQF w 5VQMF5ZQF w (FOFSJDT w *OEFYFE"DDFTT5ZQFT

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खṛͷܕఆٛ ഑ྻܕ w ഑ྻܕԿݸͷཁૉ͕͋Δ͔ɺίϯύΠϧ࣌ʹ͸ܾఆ͠ͳ͍ w λϓϧܕԿݸͷཁૉ͕͋Δ͔ɾԿ൪໨ͷΠϯσοΫεʹԿ ܕ͕͋Δ͔ɺίϯύΠϧ࣌ʹܾఆ͞ΕΔ λϓϧܕ IUUQTXXXUZQFTDSJQUMBOHPSHEPDTIBOECPPLPCKFDUTIUNMUVQMFUZQFT

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λϓϧܕͰखࡳΛఆٛ͢ΔͱɺຕҎ֎ͷέʔε ͰίϯύΠϧΤϥʔʹͯ͘͠ΕΔͷͰྑ͍ खṛͷܕఆٛ

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ͭͷṛͷ૊Έͱͭͷṛͷ૊Έʹ෼ղͰ͖Δ ͱɺ͞Βʹྑ͍ खṛͷܕఆٛ

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(FOFSJDT ܕύϥϝʔλΛड͚औͬͯɺ৽͍͠ܕΛੜ੒Ͱ͖Δ bFYUFOET`ΩʔϫʔυΛ෇͚Δ͜ͱͰೖྗύϥϝʔλʹ੍໿Λ෇͚ΒΕΔ खṛͷܕఆٛ

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(FOFSJDT*OEFYFE"DDFTT5ZQFT AFYUFOET)BOEA੍໿ͷ͔͔͍ͬͯΔA5A͸λϓϧܕ λϓϧܕ͸ΠϯσοΫεΞΫηεʹΑͬͯɺͦͷҐஔͰͷܕΛऔಘͰ͖Δ ഑ྻܕͰ΋<> <>ͷΑ͏ʹΞΫηεग़དྷΔ͕ɺ5<> 5<>ͳͲ΋ΤϥʔʹͳΒͣʹ௨ͬͯ͠·͏ खṛͷܕఆٛ

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ฒͼॱͷ੍໿෇͖͕ͩɺ खṛͷຕYηοτɺຕYηοτΛܕͰදݱͰ͖ͨ ޙ͸ɺͦΕͧΕͷ·ͱ·Γ͕৚݅Λຬ͔ͨ֬͢ೝ͢Ε͹0, (FOFSJDT*OEFYFE"DDFTT5ZQFT खṛͷܕఆٛ

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ͭͷṛ͕ಉ͡ṛ͔νΣοΫ͢Δ w $POEJUJPOBM5ZQFT w 5ZQF&RVJWBMFODF

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ܕͷ߲ԋࢉࢠ ͷΑ͏ͳ΋ͷ ͭͷṛ͕ಉ͡ṛ͔νΣοΫ͢Δ $POEJUJPOBM5ZQFT 5ΛzPzʹ୅ೖग़དྷΔͳΒ͹USVFܕΛɺग़དྷͳ͍ͳΒGBMTFܕΛฦ͢ CPPMFBOܕͰ͸ͳ͘ɺUSVFͱGBMTFͷϦςϥϧܕ

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ͭͷṛ͕ಉ͡ṛ͔νΣοΫ͢Δ $POEJUJPOBM5ZQFT ͱ͜ΖͰɺʮܕ͕ಉ͡ʯͷ൑ఆʹFYUFOETΛ࢖ͬͯྑ͍ͷ͔ʁ

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5ZQF&RVJWBMFODF Ұൠతʹ͸🙅 AAܕ͸ɺOVNCFSܕʹ୅ೖͰ͖ΔͷͰUSVFʹͳΔ AAܕ͸ɺAcAܕʹ୅ೖͰ͖ΔͷͰUSVFʹͳΔ ͨͩ͠ɺϦςϥϧܕ͕ͦΕ୯ମͰൺֱ͞ΕΔ৔߹ʹ͸ڐ༰ग़དྷΔ ͭͷṛ͕ಉ͡ṛ͔νΣοΫ͢Δ

