L
Identifieur interne : 001A27 ( Istex/Checkpoint ); précédent : 001A26; suivant : 001A28L
Auteurs : H. P. Barendregt ; I. V. Dolgachev ; G. Rozenberg ; A. Salomaa ; A. P. Soldatov ; A. F. Leont V ; V. F. Emel Anov ; I. P. Egorov ; N. Kh. Rozov ; V. V. Rumyantsev ; I. B. Vapnyarski ; L. D. Kudryavtsev ; M. K. Samarin ; I. V. Proskuryakov ; V. M. Millionshchikov ; N. N. Vil Ams ; S. A. Stepanov ; S. M. Voronin ; I. V. Volovich ; D. V. Anosov ; D. D. Sokolov ; P. K. Suetin ; Yu. A. Brychkov ; A. P. Prudnikov ; A. B. Ivanov ; M. I. Vo Tsekhovski ; V. I. Bityutskov ; V. A. Chuyanov ; G. V. Kuz Ina ; H. Maassen ; E. D. Solomentsev ; E. V. Shikin ; A. V. Prokhorov ; E. G. D Akonov ; M. V. Fedoryuk ; M. A. Shubin ; V. T. Bazylev ; N. S. Zhavrid ; V. V. Okhrimenko ; Yu. M. Davydov ; B. M. Bredikhin ; V. V. Parail ; V. I. Danilov ; V. M. Mikheev ; L. A. Skornyakov ; N. G. Ushakov ; V. M. Kopytov ; T. S. Fofanova ; V. A. Zorich ; V. L. Popov ; Yu. V. Prohorov ; V. E. Plisko ; V. V. Petrov ; V. I. Nechaev ; A. A. Bukhshtab ; M. S. Nikulin ; L. N. Bol Hev ; K. I. Oskolkov ; B. I. Golubov ; V. V. Sazonov ; P. S. Aleksandrov ; B. S. Kashin ; I. A. Vinogradova ; B. A. Pasynkov ; I. I. Volkov ; T. P. Lukashenko ; P. M. Gruber ; Yu. B. Rudyak ; V. A. Iskovskikh ; Yu. V. Nesterenko ; V. M. Tikhomirov ; I. P. Mityuk ; A. V. Chernavski ; D. A. Ponomarev ; E. G. Goluzina ; Ü. Lumiste ; A. I. Shtern ; A. L. Onishchik ; B. A. Rogozin ; I. V. Ostrovski ; V. M. Zolotarev ; H. C. Myung ; Yu. A. Bakhturin ; E. B. Vinberg ; A. A. Kirillov ; V. V. Gorbatsevich ; D. V. Alekseevski ; V. P. Platonov ; A. I. Kostrikin ; A. S. Fedenko ; B. R. Va Nberg ; L. A. Cherkas ; Yu. V. Prokhorov ; A. I. Galochkin ; A. S. Parkhomenko ; V. V. Voevodin ; A. F. Shapkin ; S. G. Kre N ; V. P. Palamodov ; S. A. A Vazyan ; A. Ya. Khelemski ; A. M. Nakhushev ; O. A. Ivanova ; S. N. Chernikov ; N. N. Ladis ; V. G. Karmanov ; V. A. Yakubovich ; V. I. Arnautov ; Yu. A. Rozanov ; A. V. Malyshev ; I. A. Kvasnikov ; A. F. Lavrik ; S. V. Kotov ; I. Kh. Sabitov ; A. V. Efimov ; A. P. Ershov ; M. Sh. Farber ; B. L. Laptev ; Kh. D. Ikramov ; L. A. Sidorov ; I. P. Mysovskikh ; N. P. Korene Chuk ; V. P. Motorny ; A. A. Mal Sev ; E. G. Sklyarenko ; L. V. Kuz In ; P. T. Johnstone ; A. A. Dezin ; M. Sh. Tsalenko ; A. I. Untern ; V. N. Latyshev ; A. V. Arkhangel Ki ; A. L. Shmel In ; L. N. Shevrin ; S. A. Bogaty ; S. Yu. Maslov ; G. E. Mints ; A. I. Orlov ; V. D. Belousov ; A. F. Kharshiladze ; V. Ya. Gutlyanski ; E. M. Semenov ; A. A. Konyushkov ; B. A. Efimov ; R. Z. Khas Inski ; N. M. Nagorny ; V. V. Fedorchuk ; B. V. KhvedelidzeSource :
Abstract
Abstract: The lambda calculus was introduced in 1932 – 1933 by A. Church [A3] as part of a theory intended as a foundation for mathematics. This foundational theory consisted of a part dealing with logical symbols and rules and a part dealing with algorithms operating on these symbols. After it was shown by S.C. Kleene and J.B. Rosser [A7] that this foundational system was inconsistent, the part dealing with algorithms only was isolated as the (type-free) lambda calculus. It turned out to be quite successful in capturing the intuitive notion of computable function. Kleene [A6] showed that exactly the recursive functions (cf. Recursive function) are lambda definable in the sense given below. Then A.M. Turing [A10] introduced his machines (cf. Turing machine) and showed that Turing computable and lambda definable are equivalent notions. These are arguments for the Church—Turing thesis that the intuitive notion of computable is correctly formalised as lambda definable, Turing computable or recursive (cf. also Church thesis). Although many programming languages are based on the computational model of Turing (imperative programming), presently the model of Church enjoys a lot of attention in the form of functional programming.
Url:
DOI: 10.1007/978-1-4899-3793-3_5
Affiliations:
Links toward previous steps (curation, corpus...)
Links to Exploration step
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<author><name sortKey="Alekseevski, D V" sort="Alekseevski, D V" uniqKey="Alekseevski D" first="D. V." last="Alekseevski">D. V. Alekseevski</name>
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<author><name sortKey="Fedenko, A S" sort="Fedenko, A S" uniqKey="Fedenko A" first="A. S." last="Fedenko">A. S. Fedenko</name>
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<author><name sortKey="Cherkas, L A" sort="Cherkas, L A" uniqKey="Cherkas L" first="L. A." last="Cherkas">L. A. Cherkas</name>
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<author><name sortKey="Prokhorov, Yu V" sort="Prokhorov, Yu V" uniqKey="Prokhorov Y" first="Yu. V." last="Prokhorov">Yu. V. Prokhorov</name>
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<author><name sortKey="Galochkin, A I" sort="Galochkin, A I" uniqKey="Galochkin A" first="A. I." last="Galochkin">A. I. Galochkin</name>
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<author><name sortKey="Parkhomenko, A S" sort="Parkhomenko, A S" uniqKey="Parkhomenko A" first="A. S." last="Parkhomenko">A. S. Parkhomenko</name>
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<author><name sortKey="Shapkin, A F" sort="Shapkin, A F" uniqKey="Shapkin A" first="A. F." last="Shapkin">A. F. Shapkin</name>
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<author><name sortKey="Kre N, S G" sort="Kre N, S G" uniqKey="Kre N S" first="S. G." last="Kre N">S. G. Kre N</name>
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<author><name sortKey="Palamodov, V P" sort="Palamodov, V P" uniqKey="Palamodov V" first="V. P." last="Palamodov">V. P. Palamodov</name>
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<author><name sortKey="Khelemski, A Ya" sort="Khelemski, A Ya" uniqKey="Khelemski A" first="A. Ya." last="Khelemski">A. Ya. Khelemski</name>
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<author><name sortKey="Nakhushev, A M" sort="Nakhushev, A M" uniqKey="Nakhushev A" first="A. M." last="Nakhushev">A. M. Nakhushev</name>
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<date when="1995" year="1995">1995</date>
<idno type="doi">10.1007/978-1-4899-3793-3_5</idno>
<idno type="url">https://api.istex.fr/document/531030899AF5495A6F5F73EE07D1B6C37A176FD4/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">001098</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001098</idno>
<idno type="wicri:Area/Istex/Curation">001098</idno>
<idno type="wicri:Area/Istex/Checkpoint">001A27</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">001A27</idno>
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<author><name sortKey="Ikramov, Kh D" sort="Ikramov, Kh D" uniqKey="Ikramov K" first="Kh. D." last="Ikramov">Kh. D. Ikramov</name>
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<author><name sortKey="Efimov, B A" sort="Efimov, B A" uniqKey="Efimov B" first="B. A." last="Efimov">B. A. Efimov</name>
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<author><name sortKey="Khas Inski, R Z" sort="Khas Inski, R Z" uniqKey="Khas Inski R" first="R. Z." last="Khas Inski">R. Z. Khas Inski</name>
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<author><name sortKey="Nagorny, N M" sort="Nagorny, N M" uniqKey="Nagorny N" first="N. M." last="Nagorny">N. M. Nagorny</name>