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ଞͷํ๏ແ͍ͷ͔ʁ

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5ZQF&RVJWBMFODF UZQFDIBMMFOHFTͷਖ਼ղ൑ఆʹ΋࢖ΘΕ͍ͯΔ&RVBMTܕ ͭͷṛ͕ಉ͡ṛ͔νΣοΫ͢Δ ׬શͰ͸ແ͍͕ɺଟ͘ͷέʔεͰ͸ࠔΒͳͦ͏ͳϫʔΫΞϥ΢ϯυ IUUQTHJUIVCDPNNJDSPTPGU5ZQF4DSJQUJTTVFTJTTVFDPNNFOU

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5ZQF&RVJWBMFODF IUUQTHJUIVCEFWNJDSPTPGU5ZQF4DSJQUCMPCNBJOTSDDPNQJMFSDIFDLFSUT- // 'T1 extends U1 ? X1 : Y1’ // 'T2 extends U2 ? X2 : Y2' are related if // one of T1 and T2 is related to the other, U1 and U2 are identical types, X1 is related to X2, // and Y1 is related to Y2. ͭͷ$POEJUJPOBM5ZQFͷൺֱʹ࣋ͪࠐΉ͜ͱͰɺ`JEFOUJDBM`͔Ͳ͏͔֬ೝग़དྷΔ ͭͷṛ͕ಉ͡ṛ͔νΣοΫ͢Δ

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5ZQF&RVJWBMFODF ͭͷṛ͕ಉ͡ṛ͔νΣοΫ͢Δ `4`͕౉͞Ε͍ͯͳ͍ͷͰɺ`4FYUFOET5`ΛධՁग़དྷͳ͍ɻ `$IFDL`͸b4 4FYUFOET `ܕͱͯ͠ѻΘΕΔ ٻΊ͍ͯͨɺ$POEJUJPOBM5ZQFܕ 3FGFSFODFIUUQTXXXUZQFTDSJQUMBOHPSHEPDTIBOECPPLBEWBODFEUZQFTIUNMDPOEJUJPOBMUZQFT ʮDPOEJUJPOBMUZQFTBSFEFGFSSFEʯͰݕࡧ ެࣜυΩϡϝϯτ͕ͩɺEFQSFDBUFEɻ࠷৽ͷϖʔδͰ͸ࣅͨΑ͏ͳจষΛݟ͚ͭΒΕͳ͔ͬͨɻ

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5ZQF&RVJWBMFODF ͭͷṛ͕ಉ͡ṛ͔νΣοΫ͢Δ `4`͕ύϥϝʔλͱͯ͠౉͞Εͨ݁Ռɺ`4FYUFOET5`͕ධՁ͞Εɺ ͨͩͷb `ܕʹͳΔͷͰɺ❌

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ṛͷܕఆٛɺखṛͷܕఆٛɺṛͷܕಉ࢜ͷൺֱͳͲجૅ෦෼Λ঺հͨ͠ ޙ͸ɺ૊ηοτɺ૊ηοτͷ৚݅ʹͳ͍ͬͯΔ͔ʁ໾͸੒ཱͯ͠ ͍Δ͔ʁϝϯθϯʁͲͷ଴ͪͰ্͕ͬͨʁϩϯ͔πϞ͔ʁූ͸͍͔ͭ͘ʁ Λ൑ఆ͢Δ͚ͩ ·ͱΊ IUUQTHJUIVCDPNNJDSPTPGU5ZQF4DSJQUJTTVFT IUUQTTQFBLFSEFDLDPNTBJZB@NPFCJVTUZQFTZTUFNPGUIFUZQFTDSJQU IUUQTXXXUZQFTDSJQUMBOHPSHEPDTIBOECPPLUZQFTGSPNUZQFTIUNM ਆࢿྉ ެࣜυΩϡϝϯτɺ๛෋Ͱ෼͔Γ΍͍͢ ໼࡚͞Μͷ54࿩ɻಛʹɺ঺հ͞Ε͍ͯΔOFWFSͷ࢖͍ํ͸ɺຊ൪ίʔυͰ΋ͱͯ΋໾ʹཱͭ 5ZQF&RVJWBMFODFͷ࿩ɻ54ͷίʔυ DIFDLFSUT ΛಡΉ͖͔͚ͬʹͳͬͨ ΋͠ྑ͔ͬͨΒຑ੃܅ͷ࣮૷ݟͯΈ͍ͯͩ͘͞🤲