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<author><name sortKey="Fedorchuk, V V" sort="Fedorchuk, V V" uniqKey="Fedorchuk V" first="V. V." last="Fedorchuk">V. V. Fedorchuk</name>
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<front><div type="abstract" xml:lang="en">Abstract: The lambda calculus was introduced in 1932 – 1933 by A. Church [A3] as part of a theory intended as a foundation for mathematics. This foundational theory consisted of a part dealing with logical symbols and rules and a part dealing with algorithms operating on these symbols. After it was shown by S.C. Kleene and J.B. Rosser [A7] that this foundational system was inconsistent, the part dealing with algorithms only was isolated as the (type-free) lambda calculus. It turned out to be quite successful in capturing the intuitive notion of computable function. Kleene [A6] showed that exactly the recursive functions (cf. Recursive function) are lambda definable in the sense given below. Then A.M. Turing [A10] introduced his machines (cf. Turing machine) and showed that Turing computable and lambda definable are equivalent notions. These are arguments for the Church—Turing thesis that the intuitive notion of computable is correctly formalised as lambda definable, Turing computable or recursive (cf. also Church thesis). Although many programming languages are based on the computational model of Turing (imperative programming), presently the model of Church enjoys a lot of attention in the form of functional programming.</div>
</front>
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<name sortKey="Alekseevski, D V" sort="Alekseevski, D V" uniqKey="Alekseevski D" first="D. V." last="Alekseevski">D. V. Alekseevski</name>
<name sortKey="Anosov, D V" sort="Anosov, D V" uniqKey="Anosov D" first="D. V." last="Anosov">D. V. Anosov</name>
<name sortKey="Arkhangel Ki, A V" sort="Arkhangel Ki, A V" uniqKey="Arkhangel Ki A" first="A. V." last="Arkhangel Ki">A. V. Arkhangel Ki</name>
<name sortKey="Arnautov, V I" sort="Arnautov, V I" uniqKey="Arnautov V" first="V. I." last="Arnautov">V. I. Arnautov</name>
<name sortKey="Bakhturin, Yu A" sort="Bakhturin, Yu A" uniqKey="Bakhturin Y" first="Yu. A." last="Bakhturin">Yu. A. Bakhturin</name>
<name sortKey="Barendregt, H P" sort="Barendregt, H P" uniqKey="Barendregt H" first="H. P." last="Barendregt">H. P. Barendregt</name>
<name sortKey="Bazylev, V T" sort="Bazylev, V T" uniqKey="Bazylev V" first="V. T." last="Bazylev">V. T. Bazylev</name>
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<name sortKey="Bityutskov, V I" sort="Bityutskov, V I" uniqKey="Bityutskov V" first="V. I." last="Bityutskov">V. I. Bityutskov</name>
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<name sortKey="Danilov, V I" sort="Danilov, V I" uniqKey="Danilov V" first="V. I." last="Danilov">V. I. Danilov</name>
<name sortKey="Davydov, Yu M" sort="Davydov, Yu M" uniqKey="Davydov Y" first="Yu. M." last="Davydov">Yu. M. Davydov</name>
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<name sortKey="Galochkin, A I" sort="Galochkin, A I" uniqKey="Galochkin A" first="A. I." last="Galochkin">A. I. Galochkin</name>
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<name sortKey="Khelemski, A Ya" sort="Khelemski, A Ya" uniqKey="Khelemski A" first="A. Ya." last="Khelemski">A. Ya. Khelemski</name>
<name sortKey="Khvedelidze, B V" sort="Khvedelidze, B V" uniqKey="Khvedelidze B" first="B. V." last="Khvedelidze">B. V. Khvedelidze</name>
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<name sortKey="Korene Chuk, N P" sort="Korene Chuk, N P" uniqKey="Korene Chuk N" first="N. P." last="Korene Chuk">N. P. Korene Chuk</name>
<name sortKey="Kostrikin, A I" sort="Kostrikin, A I" uniqKey="Kostrikin A" first="A. I." last="Kostrikin">A. I. Kostrikin</name>
<name sortKey="Kotov, S V" sort="Kotov, S V" uniqKey="Kotov S" first="S. V." last="Kotov">S. V. Kotov</name>
<name sortKey="Kre N, S G" sort="Kre N, S G" uniqKey="Kre N S" first="S. G." last="Kre N">S. G. Kre N</name>
<name sortKey="Kudryavtsev, L D" sort="Kudryavtsev, L D" uniqKey="Kudryavtsev L" first="L. D." last="Kudryavtsev">L. D. Kudryavtsev</name>
<name sortKey="Kuz In, L V" sort="Kuz In, L V" uniqKey="Kuz In L" first="L. V." last="Kuz In">L. V. Kuz In</name>
<name sortKey="Kuz Ina, G V" sort="Kuz Ina, G V" uniqKey="Kuz Ina G" first="G. V." last="Kuz Ina">G. V. Kuz Ina</name>
<name sortKey="Kvasnikov, I A" sort="Kvasnikov, I A" uniqKey="Kvasnikov I" first="I. A." last="Kvasnikov">I. A. Kvasnikov</name>
<name sortKey="Ladis, N N" sort="Ladis, N N" uniqKey="Ladis N" first="N. N." last="Ladis">N. N. Ladis</name>
<name sortKey="Laptev, B L" sort="Laptev, B L" uniqKey="Laptev B" first="B. L." last="Laptev">B. L. Laptev</name>
<name sortKey="Latyshev, V N" sort="Latyshev, V N" uniqKey="Latyshev V" first="V. N." last="Latyshev">V. N. Latyshev</name>
<name sortKey="Lavrik, A F" sort="Lavrik, A F" uniqKey="Lavrik A" first="A. F." last="Lavrik">A. F. Lavrik</name>
<name sortKey="Leont V, A F" sort="Leont V, A F" uniqKey="Leont V A" first="A. F." last="Leont V">A. F. Leont V</name>
<name sortKey="Lukashenko, T P" sort="Lukashenko, T P" uniqKey="Lukashenko T" first="T. P." last="Lukashenko">T. P. Lukashenko</name>
<name sortKey="Lumiste, U" sort="Lumiste, U" uniqKey="Lumiste U" first="Ü." last="Lumiste">Ü. Lumiste</name>
<name sortKey="Maassen, H" sort="Maassen, H" uniqKey="Maassen H" first="H." last="Maassen">H. Maassen</name>
<name sortKey="Mal Sev, A A" sort="Mal Sev, A A" uniqKey="Mal Sev A" first="A. A." last="Mal Sev">A. A. Mal Sev</name>
<name sortKey="Malyshev, A V" sort="Malyshev, A V" uniqKey="Malyshev A" first="A. V." last="Malyshev">A. V. Malyshev</name>
<name sortKey="Maslov, S Yu" sort="Maslov, S Yu" uniqKey="Maslov S" first="S. Yu." last="Maslov">S. Yu. Maslov</name>
<name sortKey="Mikheev, V M" sort="Mikheev, V M" uniqKey="Mikheev V" first="V. M." last="Mikheev">V. M. Mikheev</name>
<name sortKey="Millionshchikov, V M" sort="Millionshchikov, V M" uniqKey="Millionshchikov V" first="V. M." last="Millionshchikov">V. M. Millionshchikov</name>
<name sortKey="Mints, G E" sort="Mints, G E" uniqKey="Mints G" first="G. E." last="Mints">G. E. Mints</name>
<name sortKey="Mityuk, I P" sort="Mityuk, I P" uniqKey="Mityuk I" first="I. P." last="Mityuk">I. P. Mityuk</name>
<name sortKey="Motorny, V P" sort="Motorny, V P" uniqKey="Motorny V" first="V. P." last="Motorny">V. P. Motorny</name>
<name sortKey="Mysovskikh, I P" sort="Mysovskikh, I P" uniqKey="Mysovskikh I" first="I. P." last="Mysovskikh">I. P. Mysovskikh</name>
<name sortKey="Myung, H C" sort="Myung, H C" uniqKey="Myung H" first="H. C." last="Myung">H. C. Myung</name>
<name sortKey="Nagorny, N M" sort="Nagorny, N M" uniqKey="Nagorny N" first="N. M." last="Nagorny">N. M. Nagorny</name>
<name sortKey="Nakhushev, A M" sort="Nakhushev, A M" uniqKey="Nakhushev A" first="A. M." last="Nakhushev">A. M. Nakhushev</name>
<name sortKey="Nechaev, V I" sort="Nechaev, V I" uniqKey="Nechaev V" first="V. I." last="Nechaev">V. I. Nechaev</name>
<name sortKey="Nesterenko, Yu V" sort="Nesterenko, Yu V" uniqKey="Nesterenko Y" first="Yu. V." last="Nesterenko">Yu. V. Nesterenko</name>
<name sortKey="Nikulin, M S" sort="Nikulin, M S" uniqKey="Nikulin M" first="M. S." last="Nikulin">M. S. Nikulin</name>
<name sortKey="Okhrimenko, V V" sort="Okhrimenko, V V" uniqKey="Okhrimenko V" first="V. V." last="Okhrimenko">V. V. Okhrimenko</name>
<name sortKey="Onishchik, A L" sort="Onishchik, A L" uniqKey="Onishchik A" first="A. L." last="Onishchik">A. L. Onishchik</name>
<name sortKey="Orlov, A I" sort="Orlov, A I" uniqKey="Orlov A" first="A. I." last="Orlov">A. I. Orlov</name>
<name sortKey="Oskolkov, K I" sort="Oskolkov, K I" uniqKey="Oskolkov K" first="K. I." last="Oskolkov">K. I. Oskolkov</name>
<name sortKey="Ostrovski, I V" sort="Ostrovski, I V" uniqKey="Ostrovski I" first="I. V." last="Ostrovski">I. V. Ostrovski</name>
<name sortKey="Palamodov, V P" sort="Palamodov, V P" uniqKey="Palamodov V" first="V. P." last="Palamodov">V. P. Palamodov</name>
<name sortKey="Parail, V V" sort="Parail, V V" uniqKey="Parail V" first="V. V." last="Parail">V. V. Parail</name>
<name sortKey="Parkhomenko, A S" sort="Parkhomenko, A S" uniqKey="Parkhomenko A" first="A. S." last="Parkhomenko">A. S. Parkhomenko</name>
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<name sortKey="Prokhorov, Yu V" sort="Prokhorov, Yu V" uniqKey="Prokhorov Y" first="Yu. V." last="Prokhorov">Yu. V. Prokhorov</name>
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<name sortKey="Rozanov, Yu A" sort="Rozanov, Yu A" uniqKey="Rozanov Y" first="Yu. A." last="Rozanov">Yu. A. Rozanov</name>
<name sortKey="Rozenberg, G" sort="Rozenberg, G" uniqKey="Rozenberg G" first="G." last="Rozenberg">G. Rozenberg</name>
<name sortKey="Rozov, N Kh" sort="Rozov, N Kh" uniqKey="Rozov N" first="N. Kh." last="Rozov">N. Kh. Rozov</name>
<name sortKey="Rudyak, Yu B" sort="Rudyak, Yu B" uniqKey="Rudyak Y" first="Yu. B." last="Rudyak">Yu. B. Rudyak</name>
<name sortKey="Rumyantsev, V V" sort="Rumyantsev, V V" uniqKey="Rumyantsev V" first="V. V." last="Rumyantsev">V. V. Rumyantsev</name>
<name sortKey="Sabitov, I Kh" sort="Sabitov, I Kh" uniqKey="Sabitov I" first="I. Kh." last="Sabitov">I. Kh. Sabitov</name>
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<name sortKey="Samarin, M K" sort="Samarin, M K" uniqKey="Samarin M" first="M. K." last="Samarin">M. K. Samarin</name>
<name sortKey="Sazonov, V V" sort="Sazonov, V V" uniqKey="Sazonov V" first="V. V." last="Sazonov">V. V. Sazonov</name>
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<name sortKey="Shmel In, A L" sort="Shmel In, A L" uniqKey="Shmel In A" first="A. L." last="Shmel In">A. L. Shmel In</name>
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<name sortKey="Sidorov, L A" sort="Sidorov, L A" uniqKey="Sidorov L" first="L. A." last="Sidorov">L. A. Sidorov</name>
<name sortKey="Sklyarenko, E G" sort="Sklyarenko, E G" uniqKey="Sklyarenko E" first="E. G." last="Sklyarenko">E. G. Sklyarenko</name>
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<name sortKey="Solomentsev, E D" sort="Solomentsev, E D" uniqKey="Solomentsev E" first="E. D." last="Solomentsev">E. D. Solomentsev</name>
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<name sortKey="Zorich, V A" sort="Zorich, V A" uniqKey="Zorich V" first="V. A." last="Zorich">V. A. Zorich</name>
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